SLAC-R-336 - Stanford University
Transcription
SLAC-R-336 - Stanford University
SLAC-R-336 SLAC CONF - 336 - 880747 UC-34d (T/W PROCEEDINGS OF SUMMER INSTITUTF, ON PARTICLE PHYSICS July 18-29,1988 PROBING THE WEAK INTERACTION: Cl? VIOLATION AND RARE DECAYS Program Directors Gary J. Feldman Frederick J. Gilman David W. G. S. Leith Ed. by Eileen C. Brennan Sponsored contmct by Stanford University with the U.S. Department and Stanford of Energy. January Printed in the United mation Service, U.S. Department VA 22161. States of America. Linear Contract Accelerator Center under DE-AC03-76SF00515. 1989 Available of Commerce, from National Technical Infor- 5285 Port Royal Road, Springfield, : [I. .. .,. -: -.._ ::.:.’ ‘. : cn c4 W c : PREFACE ::-’ . . .: ‘.. -,,:. -’ The sixteenth annual SLAC Summer Institute on Particle Physics was held from July 18-29, 19S8. The subject of “Probing the Weak Interaction: CP Violation and Rare Decays” was studied in both its experimental and theoretical aspects by a total of 342 participants from thirteen countries. The school portion of the Institute featured excellent lectures on this subject by K. Berkelman, I. Bigi, B. Cabrera, L. Hall, H. Harari, J. Sandweiss, A.J.S. Smith, M. Witherell, and L. Wolfenstein. The afternoon discussion were wry much enhanced and enlivened by C. Ahn, R. Aleksan, M. Davier, C. Dibb, R. Ezmaizaldeh, R. Frey, J. Frieman, RI. Karliner, R. Kauffman, I. Klebanov, A. Lankford, B. Lockman, C. Munger, J. Ritchie, D. Shroeder, N. Wang, A. Weinstein, and M. Woods who acted as were taken “provocateurs.” As is tradit’ lonal, the last three days of the Institute up by a Topical Conference, with invited talks from ongoing experiments and the associated theory. We thank Eileen Brennan for organizing and running the meeting, and with great persistence, editing these Proceedings. She and her staff contributed much to the success of the meeting both through their hard work and their good humor. Gary Feldman Frederick J. Gilman David W. G. S. Leith Program Directors .. TABLE OF CONTENTS page Part I. LECTURES I. I. BIG1 “Precious Rarities -On Rare Decays of K, D and B Mesons” B. CABRERA “Superconducting Detectors for Monopoles and Weakly Interacting Particles” . . L. J. HALL “Cosmic Relics from the Big Bang” . . M. S. WITHERELL “Double Beta Decay” . . . . . . . . 69 . 85 125 . H. HARARI “The Bottom Quark: A Key to ‘Beyond Standard’ Physics” A.J.S. SMITH “Experimental Part II. TOPICAL Searches for Rare Decays” . . . 31 105 L. WOLFENSTEIN “Neutrino Masses and Mixings” J. SANDWEISS “&Physics in Fixed Target Experiments” 1 . . . . . . . . . . 143 145 . . 147 . . 151 N. KATAYAMA “Recent Results from CLEO -An Observation of R” - B” Mixing and a Search for Charmless B Meson Decays, B- -t p@n- and 3 -+ pfhr+lr-” ., . . . . D. B. MACFARLANE “B Decay Studies from ARGUS” CONFERENCE + e+X” . J. SHIRAI “Recent Results from TRISTAN” M. S. WITHERELL ‘LProspects for B Physics” S. CONETTI “Hadroproduction . . . . . . . . . . . . . . . . . 167 . 183 209 . . . . of $ and X States” 217 . . 241 . 253 . B. T. MEADOWS “Recent Results on S = -3 Baryon Spectroscopy from the LASS Spectrometer” . . 255 S. R. SHARPE “Calculations of Hadronic Weak Matrix Elements: A Status Report” . . . 271 J. M. LOSECCO “Recent Results from IMB” M. KOSHIBA “The Neutrino Astrophysics: H. SCHELLMAN “Neutrino Production . 289 . Birth and Future” of Charm at FNAL E744” C. N. BROWN “Twenty Years of Drell-Yan Dileptons” CONFERENCE C. YANAGISAWA “Recent Results from CUSB-II” TOPICAL D. PITMAN “Evidence for ot K. BERKELMAN “Results on b-Decay in e+ e- Collisions, with Emphasis on CP Violation” . . . . . . Part II. R. J. MORRISON “Recent Results from E691” V. CHALOUPKA “Study of K+ -+ a+e+e-, K+-+x+p+e-atBNL” . , . . . 301 . 315 . 327 . 335 and Search for . . . W. M. MORSE “Search for Flavor Changing Neutral Currents. . . . I(; -+ p*eF, e+e- and s”ete-’ ,347 . . 355 Part II. TOPICAL CONFERENCE page G. ZECH “Observation of Direct CP Violation and Status of the Qoo - Q+- Measurement in the NA-31 Experiment at CERN” . . 367 B. PEYAUD “Results from E731 - $ Measurement at FNAL” . . . . P. R. BURCHAT “Status of the SLAC Linear Collider and Mark II” . . . . . 399 D. AMIDE1 “Results from the CDF Experiment . . . . . . 415 at Fermilab” . 389 APPENDIX . . List of Participants Previous SLAC Summer Institute . . . . . . _ . . . Titles and Speakers . . . 431 445 . 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I- : ,-: [Aag) 062’S L’ ” 550~ pau!ol)suo3 Os;Z’S OLZ’E; ” ” ” ‘I’ ” udoag OC2’S ” ” OIZ’E “1 O'P0'0 O'P : pl 0’2 m c ; 0’1 0’0 O’E 0’0 : 2 0’2 O’P SEO-BBLOECZ -9T- < -iTi ZO’O 2-i 0 ETO'O .m”+“_d d --I 81‘0 +- 9 -(OZEl)ze+Y 91'0 +- 9 _ (OLZl) lp+y Il.0 600'0 01’0 19'0 89’0 SO'0 110’0 ++v oy ov dd bOO.0 CO.0 09’0 T=lq=A/qnAl (urns) +x-d odd 3 -u+d d ov EEO'O --v- d 10'0 -u+u+-acdd EO'O EZ'O 190'0 -rod STO'O ZZO'O _ (0~11) Tq,d ZE'O EE'O _ (OXI) EZ'O 103 18% 0-g z+' -%pc- -g IS% 0913 ' 'x+z Z - 1 x + 1 JZ Z--= T ZX = lpZ,(-Q+ei 3PzI (W-PII 1 = (Et _ = (St g)qOJd - a)qoxd = (gt = (gt pue <%I swb pue <Tgl ‘<(O)E I l-J,+= <CO)8 I(?,-= auo 'asuapuadap + <(O)ffl (>)-Q + <(O)gl(I)+S au:' = <(?)a I = <(?)a1 aAoqe aq~ buT?nqy>sqns 30 s"ogaTsodxadns Se ia- I pue <g, Bu-yssa;idxz = <Wbl z,q3- = <CO,hlI (~&Id= dq "aarb =q-J aq3 lsn~ =-IL 67 '<z,) 10 <lgl 'a>evxabya Le%p e 30 "OT-inToAS '_z p,'c = b = d pue s"oy2,e"~‘~~olo3 ppo-83 SSPW aq~ aeqrl OS '(am-~ axe sa>ewuab-+ KTqeqoXd) ASJap g "7 pa~lasuor, '<a lb - <gld Te"ObOq210 p"S "ana-d3 ATa>eurTxozdde 6Tuo ST da ~,eqZ, S",nsse TTTM St.5 'MO" IOJ = <%I ‘(<z lb + <dd :saqe2* s"oT7Tsodxadns axe sale2s"aKya *8 = <%I PUS og SSeU aq2, Tel="=6 SW ao "I 'palxnsse 8)qold glqold ,. -. :: .-.- 0 2’0 P’O 00’0 9’0 SZ’O 9’0 OS’0 CL.0 S P E 2 0’1 0 0 2’0 00’1 P’O SZ‘I 9’0 9’0 0’1 m x : :-, -02- . -_ c.z 0% “(3% 9.1 *.. o Z’E 0 2’0 t c-0 9-O 8’0 p’o=P) *.o=pj ‘Z’O=‘j ‘).OZ’j 07 / 2’1 ;,_ :’ -II- :, :. _...:.. .. 80'0 i SK'0 PZ 5 9EP 6 T 8 T ZE T 81’0 SO’0 T 99’0 ZK’O ZK 3 LKK S T 6T T OLZ KK'O i KK'O SO'0 F KZ'O Vi8 is1 ST5 -8+8 PX A a6exar.e x03 P,X103 'A c-a+a1 N (-if-I)N + (+if+a)N .’ .-‘-, ._ ._ -. nxaa naa -\ \ ‘n a0 X’C4 \aa t- \ \ -tz- n (3)” n -- (?I!! q P 9-c + I? (3)” (i?)C P EZO- \ 7 /, n 4 aaaosoo PZO-eaaOEO0 \ \ [+&-a] ‘\ \ i \ 820 -886OSOO : : .. ,Q,b z- L dmvz “7s 7, + zlQI & z- 21 'J- a = (2!3c- Q)A -9z- :... .; ::.: .. .-. ‘::? ,’ 1:,,,_ 3’ ,, .: :,,, ‘. .,, : .‘, ,‘. ,,o:, I. “,, ‘. -62- . -OE- :. -. Precious On Rare Decays Rarities - of K, D and B Mesons I. 1. Bigi : ._,: . . : Department of Physics University of Notre Dame Notre Dame, IN 46556 Abstract: A detailed analysis of K decays has been quite instrumental, if not even crucial for developing the present Standard Model of particle physics. There is no reason to believe that such a line of research has already exhausted its discovery potential. Quite on the contrary we can suspectthat further dedicated studies of the rare decays of K, B and maybe even D mesons will reveal “New Physics.” At the very least they will provide highly sensitive tests of the Standard Model. A crucial element in any such analysis is the reliability of the theoretical tools that are employed. I attempt to give a comprehensive and detailed evaluation of the scope and the Iimitadons of the various theoretical technologies that are presently available. : . -..,.1. .-. @I. Bigi 1988 -31- ‘.: . . .. . . :. _ ,.. _-’ I believe that “praying” for inspiration coupled with “working” hard to make 1. INTRODUCTION An event is called m if it occurs with a probability much smaller than unity. This, however, does not make it automatically an interesting object for study. The case of elephant-antielephant fluctuations is sometimes used to illustrate this point. While there exists no first principle forbidding them to contribute to, say, (g-2) for muons it is measurements and to calculate rates represents the appropriate method for our field; therefore, I will use this approach as guidance in the subsequent discussion. May I add in passing that any similarity between the approach sketched under b and an existing theoretical school is purely accidental. The question we want to addressthen is: “Flavours: Whence do they come - where do they go?” Yet it has to be understood that even a detailed study of flavour decays (“where do they go”) will not reveal directly and immediately the reason behind the existence of different flavours (“whence do they come”). What can be achieved or learnt is the following: (a) There has to be a dvnamical distinction between the different flavours; the utterly obvious that those contributions can safely be ignored. In the following I will call a rare event precious only if there exists a realistic chance for it to be ever ohserved - even if it takes many years Since I am the first lecturer at this Summer Institute, I can be forgiven for making a few general remarks although later speakerswill address these issues in more detail and with presumably more eloquence as welt. The theoretical landScapepresents itself today as a combination of strong and .-. . I ._._: _- existence of such new forces - i.e., “New Physics”, hereafter referred to as NP would in general lead to decay processes (l.lj M-1; 1; electroweak forces which are described in terms of a gauge theory based on the group SU(3), x SU(Z)L x U(1). (For these lectures 1 ignore the existence of gravity and I do so without feelings of guilt.) Tomorrow’s theoretical landscape will stilt contain QCD as the theory of strong interactions; yet the question on the underlying electrowcak theory remains quite unsettled. This is to sdy that QCD is the “only thing” whereas the Sum x U(1) gauge theory is only the “best thing”; for the latter merely incorporates many of the fundamental mysteries of particle physics without offering any explanations: what is the origin of the various flavour degrees of freedom, why do they exhibit a family structure and family replication, etc. etc.? M----ml: (1.2) 1; where M and m denote mesons and .-!I and 12 different charged leptons. Examples are Enlightenment can be sought via two alternative routes: & _:: ,^ K,--.+ e*p’ K+- K+,*$ These processes are strictly forbidden in the Standard Model since they would violate the individual lepton number. One can adopt the approach pioneered by the “Eastern Monks” --- These sages living typically by themselves or in very small groups sought enlightenment by pure thinking and meditating. Their contacts with the rest of society were rather limited: Processesof the type M- pious people from the surrounding villages and towns would come out to see these venerable monks and would do so in the hope of being addressedby them (though with 1’1. (1.3) (1.4) M-m1 2 on the other hand can be generated in the Standard Model as a l-loop quantum effect; yet NP can boost their nansition rates very significantly, modify the kinematical distributions of the decay products or it could even produce CP asymmetries! scant hope to understand such teachings). B_1 One can follow the example set by the “Western Monk Orders” --- Large collaborations that set out to cut down forests, take virgin land under the plow, baptize the heathens (with occasional, unfortunate losses) and do all of this under the motto of “ora et labora”! I had already stated the obvious: discovery of this kind of New Physics per se would not resolve the flavour mystery. However it would teach us lessons that -32- .. :. !.-,,: ,: :, Perturbation Theory; rare D decays are treated in Sect. V and rare B decays in Sect. VI; the conclusions are presented in Sect. VII. I had already stated the obvious: discovery of this kind of New Physics per se would not resolve the flavour mystery. However it would teach us lessons that are of crucial importance for any such resolution, namely (i) that a dynamical distinction does indeed exist and (ii) by which mass scale it is characterised. Measuring the rates of those transitions that within the Standard Model - can ._ 001s proceed only via l-loop effects will allow us to probe fundamental parameters like - quark diagrams - ;. ChPT I/N QCD SR .:. ..,: :, :..: : .’ ‘;.. .-. ~_/ lavour m(top) and the KM parametersV(td), V(ts). At the very least we will learn important or even crucial lessonson QCD lessons that are rather unique due to the interplay of weak forces and strong forces that occurs in flavour decays. The last item points also to a central problem in this line of research: when one finds a difference between an expected and a measured decay rate one would like to claim that such a discrepancy indirectly establishes the existence of New Physics! Yet one has to be concerned that this merely signals the need for “New, i.e., better Physicists or Theorists” meaning that our theoretical computations contained hidden uncertainties. Therefore we have to subject our tools to a very careful evaluation and re-evaluation. There exists a naive folklore about the available theoretical technologies, namely that our calculations become necessarily more reliable for heavier flavours, i.e., when going from K decays to D decays and then B decays. One usually cites as supporting evidence for this folklore that the heavier a flavour hadron is, the more short-distance dominated its dynamics become. This is reflected also in the emergence of a more and more universal lifetime for flavour hadrons when their mass increases: ‘T(K*) - 600 z(K,) vs. r(D*) - 2.5 r(Do) vs. r (Bi) c 2 1 (Bd). 0 44 4 ?? 0 4 t 0 i Table I Pattern of reliability that different theoretical tools offer for heavy flavour decays However I want to urge you not to accept this folklore at face value. For it is based on rather simplistic considerations read off from quark diagrams. There are other theoretical technologies that enjoy a much less tenuous relationship with QCD and that yield quite a different pattern of reliability for their predictions This is sketched in Table I, where the symbol ” 0 ” means “not applicable”, ” 44 ” “quite reliable application” and “4” “order of magnitude estimates.” Thus we see that the ‘: trustworthiness of a theoretical computation has to be evaluated almost on a case-bycase level - a central point of these lectures. These lectures are organized as follows: ;. -. in Sect. II, I discuss K, D and B decays that are strictly forbidden in the Standard Model; in Sect. 111and IV, I treat K decays that occur due to quantum corrections; in Sect. III it is the process K+ + rt+ + “unseen” whereas in Sect. IV, I analyse radiative K decays in the framework of Chiral -33- :, ..:..,. .::: ..- . . .~.. . II. “A FARMER AND HIS SON VISIT VIENNA” OR “BREAKING THE FLAVOUR CODE” Our understanding of the flavour puzzle - why are there families, why are they so much alike? - can be illustrated by the following story: A farmer from a little town had to visit the great city of Vienna to take care of some business. He decided to bring his little son along who had never seenVienna. While they walked through the streets the little boy was all eyes and looked left and right. He then pointed at a big building and asked: “Hey, Daddy, what is this.7” His father looked at it, scratched his head, A very convenient classification of the effective couplings that generate these reactions has been provided by Buchmiiller and Wyler.(l) Only “low energy” fields appearexplicitly, namely matter fields photons weak bosons light Higgs fields &SW denotes the Lagrangian of the Standard Model and A: Anticipating that ANP >>A (2.2) characterize the mass - otherwise we would have seen already these processes - we conclude that ZN~ better be invariant under SLJ(3)ex S(~)L x U(1) rotations. Exchanges of such bosons would produce processeslike e+e- + ep, er, pr G describes the coupling of two scalar fields - @or $* - to two fermion fields fl and f2 as shown in Fig. 1. Since the two fermion fields have to form a scalar (or pseudoscalar), one of them has to be left-handed and the other one right-handed. Accordingly they carry the same electroweak quantum numbers as the left-handed field alone, namely a weak isospin of half a unit and a non-vanishing hypercharge. If the two scalars that couple to these fermions are the Higgs field $ and its conjugate $’ then or ep --t IX, 7X which can be searchedfor. At low energies they will produce decay processes . :_ scale of the new interactions - again in analogy to the Fermi constant GF = lMk families, i.e. one that goes beyond the mere difference in mass; in particular there could be a neurral boson Y which connects members of different families Y-il~2>l* #I,. Ltj, and tCd=@ NP + be secured; it only means that we have to be more persistent and maybe have to rephrase our questions. In all likelihood there has to be a dynamical distinction between the different M-m Y W,Z Q they carry zero hypercharge; such a coupling cannot be SU(Z)L x U(1) invariant and, following our prescription stated above, is therefore ruled out. If on the other hand the two scalars are I@$or $*I$’ then they carry weak isospin one. The two fermions would (2.1) It is those that we are going to analyze. have to cany isospin one as well which - as mentioned above - is not possible. There is one tiny loophole in this last argument: the right-handed fermion field could be the charge conjugate of a left-handed field and a weak isospin of one unit is thus attainable. However such a coupling violates fermion number by two units and is thus allowed at -34- ‘.. generatenon-renormalizable interactions of dimension d > 5: questions?” whereupon his father replied: “Of course not, my son, how can you learn something if you don’t ask questions!” The fact that we have not received yet a satisfactory answer to the flavour puzzle does not imply that no such answer can ever r,m, (either leptons or quarks) All other fields are “integrated out” in the same fashion as W boson fields are “integrated out” in the effective weak Lagrangian. There this procedure introduced the non-renormalizable Fermi interaction of dimension six; here more generally it will looked at it again, shook his head and said: “I don’t know, my son.” This sequence the son asking a question and his father being unable to answer it - repeated itself a few times, Then the son said: “Daddy, are you getting mad at me for asking all these M- f :. ,-. . . .. best for neutral fermion fields, namely neutrinos, where such couplings produce Majorana mass terms. Yet the corresponding scale A,“p has to be huge’and a term + c”. NP ts quite academic in the present context. Aw Thus one arrives at a result that one would have guessedimmediately and quite naively, namely that the New Physics can be described by a dimension six term: (d = 6) a; L elf- -c(Wciw +A (2.3) i@j2 w f, f2 v Zg” =C ci l current x current ^_ I ‘- ‘.. (2.4) I The c number coefficients cl are determined by the specific dynamical model one has in mind. There is no shortage of such dynamical models: there are many GUTS on the market that contain “horizontal” interactions, i.e., flavour changing neutral currents (= FCNC) mediated via spin one or spin zero bosom; extended technicolour models can be accused of many vices, but not of forbidding FCNC; the same holds for composite models. Such new forces can in particular be mediated by so-called “leptoquarks” (= LQ), i.e., bosons that carry both lepton and quark quantum numbers. They Fig. I emerged first in Pati-Salam models based on a gauge group SU(4) where lepton number is treated as a fourth colour. Yet they appear in many other models as well and Fig. 1: represent a rather generic feature of models that are inspired by a superstring ansatz. Even “ordinary” Supersymmetry enters this arena if sneutrinos develop a nonvanishing vacuum expectation value. In summary, there are many models that will produce non-vanishing values for the coefficients ci in (2.4); however nothing definite can be said or predicted concerning their actual values. In addition, the couplings of FCNC to up-type quarks - u, c. t - could a priori be.completely different from those to A dimension five coupling of two scalar fields to two fermion fields. down-type quarks - d, s, b. In that senseone gains independent pieces of information when searching for K + elt &D + elr decays. B. The Down Side So far we have looked at the optimistic side of things; now let us review the more depressing aspects. -35- .. (i) (ii) No decay that violates lepton flavour conservation like K + ep, R ep. D -+ ep, eprr, or B + ep, epK has been observed yet. The bounds on ANY that can be derived from that will be given below. Exactly becausethe New Physics contributions are new they cannot interfere with the Standard Model conuibutions. Therefore one finds for the branching ratios ., .. .. : 21 _ .. -. (2.5) where My denotes the mass of the “new” boson Y and gyq[gyl] its couplings to quarks [leptons]. An increase in experimental sensitivity, as far as branching ratios are concerned, by a highly impressive factor of 1O‘ttranslates itself into a much more modest increaseby a factor of 10 in sensitivity for the mass My! This is not encouraging when one keeps in mind that no theoretical upper limit on My has been suggested so far that is reasonably reliable. A non-observation of these decays will therefore not lead to a breakdown of any meaningful theoretical benchmark. Such searchesare therefore not for the faint-hearted! ==& Y ---- s Fig. 2 (iii) However they are not for the reckless either! The decay of a pseudoscalarmeson PS = (Q 4) + 1t1, (u) is represented in Fig. 2 for an s-channel exchange of the Y boson. Its transition rate is subject to two concurrent suppression mechanisms: If Y carries spin one then the rate is helicity suppressed, i.e., it vanishes for Fig. 2: Diagram for the decay of a pseudoscalarmeson into a lepton pair. m(It), m (12) + 0. More specifically (2.6) If Y is spinless there is no such “kinematical” suppression. Yet scalar couplings violate chiral invariance; since this symmetry is apparently the only principle that can keep fermion masseslight one (as a theorist) is very reluctant to give it up. Accordingly, one susoects that all such scalar or pseudoscalar couplings depend on the mass of the field they couple to - exactly Eke Higgs : .< bosons. Thus -36- .: ‘. : : I believe that x”, (2.7) (p) M --f m ltz2 transitions whereas without mass ANY suppression factors. The existing bounds are summarized in Table II, where I have underlined the “most likely” bounds as explained above. as before, but this time due to genuine dynamical considerations - as perceived by theorists. The exchange of these massive Y bosom produces pointlike interactions, i.e., forces of zero range. The transition amplitude then depends on the wave function of the decaying meson at zero separationor the decay constant: Process (2.Q For K + ep we have l Mtc rnN--;s fk- is the appropriate quantity for M -+R,l, decays offer a much better chance to probe BR ANP KL-+v < 10-8 < 35 TeV K+ -+ tr+ep Do+ep B + ep < 4.8 x 10-q < 4.1 x 10-5 < 3 x 10-S < 20 TeV < 1 TeV < 3.4 TeV ;. _. : ‘. : : .: Aw < 16TeV <9TeV < 0.24 TeV c 0.5 TeV Table II f M, and these suppression factors are not huge. For D + el, B --f ep on the other hand, we encounter huge suppression factors since rn+ C< rnD < mg, fD << mD and fB << mg. Let me list just one telling For details on the experimental numbers see the lectures by K. Berkelman and A. J. S. Smith.@*5) example: the mode Do + e$’ has been searchedfor unsuccessfully leading to(z) BR @” -+ e’p’ ) < 0.41 x lOA E691 (2.9) C. Resume on the forbidden decavs M+(m) Rt& (i) Yet this apparently impressive bound loses its luster if compared to the upper limit on the quite ordinary mode D+ --f @u:(3) There is an obligation to continue careful and dedicated searchesfor these striking decay modes. (ii) Improved experimental upper bounds just raise the bounds on ANY, the mass scale characterizing the New Physics that distinguishes between the different BR(D++D+v,, )<6x104 MARKIIJ (2.10) From this number one extracts fD _<290 MeV; theoretically one estimates fD - 150-200 MeV and therefore families, and they do it very slowly A NP*min-Qii& 2 BR(D+-+~+v~ ._” “.._: ,: :.. )=1.5x104 & (2.11) i 1 Compare (2.9) with (2.11). and I can rest my case. When extracting bounds on mass scales that characterize New Physics one Unfortunately, no sound theoretical upper bounds on Arqp have been established so far. but this might change in the future. (iii) Searchesfor D + ekt or B + ep are classical examples of “lamp post searches”: should therefore quote numbers for two quantities, namely ANP as it appears in (2.3) one looks for something where it can be seen most easily, not where one has the best chance of finding it. Nevertheless it would be imprudent to discontinue them. M, -2 = r\2 M, with ci = 1 (see 2.4) and ANP up x M, ( i.e., ci = M Ps As explained above, -37- ;. ;. .: ._ - (iv) In any case one m search for D -r x/p ep and B + K/K’ ekr decays as well, or even better for the inclusive modes D + ep + X, B + ep + X. They are not (v) III. K+ + z@+ “nothine seen” - THE PRECIOUS RARITY PAR EXCELLENCE affected by helicity suppression and the inclusive rates are also not reduced by (f&n& or (‘B/m&* respectively. Furthermore the different decays are governed by different hadronic matrix elements; e.g., ~0 I~fllD> CJ D --t ep The transition K++ x+vv (3.1) requires a FCNC; in the Standard Model it has therefore to proceed via a one-loop process as shown in Fig. 3. Computing the contributions of these diagrams -- which amounts to integrating out the heavy fields W, Z, t, c -- one obtains the effective interaction Z&AS = I).(@ To cakulate a rate one has to form the appropriate matrix <K IV&t D> D+rtek G D-r pep t) <p IA&D> where S, P, V, Audenote scalar, pseudoscalar, vector and axialvector currents element respectively. (vi) The mixing angles that are contained in the couplings of these FCNC could in principle be “dialed” in such a way as to greatly suppress, say, K --f ttep, while not reducing D -+ nep. In that sense studies of rare K and rare D decays are <n+v? Ize,(AS=l) 1 K+>=coeff. jT<x’ IJF IK’> (3.2) With this perturbative treatment one can compute the c number coeff., the leptonic 0) current J tr and one can identify the general transformation properties of the hadronic (4 current ’ a. Yet one cannot obtain the magnitude of the on-shell matrix element complementary, not competitive. It is however a different question whether this can make up for the much smaller branching ratios that can be reached in K decays vs. D decays. <I[+IJFIK+>this way since the latter depends on long-distance dynamics. Fortunately the well-measured decay K -r tt ev depends on a matrix element < 8’ IJtI K+ >that can be related to < x+ 1J,“I K+> via an isospin rotation of the hadronic current and that is probed at almost the identical momentum transfer. There is a small loophole in this line of reasoning which is analyzed in the Appendix A and then discarded. BR (K+-trr+ w) can thus be expressed mainly in terms of quark and lepton parameters- masses,KM angles; the impact of long-distance dynamics is isolated into one hadronic matrix element whose size can be obtained from the memred decay K -+ xev: 2 BR(K+ -+ IC+v v) z 1.43 x 1O.5c c I V* (qs) V (qd) D(xa, y, ) 4 1 = e, p, 7 ; q = u, c, t -3s (3.3) V(ij) denote the corresponding KM matrix elements and the function D(x,+ ya) enter when one integrates out the internal loop in the diagrams of Fig. 3. They were first calculated by Inami and Lin(6) and for y,~= 0 they read ,‘i D(x,O)=$ [I+& -[$)xlogx+; - &. ..; : _.: : (3.4) With three families there are thus three unknown parameters - mt, V(td) and V(ts) - that determine the rate: BR (K+ + x+ v, 5, ) = 1.43 x 1O-51V’ (cs) V (cd) D(x,, 0) I2 x d , + v’ (ts) VW) X D (x,, 0) 2 v’ (cs) V(cd) --i D (XC.0) (3.5) =BR(K++n+v,O,) RR (K+ --f n’v,vT ) is slightly smaller (at most 20%) since the T mass that enters in the loop cannot be.completely ignored. Using the unitarity of the 3 x 3 Kh4 matrix one obtains V (ts) =. -V (cb) = AX* (3.6) where the last equality refers to the Wolfenstein representation P1) (cl h = sin9, Fig. 3 A= 1.1 kO.2 For V(td) no such definite statementcan be made: V(td)=Ah3 (I-p-iq) (3.7) (3.8) V fub) - Al3 (P-in) I 1_1 Bounds on IV (ub) I yield information on d P*+qL only, but not on the sign of p Fig. 3a, b, c: Quark diagrams that generate the transition operator s + d j C which is quite relevant for IV(~)I =a3 JFZT . Using I p I 2 0.8 as inferred from semi-leptonic B decaysone finds <BR(K+-tx+vv) x10” <{i\f} form, = {i} GeV (3.9) where the upper [lower] bound holds for p = -0.8 [+O.S]. If one ignores the top contribution completely one gets BR (K+ --f B’V C’)= 3 x IO‘“. -39- : :_ 1.. -: . The strength of B, -Ed mixing is directly and crucially affected by I V (td) I Physics of which I will sketch just a few typical examples that can produce sizeable rates for K+ -+ tt+ + “unseen” and mt. The signals observed by ARGUS and by CLEO strongly favour p < 0 and tend to push p towards -0.8 unless top quarks are very massive. For the range 50 GeV < mt < 200 GeV one can use the auuroximate scaling laws bmg =(mt)‘.75 ,-__ 1. The least radical extension: a fourth family Dh, 0) = mt The predictions in (3.9) have to be taken with a certain grain of salt: they were 5;...-. study are the mass m(t’) and the KM parameters V (t’s) and V (t’d). (For the quark contributions act coherently whereas the lepton terms are incoherent due to the absence of lepton flavour mixing. This is explicitly expressedin (3.3)) Making V(t’d) and V(t’s) as large as still allowed by the unitarity constraints on mc=1.5GeV. (3.10) While this representsa reasonablechoice, it is not a uniquely determined one. A range m,-- 1.2 - 1.8 CeV has to be allowed for; this in turn leads to a non-negligible variation in X’V : There could exist a fourth family with two new quarks t’ and b’ and two new leptons A and VA. The new parameters that are most significant for the process under obtained using BR (K+ + -, a 4 x 4 KM matrix would allow to push BR (K+ --f tt+vv) up to the present v) in particular for moderate top masses. Using “reasonable” and experimental upper limits. On the other hand generalizing a Wolfenstein ansatz to four families or inferring the t’ and b’ parameters from fixed point solutions to the renormalization group equations leads typically to “typical” values for the KM parameters,namely A = 1.1, p = -0.7, q = 0.25 one finds for example a roughly 50%[35%] variation in the branching ratio for a top mass of 40[100] GeV. With these caveats in mind we conclude that the present findings on B, - B, mixing Br(K++ 10-9, 10.’ (3.13) 2. Jhe most e&ant extension: SUSY Supersymmetry introduces new neunino-like states,namely photinos 7 (which can contain some admixtures of other neutralinos). The process K+ -+ X+ + “nothing imply BR (K+ -+ tt+ v v) - 10”’ - 1O-9 x+@)<fewx (3.11) seen” can then be realized by More accurate information on mt, B,- Bdmixing, etc. when it becomes K++tt+*Iy (3.14) available will enable us to restate (3.11) in a more precise way. To say it differently: there is an upper limit on BR (K+ -+ tt+ V v) that the Standard Model with three if the photinos are sufficiently light - a possible, though not very likely scenario. Flavour mixing among the different down-type squarks fi = (a, ~.b)can families can accommodate; its present value is given in (3.11): generate K+ + x+ 7 7 already on the tree level as shown in Fig.4 where the dots point BR(K++rr+vQ St-M 3fam, <L out the odd R-parity of the field involved. One finds that(7) (3.12) BR (K+ -+ X+ yy) 2 10-r”. 10.’ L (“now”)’ - 1o-9 (3.15) represent conceivable cases. Without such flavour mixing in the squark mass matrix, one has to invoke oneloop reactions as sketched in Fig. 5. They typically yield rather small numbers, If data were to show a branching ratio in excess of such a limit we would have to conclude that New Physics were at work. There is a whole host of candidates for New -4o- : : ,: :; . 1. :. .- namely BR (K+ -+ x+ 77) - 10-t’ - lo-” (3.16) 3. The most stirring extension: direct FCNC via ETC. LO, ,., With direct FCNC mediated by the exchange of a new boson of mass M, one finds BR (K+ + x+ v&, + n+v,&) - 16” (3.17) where I have ignored any helicity suppression. 4. The Fig. 4: Adopting a phrase coined by M. K. Gaillard one includes here K+ + n+ + “funnies” Tree level diagram for K- + R- yf, where “funnies” stand for axion. familon, majoron, Higgs and all the other even more fascinating objects that have not been invented yet. I will list just two examples which are - relatively speaking - the ones with the most specific phenomenology. (a) Higgs: The Standard Model contains just one flavour diagonal neutral Higgs field; its mass mo is - strictly speaking - undetermined. Theoretical constraints like the Weinberg-Linde bound can be evaded if there is a sufficiently heavy quark field Q, i.e. MqZSOGeV (3.18) This has actually become a more likely scenario in the absence of a direct observation of top quarks. A very light Higgs becomes then conceivable and the process K++ A+ cp, ‘p + p+ p-, e+ e- , “unseen” (3.19) Fig, 5: could occur due to higher order processes.@) One-loop diagrams for K’ --t X- “Jy. No decay of this type has been observed; unless some delicate cancellations between different contributions occur one has to conclude that K+ + x+ ‘p is forbidden kinematically. i.e. mcpZ36OMeV (3.20) Going beyond the Standard Model and extending the Higgs sector will lead to more flavour diagonal neutral Higgs fields cpi. Their Yukawa couplings are not -41- .: I._ ,, .. . ‘. ... : uniquely fixed anymore by the requirement that they give mass to the gauge bosons and fermions. Thus m (Cpi)c 360 MeV (3.2 1) (0) IV. OTHER PRECIOUS RARE K DECAYS -- A FIELD DAY FOR CHIRAL PERTURBATION THEORY There is a rich class of rare K decays that involve photons both on-and off-shell: is still allowed if the Yukawa coupling of this light Higgs boson is roughly an order of magnitude smaller than prescribed by the Standard Model. Majoron: KL~Ks+w,w* + Neuuinos can obtain a Majorana mass only if lepton number is violated. If this 1+1- K-+X?’ global symmetry is broken spontaneously then a Goldstone boson will emerge the (generic) Majoron. It can be accomplished by a scalar partner, and both are typically rather light objects. Then the decay@) K+ + A+ + 2 light scalars (4.1) (4.2) 4 1+1- K-+lty( (4.3) [K + n y is forbidden by gauge invariance (or alternatively, by angular would be allowed kinematically. Unfortunately it is unlikely that its branching ratio would exceed that for K’ -+ x+ v v (with three families). momentum conservation).] Unfortunately there exists a certain complication that we have to addressat this juncture - a complication that is sometimes referred to as the “Problem of the Two Worlds.” (i) On the one hand there is the world in which theorists work; it is characterized by distances d 5 lo-** cm; it is populated by quarks and gluons (and... and ...) and it is this world where theorists indulge themselves in building models and computing transition rates. This tour d’ horizon of Old and New Physics can lead to one conclusion only: Dedicated searchesfor K+-,+ + “unseen” are a definite must for seriousresearch! (ii) On the other hand there is the “Real World” where everybody else works and everybody (theorists included) lives; it is characterized by much larger distances d 2 IO-t3 cm and is inhabited by hadrons: pions, p mesons, protons etc. It is in this world that detectors are built and transition rates measured Obviously one has to establish communication between these two worlds which allows to translate results that have been obtained in the Theorists’ World into those that are testable in the Real World and vice versa. This task is, we all believe, performed by QCD - in principle. In practice however we have so far fallen short of realizing this noble goal in a comprehensive way. To cite but one (relevant) example. The decay KL + ?~yis viewed to proceed via the diagram in Fig. 6a (and related ones) in the Theorists’ World, whereas it is represented by Fig.6b in the Real World. A. Fundamentals Fortunately there are some favourable circumstancesthat can come to our rescue -42- .^ ,: .‘. .., -. ... l if properly exploited: the only hadrons that appear in K decays are pions and kaons; they double as @l bound states and as chiral Goldstone bosons, i.e., bosons that emerge due to the spontaneousrealization of the chiraI (and global) sum. group: su (3)L 63 su (3), -3 su (3)L + R + E’S,K: s, q8 l :, . . ._.~ (4.4) the massesand momenta that appear are “soft”: 1p 12 _<rnk << (“normal hadronic scale” - 1 GeV) (4.5) This vague statementwill be made more precise later on. Chiral uerturbation theorv (hereafter referred to as ChPT) describes the theoretical framework that exploits these two facts: it starts from the fundamental Fig.6a dogma already mentioned, namely that (approximate) chiral symmeny is realized spontaneously in nature. This dogma consists actually of two parts: (i) For massless u, d and s quarks, i.e. Fig. 6b m,=md=ma=O there are eight masslessGoldstone bosons (4.6) A= , lf Fig. 6: The decay KL + ‘myviewed in the Theorist’s World (6a) and in the Real World (4.7) K*, K’, d (6b). rl and one mass scale 47t B = 1.2GeV (4.8) where TX = yy = 93.3 MeV (4.9) .- . .. .. . : : :I -. :.. denotes the pion decay constant. The Goldstone nature of these mesons puts severe consnaints on how they couple to each other and to electromagnetic and weak currents (ii) When u, d and s quarks obtain non-vanishing masses,chiraIsymmetry is broken -43- explicitly and the eight pseudoscalarmesonsceaseto be massless with the six operators O?4s) expressedas a product of two currents. Yet I$, rn$<< 4 << (4n FJ2 (4.10) - There are stm&al similarities between (4.12) and (4.14): (445) The operators Oi are expressed solely in terms of the u, d and s quarks, Q3 i.e., the m fields. The operators G, also contain only the I.&&l fields, - namely the Goldstone bosons rt, K and q. The coefficients c” represent the effects due to the existence of the heavy & << rni << (4x TJ2 still holds; thus the real world where pions and kaons do have a mass is not expected to be so different form one where they are massless. Mom specifically, the real world can be described as a perturbation around a world where chiral invariance is realized &l& - the c. b and t quarks and the W bosons - that have been “integrated out” and do not appear explicitly in the low-energy Lagrangian. Similarly the &ayy fields - the p and At mesons etc. - do not appear explicitly in (4.12); however spontaneously. The small quantity which serves as an expansion parameter in this treatment is given by they determine the magnitude of the coefficients ci in (4.12, 13). Yet them are essentialdifferences as well between the expressions (4.12) and (4.14): There is a fi& number of operators appearing in (4.14). namely six, and their coefficients ci44 are &&& through an analysis of renormalization group (4.11) equations, at least at sufficiently high momentum scales. In (4.12) on the other hand an in&t& string of operators Oy appears; furthermore the coefficients ci (where q = u. d, s; a = IL, K, ?I). ChF’T thus generates an effective Lagrangian for the strong interactions among are, as a matter of principle, completely undetetmined by ChPT. These findings should not come as a surprise: for the chiral Lagrangian describes a non-renonnalizable interaction as is explained in more detail in Appendix B. Quantum corrections do therefore force upon us new effective operators at each loop level and pseudoscalar mesons (4.12) i=l their coefficients are undetermined as a matter of principle. These coefficients will in general be scaledeuendent since the higher loop contributions will typically contain ‘Ihe Oy denote operators that describe the couplings of Goldstone bosons; 5 am numerical coefficients that contain the small expansion parametersgiven in (4.11) --it'E; = (4n f )z ( divergent momentum integrals. Details can be found in the literature.(ll) What we should keep in mind for our subsequentdiscussion is the following: ChFT is more than just another cute model; it is god based on any assumption (9 concerning the smallness of the strong coupling as -- instead ChPT is OCD at (4.13) ‘i 1 where $zP denotes quark masses, meson masses or the momenta carried by the mesons; in K decays we have for on-shell fields p’ s rnk. (ij) --itgo to higher orders in the expansion parameter (4x2$ new operators with undetermined coefficients Ci (though structure). Their values can either be extracted from applied to another; or one can attempt to estimate their It is instructive to compare the expression (4.12) with the one that is usually written down to describe the effective weak interactions of u, d and s quarks: Csff(AS=l) QO (44s) ci 0., = (.suffcientlvl low enemies! Not surprisingly, a certain price has to be paid up-front for this panacea: when we i=l -44- we are forced to include with a well-defined chiral one set of data and then magnitude by employing : .. :I -. ..y:. : .:::: 1: ._._ additional theoretical technologies: phenomenological models like p exchange dominance, l/N expansions, QCD sum rules and blessed be the day! - lattice QCD. This leads typically to a very involved and lengthy analysis and it costs us in predictive power, but there is nothing ad-hoc about it! And there is still lots of predictive 0 m, (4.19) md 0 m, . The meaning of the fust term in (4.16) becomesclearer when one expands (4.17) in the pion fields power left as can be studied in the literature. Here we concentrate on the radiative K decays listed in (4.1 4.3) where strong, electromagnetic and weak forces are intertwined -2 4f* a(J&JJ,Jl+, = J,nJ,n+& Jgt’J,r~~ (4.20) fn + i.e.. it contains the kinetic terms for massless meson fields and their (derivative) interactions. The second term which contains the quark mass mahix represents the & breaking of chiral invariance that yields non-vanishing meson masses The reader that is interested in results rather than how to obtain them can skio the next section and go to section C. B. Construction of the effective Laprannian -2 f, M;. The strong Lagrangian can be expressedby three terms: 2(m,+m,) F2 ZeE =$ u(J&!J,Y+) +vtr@J4111+Y+M)+ + higher order terms (4.21) Finally the last term in (4.16) is produced by loop corrections that generatecouplings of the meson fields that contain four, six etc. derivatives (or momenta) each of which is scaled by ‘f, (4.16) with (4.17) (0 where the matrix I$contains the eight Goldstone boson fields As usual the elecaomagnetic couplings are obtained by replacing the normal derivatives with covariant ones: J,U+D,,Y=J,P-ieA,Q.Ul where Au denotes the electromagnetic field and Q the quark charge matrix (4.18) (4.22) .(;.. .~ ; . .. .: :. ,. and M denotes the quark mass matrix -45- . _. -..: ‘: :: . Otherwise if those discrepancies turned into failures or new ones emerged one would face a very awkward situation: keeping in mind that ChPT is QCD at low energies one would have to adapt a dictum by B. Brecht: “I suggest”, says Mr. K., “that QCD dissolves Nature and elects a new one.” (4.23) There are now additional higher order terms, two of which are of relevance for radiative K decays(l2) z: = -ieL9F,,tr(QD,yD,U+ Ecker, Pith and de Rafael (hereafter referred to as EPR) using the pioneering work of Donaghue et .l.(t6) have shown in a beautiful series of papers (t4) how to implement the weak interactions in a china1Lagrangian. One starts from the samequark level Lagrangian that was already discussed: - + QD,!.!‘D,U) +e2 L,,F,,F,,~UJQY’Q) (4.24) F &v = J, A, - Jv A, Z The two quantities b, Llo are undetermined parametersof the type discussed before. With the couplings written down so far (ii) n”,q (4) G (AS=l)=LV(ud)V fi + h.c. i=l SU(3)n. According to the AI = l/2 rule the 8 piece is by far the dominant one. In the --f -f-r following we will mostly ignore thea-plet. mimick in ChPT: 1;: (AS = 1) = G, @+&& (c) An intermediate resume It is this algebraic structure that one has to + hc. + non-octet terms + higher orders % V (ud) V’ (us) g, G, = E .g+.y describes the strong and electromagnetic interactions of K’S, K’s and q’s - to fl orders in the strong coupling - for “soft” momenta 1p 1 < 1 GeV - in terms of a priori undetermined parameters: L,, L,, (us) (4ds) The operators Oi which are products of two currents can belong to an 8 or a 27 of cannot proceed, to implement it one has to include the Wess-ZuminoWitten term f, -* (4.26) (4.27) where 4 denotes the man-ix that represents the Noether current for the V-A chiral rotation: . .. It has yielded a successful phenomenology with two possible exceptions, namely an underestimate of I- (tl --f X+ A-X”) and F (rl + x0 n). One can actually give some The appropriate numerical size of the parameter gg is obtained from the observed width forK,+ xx: rather natural arguments why terms that are of higher order in CbIT are neverthelessof great numerical importance in those particulaEcases.(t3) lggl z5.1 (4.29) For radiative K decays we still need electromagnetic corrections to these weak -46- ‘:.. :_ -,_:_ -- ,- couplings; as before they are implemented by introducing covariant derivatives, see (4.22). They also induce terms of higher order in ChpT: ‘W20.Qf,~,.;,L) + ~~%v~,tiQL$u(h~.~,&) their coupling strength: a priori undetermined parameters are introduced as the coefficients of the chiral operators. There are three such parameters to the quadratic order in ChPT cC2): i;,(g,[ ’ 1 (4.30) 57 1 (4.34) and six additional ones to the quartic order: + he tC4) : Lg. L,, ; wt. w2>wj, w4 e2f2G Zc4) (AS = 1, (em)2) = 8 i (4.35) These parameterscan be momentum scale dependent, i.e., w4 F, F,& (x6. i7 Ql! Q Y+) + kc. (4.3 1) Wi = Wi where (q2/ A2 ) (4.36) and this happens when the loop integrals that are generated by quantum corrections diverge. and 116_i7 denote the appropriate GelI-Mann matrices acting in Sum space; wt, wf, The numerical value of these parameters can be inferred from data: e.g., f, LL. This, by the way, does not mean that we have x + Iv andgg from Ks -+ wg and w4 are new a priori unspecified parameters. from (e) Summary on the theoretical tools ChFT describes the suong and elecuoweak interactions of pseudoscalarmesons by an effective Lagtangian that contains Goldstone boson fields GB, their (covariant) finally understood the dynamical origin of AI = l/2 rule and its range of validity. However once the A1 = l/2 rule has been postulated in one reaction, then ChPT allows us to implement it in a theoretically consistent way and apply it to other processes. C.$ derivatives, elecuoweak currents and c number coefficients: ze,= z- (GB, D, GB, ji”“‘“k, coeff.) There are two simple, yet important theorems that apply to radiative K decays: Theorem I (4.37) Ampl(K+xy)=O (4.32) It describes the dynamics to all orders in the suong coupling and to the appropriate perturbative order in the elecuo-weak couplings. The conflicting requirements of gauge invariance and conservation of orbital angular momentum enforce the vanishing of this amplitude. Theorem II Feynman diagrams can be written down which contain as building blocks - propagators of Goldstone bosons - vertices that describe their couplings among themselves - vertices that in addition contain couplings to elecuo-weak currents. Amp1 (K + (IL) + y’ s + I’s ) = 0 The expansion parameter is given by P2 (4n P2 -------T (1.3 GeV) where the final state contains any number of photons and charged lepton pairs and at most one pion. It is again the conflict between two requirements, this time between those of gauge invariance and chiral invariance, that leads to a vanishing amplitude to second, i.e., lowest order in ChFT. There is a two-fold motivation for studying these decays in a dedicated fashion: (4.33) making ChF’T applicable if only soft momenta are present. There is a price to be paid for including the strong interactions to all orders in (i) -47- They provide stringent tests of our understanding of chiral invariance - a concept that is deeply rooted in QCD (remember “B. Brecht”). (ii) Direct CP violation represents itself as a minute (though highly important) phenomenon in KL + RX decays. This is partly due to the dominance of the AI = l/Z over the AI = 3R amplitude in these non-leptonic decays. In radiative K decays on the other hand one finds, as stated above inTheorem 11that the large A I = l/2 enhancement is at least partly off-set by the chiral suppression K, - P2/(4X Fn )*. This can make AI = 3/2 and 5/2 amplitudes more significant thus allowing direct CP violation to manifest itself in a less suppressedmanner. ----- Tz- +,i-: I *. I ‘.I --f-Y Ir;K+ Y KS---- (a) K” .K’-+~Y CP invariance is assumedfor this discussion. The mass eigenstates KS and KL have - in this approximation - to be identified with even and odd CP eigenstates KS em respectively. Y -c---x: --__-- T* K /-. \ ,’ ’ 1\ I -- ‘.- d’ Y < Y . Y Fig. 7a (7b) contains the diagrams of lowest order in ChPT that generate K, + yy (KL -+ fl). They are not shown to establish bragging rights, but to illustrate two points of general interest for the serious student of ChpT: - Fig. 7a: Diagrams of lowest non-trivial order in ChPT for KS --t -r-r. some vertices have a decidedly hedgehog-like appearance which will actually intensify in higher orders. This should not surprise us - after all ChPT is produced from a non-renormalizable dynamical description. - The reactions Ks --3 myand KL --f -r-fthat look so (deceptively) similar on the quark level are described by very different diagrams in ChpT. The diagrams of Fig. 7a yield BR(K,+yy)=2.0x10-6 I& 1’ where we have calibrated gg according to (4.29). experimental number from NA 32 on it (4.39) There exists a preliminary (4.40) BR (K, -+ yy) = (2.4 rt 1.2) x lO-6 which agrees with this prediction although the statistical significance is not Fig. 7b: Same as Fig. 7a, but for KL + w overwhelming. So far no reliable number on BR(KL + yy) has been derived within ChPT. For -4a- Y l The theoretical predictions on r (K, --t y p+p- ) differ by 10% to at most 20%. The experimental sensitivity level therefore has to reach the few percent level before the different predictions can be distinguished. . .:: ..‘i;. _:: The ratio I- (KL + y I+& )/r (KL + v) is not sensitive to SU(3)n breaking and can thus be predicted: I-(K,+yL+l-) 1 1.59 x 1o-2 rwL-+W) = for 4.09 x 10.4 1 dr -r dZ t L=e t =p (4.41) K,- +'YY peak just above ~0.2 and to drop off rapidly for larger z both in ChlT and in a phase space descriptionYet in ChfT the peak is even more pronounced and me drop-off is even steeper than in the phase space ansatz. These differences occur roughly on the 20% level. Details can be found in Ref. 14. (c) K” , p --r LO“IY ChPT allows to relate KL -+ x0 yy to K, -+ r( independently of the value of gg: rq-+ x”YY)= rcew (4.42) 5.9 x lo4 which translate into [see (4.39)]: 2 -7 gs (4.43) 51 I. I In describing K, + x0 w one introduces a cut-off in m (n) to avoid the physical x” BR(Kt,-+rt0~)=6.9x10 Fig. 8: pure phase spaceansatz (broken line); from Ref. 14. pole since here one is not interested in studying KL --f rt”rro, R’ + w where both pions are on-shell. One then finds -8 BRO(,+rr’yy) withz=m2(r()/ z5.0.;4x10 The cl-photon mass distribution in KL --t 8’ yy, both for ChPT (solid line) and a (4.44) 4. Again ChPT leads to a different distribution in z than, say, a phase space ansatz. As shown in Fig. 8 this difference is really striking for 5 r (KL -+ K” I’$: chiral symmetry produces a dramatic suppressionat low values of z. -49- which overshoots the observed ratio (4.48) even in the absence of a non-leptonic enhancement (d)K’-+rGW The transition rates for the decays considered so far depended on g8 and ?, , but on no other hadronic coupling parameters. This is not uue for K* + K* fl higher Yet what we have ignored so far is Theorem II, (4.38). which states that we have to go to the quark order in ChPT. Accordingly, one estimatesroughly order terms Z(4) that are produced by quantum corrections contribute here; they acmaby enter via the following combination of their ccefficients & ‘.: r(K+-tx+e+e-) r(K++xOe+v) 32n2 4&,+L,,)-$ (w,+2w2+2wq) . (4.45) 1 1 The parameters b + Lto can be extracted from the observed width of x --f e v y. no That shows that even the dny ratio (4.48) allows for a sizeable non-leptonic enhancement in K+ + rr+ 1+1- if one takes into account the chiral suppression such reliable information has so far been obtained on the parameters wt, w2 and ~4. However we can state a lower limit BR(K+-trt++~)>4xlO-~ expressed in (4.38). (4.46) To turn this qualitative “success” of ChPT into a quantitative one is, however, quite a different matter: for the counter terms that are produced by the l-loop quantum corrections contribute to K+ + x+ 1+ 1-. Their impact is represented by the and a “most likely” value (4.47) BR(K++rr+r()-10d coefficients b , Llo, WI. ~2, WJ, ~4; since the one-loop integrations now yield divergent results one has to deal with the scale dependent part of these coefficients. This represents an additional complication relative to me case of K+ + x+~r where since a QCD treatment suggests ‘t?= 0 (1). (e) Kk --f rtf ,!+R- only the scale independent part of these coefficients entered EPR chose the following procedure to deal with this complication: At last there exists a measurementof one of thesedecay modes: r-w++ x+e+e-) = (5.6 f 1.1) x 10. 6 r(K+-+aOe+v) - lix, within reason, me parameters such that the absolute width r (K+ + x+ e+e-) is (4.48) reproduced. - Then predict r (K+ -+ K+ p+p-) and the distributions +.-$ The ratio in (4.48) appears surprisingly tiny since naively one might give a different guesthate: r(K+-+rr+i+,t+), z=m2(R+1.)/M:. IY(K+-+x+e+e-) r~+47t"e+v) - 0 (e4) - few x 10e3. This program can be fulfilled up to a twofold ambiguity; for details consult Ref. 14. (f) K”,p +x01+1- (4.49) Of course one can do better than this overly naive ansatz: one can describe K++x+e+eas an electromagnetic correction to the non-leptonic (pole) transition K + x with its The discussion of Ks --f 1~” I+,!- proceeds in complete analogy to K*+x*L+I. A completely new element - and one of fundamental importance - non-leptonic enhancementfactor m: however enters when one analyzes KL + x0 R+k 2 r(K+-tx+e+e-) r(K++xOe+v) e2% 2gm _ t nk - 1o-5g’, : ::. ..I... (4.50) (4.52) For the final state in I K,-t-+fy’ !, 1+ Irepresents an a -5o- eigenstate of CP (4.53) .I ,,: .:. .- cpr @” r’ ) I=, 1 = CP [x”] CP [fl(-lf = (-1) (+1) (-1) = +1 (4.54) Yet the initial KL is CP odd in the (almost realized) limit of CP invariance; since The ChPT loyalists of EPR and previously the authors of Ref.16 as well have arrived at quite different conclusions: . KL + IL’ e+e‘ is dominated by the CP violating one-photon process therefore Cp [initial1 f Cp [final] (4.55) (4.61) one realizes that the reaction (4.53) can proceed only via a violation of CP invariance! Accordingly one obtains as an order of magnitude estimate I 1.5 x lo-r2 BR(KL-+r?Y*+rtoefe-)={ BR(JSt,+rtO~+rcoe+e~)- ~e,~2BR~~~rr~e~e-)-10“2-10~‘1 manifestation of CP violation in KL decays one has to guard against two other possibilities: (a) The R+1- pair is produced not from a (virtual) photon, like in (4.53); instead it comes from a Higgs scalar (that can be on-shell or off-shell for that matter). The observation of KL + no ,I+,!- --- with presumably BR (KL + rsOp+w ) >> BR (KL + no e+e- ) --- would in this scenario not represent a CP violation, but @) instead the presence of New Physics. This would obviously constitute a highly desirable interpretation. Unfortunately there exists a much more mundane process leading to KL --f x”l+,t-, namely ...::. -. : (4.62) (1.5 x IO’” (4.56) Yet before an observation of KL -+ x0 .I+.!- can be listed as another .‘j. where the two values listed in (4.62) reflect the two-fold ambiguity in the size of the higher order parameters wi that was mentioned in our discussion of K+ + is+l+i-. No direct CP violation has actually been included in obtaining (4.62). . Acordingly very little manifest CP violation is expected in the lepton distributions . etc. The two-photon contribution to KL + A’ p+p- is not suppressed leading to a relatively sizeablebranching ratio BR(KL4~‘~‘~)-~BROCL-)11’e+e-) . (4.63) CP violation can then manifest itself in a PansverSEpolarizationof the muons in KL -+ x0 p+p. Rough estimatesfor the degree of hansversepolarization yield PO1I (Jl) - 0.05 - 0.5 (4.64) I want to address the conflict between (4.59) and (4.61) with the following two preconceived notions: i.e., a process of higher order in QED, yet without CP viotation. There is no simple way to estimate the relative weight between the two reactions, namely the CP violating one-photon processes(4.53) and the CP conserving two-photon process (4.57) since they are characterized by parameters of comparable size: (4.58) A more detailed dynamical treatment is therefore called for. Sehgal has applied an analysis that is basedon vector meson dominance and found (*n (i) (ii) ChPT when applied carefully and properly cannot be wrong. It is highly unlikely that this conflict is due to algebraic mistakes. BPR have examined the most general effective chit-al Lagtangian where vector and axial vector fields appear explicitly. (In the usual approach these fields are integrated out and enter only indirectly via the coefficients of the Goldstone boson operators). They find that the vector coupling employed in Ref. 15 cannot appear directly due to the constraints imposed by chiraI invariance. Although they can be induced indirectly by higher order contributions their coefficients in ChPT are so tiny as to render them totally insignificant. To say it differently: it would constitute an exmemelyheavy blow to ChPT ifthe dynamical description ofRef.15 were borne out by experiment! Let me add two more notes on CP violation in radiative K decays before i ‘-. .. concluding this section: rCK’jx+e+e-)-rCK‘jrre+e-) r(K+-+ a+e+e)+r(K-+ a depressing result and temptation, at least for a theorist: prediction that can be made there am typically more reliable man for Thethemxical . . - 1o-5 7t-e+e- ) r(K+-tn+yf)-r(K-+7r~) < lo.3 r(K++x+fl)+r(x--t7t-v) - (4.65) K decays; Finding them or not finding them has very obvious implications for or against the KM implementation of CP violation; A very rich suucture exists in their phenomenology. (4.66) I subscribe quite strongly to these statements, Nevertheless I would consider it quite foolish to suspendfurther searchesfor CP violation in K decays: After all, nobody has really demonstrated yet that sufficient experimental which does not appear to be beyond our experimental capabilities. Resumeon Ram K Decays (1) sensitivity can be acquired in B decay studies. It should not be forgotten that theoretical predictions could be contradicted by the A study of radiative K decays will teach us significant and quite important lessons on QCD; in particular it will provide us with crucial tests of our understanding of experimental tindings. If that happened as far as CP violation in B decays is concerned we would have made progress in a negative way: we would have learnt that me KM ansatz does not represent the leading source of the observed CP violation in KL decays. Yet we would not know which force it is that generatesthis fundamentally important phenomenon. Dedicated searches for CP asymmetries in K decays and in B decays should therefore not be viewed as competitors, but as comolementine each other. chiral symmetry and its breaking. (2) A well developed theoretical technology has emerged that provides us with a quantitative treatment of these K decays: Chital Perturbation Theory. (3) As always mere is a prize to be paid: ChFI inuoduces - as a matter of principle a priori unspecified parameters: gg, g27, b, Llo, WI. ... wq. Yet ChPT produces many highly non-trivial relations between different transition rates: Therefore one has to measute many decay rates and distributions to fully exploit the opportunities that are offered by K decays. This makes a K factors a hiehlv desirable undertaking. Item (1) - (3) concerned our understanding of QCD. Yet also our understanding of the weak forces and of New Physics can be extended by further experimentation in this field (4) :-. A dedicated searchfor K+ + rt+ + “unseen” (5) is an unequivocal must - as stated before. Helicity suppression etc. presumably do not affect K -+ ep, xep in a crucial way. (6) CP violadoq: It has been stated with increasing vigour (though not necessarily rigour as well) that dedicated searchesfor CP violation in B decays present an almost irresistible -52- V. “Waitine for a Miracle” -- Rare D Decavs According to the Standard Model D decaysrepresent a decidedly dull affair: the relevant KM parameters -- V(cs) and V(cd) -- are “known” since they can be inferred from V(ud), V(U) and V(cb); at most tiny Do-w mixing, no observable CP violation or other flavour changing neutral currents are expected. This apparent vice can however be turned into a twofold virtue: Our alleged understanding of the elecnuweak forces in the charm sector allows (9 us to use charm decays as a unique laboratory for studying the strong forces in a novel environment. c (ii) If -- connary to our jaded expectation -- an interesting weak phenomenon like flavour changing neutral currents were observed we would have found unequivocal WT Tj &s evidence for “New Physics” beyond the Standard Model. Of course, it would still be ambiguous as to the precise nature of this New Physics. 0 Fig.9a u c Fig.9b In the following discussion of one-loop D decays and doubly Cabibbo suppressed decays (hereafter referred to as DCSDl I will expand on these general statements and make them more specific. But first I want to mention briefly two technical complications that arise in treatmentsof D decays. (9 Fig. 9a, b: Quark level transition operators with AC = 2 and AC = 1, respectively. The one-loop AC=i,2 operators are non-local: the internal quarks that appear in the diagrams of Figs.9 are lighter than the external charm quark The strange quark can therefore m be integrated out to obtain a local effective AC=l,2 operator. The opposite situation arises for AS=2 etc. transitions. There cannot be a trustworthy application of CWT. For the hadrons that appear w in these reactions, e.g. D-tp+X (5.2) -53- from different intermediate statesin (5.8). Describing D” -+ non the other hand by a cannot be described as Goldstone bosons and “hard” momentum transfers appear rn& p2 >> (4rrfJ2 A. quark diagram that is analogous to the one in Fig.6a would presumably lead to a gross underestimateof the rate. (5.3) Qne-looo Decay Supersymmetry introduces the decay channel There are quite a few processesthat come to one’s mind here (5.10) D-tnlp+R D” -i )+a- (5.4) D” --+ yy (5.5) Do + n/p + “nothing seen” (5.6) Do + y + “nothing seen” (5.7) if the photinos 7 are sufficiently light. The relevant tree-level diagram is analogous IO the one shown inFig. 4; the corresponding amplitude is subject to GlM suppression - -that enters through the couplings of the internal squarks U = (u. c, t). Unfortunately -for the present analysis -- almost all SUSY models that are imbedded in a supergravity environment exhibit the following property for the squark mass splittings: (5.11) Am2 (D) - d, 4 (5.12) The GIM suppression that results from (5.11) makes considering D --f n/P + fi (iii) w (5.13) DO--+y+W (5.8) if the sneutrinos are sufficiently light. GIM suppression enters via the couplings of an internal b squark where the more favourable scenario (5.12) holds. Yet even so it is Since the first step representsa Cabibbo suppressednon-leptonic transition and the second one a second order electromagnetic processone guestimates BR(D’ + yy) 5 0 (tg%?s,a*) - 2.7 x 10’ Do + Y + “nothinr! seen” SUSY again allows for a realization of such a mode, namely In analogy to KL -+ yyone can describe this reaction as a two-step process Do -+ “x, n, KK, K% 37tI...” + yy a completely academicaffair. A few semi-quantitative comments can be added: (0 4 Am* (ii) -d, Unfortunately, one has to expect truly tiny branching ratios for these modes since more than one suppression factor will typically intervene -- like helicity suppression in (5.4). wavefunction suppression in (5.4,5,7) and GIM suppression in all four of them. And in addition, the normal D decays are not -- unlike K decays -- Cabibbo suppressed. hard to see how a measurable branching ratio could result. ,. I (5.9) :: This is probably a very generous number if not even a considerable overestimate (which is why I used the “<” sign in (5.9)). For on general grounds one has to allow for -- if not even expect -- sizeable cancellations to occur between the connibutions -54- :.’ l Doublv Cabibbo SunmessedD Decavs -- DCSD B. These are necessarily non-leptonic decays. Thus one has to tackle the “Problem of the Two Worlds” as described in Sec. IV, although it appearsin a less virulent form here. Starting from the observation that almost everything is of order one in the strong interactions -- the relative weight of higher order corrections, Clebsch-Gordan coefficients etc. -- two thinkers arrived quite independently at the Ma-Ik Theorem: To be off in one’s predictions by an order of magnitude or more one has to be quite unlucky or a) rather dense or, PI most likely, both of these two requirements are fulfilled simultaneously. Y) The AI=]/2 rule is the classical example for case (a); everybody will know examples of cases $3) and (y) from his or her own experience. One consequenceof this theorem is that one cannot claim reliability for a model just because it predicted a handful of decay rates more or less correctly. For a proper evaluation one has to keep the wider theoretical and phenomenological landscape in mind. An expansion in l/N, N being the number of colours, provides a very compact and rather successful phenomenology of Cabibbo allowed and once Cabibbo suppressed D decays (a detailed description can be found in the literature (17)). It is There exists a certain (though by no means large) potential for New Physics to show up. For example, New Physics could be realized by the existence of charged Higgs fields H the exchange of which leads to c + s(d) as well as c --f d(G) transitions. In the first case the Higgs exchange produces a coupling proportional to mc*md (or m+n,Jm~, in the latter one to me*ms/4. The highly forbidden DCSD can thus have a much higher sensitivity to New Physics than Cabibbo allowed D decays(‘9): rate (“NP”)/rate (“Old Physics”) [c+d(uS)J rate (“NP”)/rate (“Old Physics”) [c+s(u&l DCSD of Do: (a) Invoking the l/N ansatz as rationale for including factorizable contributions only, ignoring W exchange and putting the Bauer-Stech parameter 5 to zero one finds (5.14) BR@’ -+ K+p-) - 0.5 tg” 0, BR@” + K-p+) (5.15) +’ WD” -+ K n-) _ 3 tg4 @, (5.16) BR@’ + K- * rt+) quite natural then to apply it to DCSD as well.@) It is of course the Cabibbo angle Be that sets the overall order of magnitude for DCSD. The coefficient of tg%, which reflects hadronization effects is of order one -- in Before I do that I would like to recall to your attention the four-fold motivation for a detailed and dedicated study of DCSD: accordance with the Ma-Ik Theorem; for example the enhancement in (5.14) can be traced back largely to lfK/f#-1.6 etc. Furthermore l As is well known by now a good understanding of DCSD is relevant in searchesfor Do-p l mixing. As explained below interesting lessonscan be obtained on QCD . Such lessons are of obvious significance for attempts to extract the values of the KM parameter V(ub) from non-leptonic B decays. .-_. .: ,. : .-.,..I. . .. BR(D’ --f K+rr-, K+p-, K+‘x-) _ 1,2 _ ,,5 (5.17) BR(D’= + K‘x+, K-p+, K- l n+) i.e. summing over these channels yields an amusing (semi-quantitative) realization of quark-hadron duality. .. . : : . (b) DCSD of D+ The first factor -- fK/frt -- reflects SD(~)F, breaking in the K and n w; the last one -- l/42 -- the Clebsch-Gordan coefficient that et A rather intriguing scenarioemerges here: ..-:. ‘-. ._ BR(D+ --f K+tr’) - 3 tg” 0, BR(D+ -+ px+) : ,.. .. ..:- wavefunction. The coefficients c+, c. finally denote the renormalizatio weak quark couplings by QCD radiative corrections: c+-O.7, c-2; term does not contribute to D+-t(S=-1) modes due to the destruct (5.1R) mentioned above (‘9). (5.19) Analogous effects occur in (5.19. 20). The expected enhance, much larger, but also numerically more uncertain there: the destructi\ quite considerable in DC -+ K’*R+ and at the same time very sensitiv changes in the model parameters. Comparing r(D’ --f ~*tt+)theo (5.20) BR(D+ -+ K+p’) BR(D+ -+ ?T”p+) suggest that the lower end in (5.19,20) should be favoured. - 0.35 tg40, (5.21) Therefore I have to stress a general caveat concerning this ana tinal state interactions have been completely ignored in the true spirit 01 While matters of practicality favour this procedure there is good real universal wisdom. A detailed analysis of DCSD that is based on QC quite desirable, but is not yet available at this time (1% The apparently dramatic enhancement factors in (5.18-20) reflect actually the destructive interference that occurs in the Cabibbo allowed D+ decays which in turn is the main motor for the D+-Do lifetime difference (1%. Such a desuuctive interference does not occur in DCSD and their relative weight is thus enhanced. This can be seen most easily by considering the isospin of the final states rather than drawing cute diagrams. l C. The prospects of ever observing l-loop decays of D mesons (9 gloomy since quite typically several concurrent suppression factor mechanism, helicity arguments, small wavefunction overlaps, small I The tinal states in D+-+ (S=-1) transitions carry a unique isospin, namely (I,l3) = ($, + 9; these decays are therefore described by a single amplitude in isospin space, etc. namely (AI, AI3) = (1, +l). Interference can thus occur. l Resumeon Rare D Decay (ii) D+ + (S=+l) transitions on the other hand are described by the combination of two Do-B0 mixing could be as “large” as to produce (18) amplitudes that differ in isospin. namely (AI, AI3) = (0.0) and (1.0). This curtails the possibility of interference. New Physics could lead to The coefficient in (5.18) can then be understood as basically due to +0.1 (5.22) (ii) A detailed study of DCSD of D mesons appears to be experimentally as well as theoretically. An intriguing and instructive patn -56- to emerge teaching us unique lessonson the strong interactions at the interface between the perturbative and non-perturbative regime. (iv) VI “GUARANTEED DISCGVERIBS” - RARE B DECAYS The B decays are simply “exciting” - even within the confines of the StandardModel: * A priori unknown KM parameters - V (cb), V (ub), V (td), V (ts) enter. * B” B0 mixing had been predicted and - even better - it was observed (actually Miracles can occur. Do not let them slip away by not watching! * * -:- “.’ : on a higher level than anticipated). B decays present the best odds to observe CP violation outside K decays. Charmless decays like B +K*y will occur. Since one is dealing here with reactions that typically require the presence of loop processes, i.e., that represent genuine quantum effects, one encounters a rather high sensitivity to New Physics in these transitions. The three generic scenarios for New Physics that 1 am going to invoke are - a fourth family; an extended Higgs sector; - Supersymmetry ( = SUSY). Unfortunately there are a few technical complications we have to face here: * ChPT is clearly not applicable in decays like B --f D p , B +K’ yetc. * The two-body modes B -+ PP, PV, VV where P [V] denotes a pseudoscalar [vector] meson are not the dominant decay channels anymore (although they are not insignificant either) QCD sum rules that have been developed for these l exclusive modes are therefore of restricted use in B decays. It seems that rare inclusive decays like B + (C=O,S = 1) are hard to measure. This is quite unfortunate since theoretically they can be treated more directly. A. KM suauressedtree level B decavs There are charmless B decays that occur already on the level of tree diagrams via the KM coupling V (ub). Among these there is a certain subset of modes with a particularly clean experimental signature: two-prong, two-body decays of beauty of which there are six channels B --f x+x-, K+K(6.1) -57- .: ./’ I’ -, B--+K’rr* (6.2) B+P? (6.3) 3,-fprrr,pK(a) BR(B,+rr+x-)< BR @,-+K-x’+) (6.4) BR(B,+pF)<4 9x IO-~ CLEO (6.5a) s 9 x low5 CLEO (6.6a) ~10.~ CLEO (6.9a) The bounds (6.5a) and (6.9a) have already reached theoretically interesting territory as expressed by (6.5) and (6.9). The bound of (6.6a) appears to be still an order of magnitude above it -_ yet, as already indicated -- this is a point to which we will return. Following the same procedure as in Sect. V.B - i.e. including factorizable contributions only, setting 5 = 0 and ignoring final state interactions (hereafter referred to as FSI)- we find (20) (6.5) (b) t&I, BR (Ed -+ 11+x- BR (Bd --f K-x+ ) z BR (B, -+ K+K-) ” (6.6) 2 BR(3,+pn-)-3x -3 ___ V Cub) /VW ! 10 tg2e,BR (3,+ BR(Bd-+p$)<fewx10-4 pn-) - 2.3 x 1O-4 V Cub) K-x+ and Bs +K+K- (6.10) BR (B, --f x+x- ) << BR @, -+ K+K-) (6.11) BR(B,-,plj)<<<BR(B,~pjj) (6.12) The reason for that is the following: the decays B,-+ K+ K‘ , B, + x+x- and B, + pp cannot proceed via simple tree diagrams; instead they require the intervention of FSI (i.e., rescattering and channel mixing), of annihilation or of KM suppressedpenguin contributions - (6.8) circumstances which are expected to reduce the rate (maybe I should add that 2 -V (cb) BR (& -+ K+K-) << BR (i$ + x+r ) (6.7) it is somewhat academic on this level to distinguish those three mechanisms). (6.9) A violation of the relations (6.10-12) might not necessarily amount to a disaster for theory - after all we have included factorizable conuibutions only yet it would at least represent an acute embarassment for our theoretical description of heavy flavour decays. Cc) The three modes 2 < 0.05 These processes, in particular B,+ There are three more of these decay modes, but they should be further suppressed, i.e. can receive contributions from Penguin graphs which we have ignored here; this point will be re-addressed later on. Altogether we estimate the uncertainties due to on the other hand could be significantly enhanced over the rates given in (6.5- the hadronization process to amount to factors of 2 3 roughly. None of these rare decays have been observed yet -- which is not surprising in view of the predicted tiny branching ratios. The present 90 % C.L. upper 6.8) due to the intervention of FSI, annihilation and/or KM favoured penguins. Let me sketch just one scenario involving a two-step process limits read as follows (for a more detailed discussion seeRef. 4): -58- _ -. -:.: __ :::.: .. Bd+“D, -c*) D C),, *K-X+ (6.13) The first transition has a huge enhancement factor over the &xcJ process Bd+ K-K+ : EF w- : . ‘2. _ ” .,. (6.14) .., The re-scattering efficiency for the second transition in (6.13) will certainly be quite small; yet we do not know how tiny it is. A re-scattering efficiency of 1% might not represent an inflated number - after all the process takes place less than 1.5 GeV above the DI D* threshold; even then this two-step process would dominate the Be -+ K-x+ mode in view of (6.14). :’ ._. -: .-- Ypzig Clearly more theoretical work is needed here. A refined analysis based on QCD sum rules appears quite promising, be it only to give a theoretical underpinning to some of the rather ad hoc phenomenological assumptions made so Fig. 10: Quark level diagram for induced FCNC. far. In any case, dedicated experimental searchesfor these decay modes should receive a high priority, Determining their branching ratios will yield new and unique informations on the hadronization process and thus on QCD. For that purpose it is not essential to obtain these branching ratios with high precision - I would consider a 30% measurementas quite adequate: on the other hand it is hi&.& desirable to obtain data on&of thesedecay channels. These informations on hadronization can then serve as essential input for even more ambitious searchesin these rare B decays, namely for BO-ED mixing and - ultimately - CP violation. (32) tand rd Model 3B On -I Fig. 11: Quark diagram for b + “w” s + ys (a) Generalities The generic diagram for Q + q + yor Z or g is shown in Fig. 10 where the loops with a charm and a (virtual) top quark have been singled out; the u quark contribution acts mainly as a GIM subtraction. It is understood that the photon or the gluon can be on- or off-shell (a somewhat murky distinction for the gluon). The dependence on the KM parametersfor such a transition with an internal t quark : I : I is then given by -59- :. .: 1. rate (b + s + y/Z/g ) = b’ (lb) v (ts) f = A2 A4 of this width on the KM parameters can be eliminated by considering the ratio r (b + sy) / r (b + c” V ) since 1V (tb) 1 r 1 , 1V (ts) 1 z / V (cb) I. One then (6.15) finds (23) rate(s+d+yNg)= tV(ts)V(td)?zA4h10((1-pf+q2) (6.16) 2x 10” r (b -+ where I have used the Wolfenstein representation (21)of the KM matrix. Therefore we find for the branching ratios BR(b-+s+y/Ug)= r(b-+sy) C ” C) = 1O.3 m,= 65 GeV for m,= 150 GeV (6.21) :_ . . ‘. .-.: Equating r (b + c”v) with the measured width T(B -+ “v X) one obtains for the 1V (tb) V 0s) r” = 1 branching ratio (6.17) m, = 65 GeV for 1V (cb) f BR(s-+d+y/Z’g)= m,ll50 GeV (6.22) =A4hs((1 - p?+Tl*) Yet - as discussed before what is measured are (exclusive) transitions involving - (1 - 2 ) x 5.5 x 1o-6 hadrons rather than free quarks. Gauge invariance again implies I-(B+Ky)=O Iv (us) f (6.18) (6.23) The mode B --f K*ycan proceed; since BR(B --f K*y) can neither be 100% nor 0% i.e., these rare decays of beauty have a much higher sensitivity to the presence of heavy quarks - the top quark in particular - than rare decays of stangeness. This one “infers” as an application of the Ma-Ik Theorem BR@+K’y) I 5-10Q 0 (6.24) BR(b+sy) a guestimate that is “confirmed” by computations (24)employing specific models for makes them such an exciting field of study ! cz2) the hadronic wave functions. The final estimate then reads (b)B-+y+(S=-1) 2x d BR(B-+K*y)- m,z 65 GeV for (6.25) 1 x 1o-5 rn,ll50 GeV 1 This steep dependence on mt does not allow us to make a reliable prediction on the branching ratio. Yet such an apparent vice can swiftly be turned into a virtue by noting that a measurement of BR (B + K*y) would in turn give us a good handle (i) Quark-level results. From the diagram in Fig. 10 we obtain (23) the effective coupling for the auark-level transition b+sr (6.19) I eB(b -+ sy) = G,mb bL oPv q, A, s I?, (q’ ; m, m, ; KM param.) 4-i where Av denotes the photon field and q, its momentum. Gauge invariance tells us that for q2 = 0, i.e., real photons, there can be only one form factor, namely F;. on Nature’s value of ml! Before however jumping to this conclusion it behooves us to pause and think whether such a strong dependence indeed makes senseor not. After all, we have considered mainly quark level diagrams so far, i.e., shortdistance dynamics. It depends, due to the GIM mechanism, approximately on the square of the internal quark mass, i.e. F; (top) = 3 > (6.20) 6 This makes the charm contribution numerically quite insignificant and at the same time introduces a strong sensitivity of T(b + sy) to the top mass. The dependence (ii) On the impact of long-range dynamics Duality lost? The authors of Ref.25 addressed the question whether there is another mechanism leading to the same final state; in particular they considered a two-step processa la Vector Meson Dominance -6O- __ .: - (6.26) One can make a very crude estimatefor its branching ratio BR(B+yK*)-BR(B-t”y/‘K*) xProb(“W”-+y) -(5x10-3)x~-10-5 - Diagrams like the one in Fig. 12 produce “soft GIM suppression”, i.e., actually an enhancement - log (MJm$ which is particularly effective for mt < Mw. (For mt > Mw also the expression in (6.28) yields an enhancement. This at first sight paradoxical result is due to the coupling of longitudinal W bosom). New and more leading log terms emerge for mt - o(Mw) since (6.27) a, Cm’) The point of this exercise is not to produce a reliable prediction, but to point out that there could be a contribution to B -+ yK* that is indeuendent of mt, yet of ---L n m2 log * 5 1 % in that case. Putting everything together and including leading log terms only the authors of Ref. 26 found the results shown in Fig. 13. From it we draw the following conclusions: * The QCD radiative corrections am very large indeed. * They decrease somewhat in relative importance as mt increases: e.g., for mt = 50 GeV they produce an enhancement by a factor 17 whereas for mt = 125 GeV this factor has shrunk to 4.3. As discussed above such a trend was to be expected since the biggest difference between soft and hard GIM suppression occurs for small values of mt. . lhe dependenceon mt therefore becomes less steep. This makes it doubtful that the decay B + K* ycould reveal information on the comparable magnitude to the numbers listed in (6.25). Furthermore these two contributions are coherent; therefore their amplitudes could add or subtract thus influencing the overall result quite dramatically. Such an observation -- namely that there is a numerically significant contribution to B + K*y that is not produced by the diagram in Fig. 10 -- would spell trouble for the applicability of quark-hadron duality in B decays if it were true. (iii) QCD radiative corrections Duality regained! The suggestion made above that there is no quark-level diagram corresponding to (6.26) has to be examined more carefully. The diagram shown in Fig. 11 would fit the bill and it merely represents a permissible distortion of the charm loop in Fig. 10. However we had argued before that the GIM mechamism relegates this diagram to numerical insignificance! l * A more careful analysis of the GIM mechanism will help here: If two quarks Q and q with masses mQ and nk, respectively appear in a loop diagram * together with W bosons then such a diagram has to yield a vanishing contribution in the limit mu = m,+ However this czanhappen in two different ways: m* -m Q q . Ampl. = 2 (6.28) MW this is usually called “hard” GIM suppression(at least for 4, mi C M$), l presenceof a fourth family. The lowered sensitivity to mt implies that the charm-loop contribution becomes numerically much more significant. This means that the concept of quark-hadron duality escapesthe disaster it was facing before QCD radiative corrections were included. These radiative corrections obviously contain sizeable numerical uncertainties; for example, the appropriate normalization scales have not been uniquely determined so far. Yet the fact that they are large or even dominant per se does not make them completely untrustworthy. For - as discussed before - we do understand on fairly general grounds why in this particular case these correction terms are so large: it is fvstly the conversion of hard GIM suppression into soft GIM suppression; secondly the appearance of large logarithms log rnf which Ampl. = log z4 (6.29) 9 which is commonly referred to as “soft GIM suppression” although it actually amounts to an enhancementfor 4 << n$ . have been summed to all orders on the leading log level. Higher order terms which have been ignored so far cannot benefit from additional enhancements over the terms already included. The situation here has something in common with the one encountered in e+e- annihilation: the two-photon process Returning to the case under study here: as already stated, the diagram in Fig. 10 reproduces hard GIM suppression, (6.28). However QCD radiative corrections change the situation very significantly: -61- : dominates the one-photon reaction at the highest presently available energies; yet nobody claims a breakdown of perturbative QED since we understand the structural reasons behind the prominence of the two-photon process. As an (optimistic) reference point we can then state: BR (B --f K*y)- 3.3 x 10m5 for rn,= 150GeV This is to be compared to the upper bounds (4) 2.9 x lO-4 WBd4’ y)-4 2.8 x 10 ARGUS CEO Cc) B --f “+“- + (S = -1) Some new features emerge in a treamlent of the transition b + s “+“- : * It can proceed due to the exchange of a photon in b + s “y” -+ s ‘I+“- Since this photon is off-shell a new form factor that is not present in b + s y appears Fig. 12: QCD radiative corrections that produce “soft GlM suppression”. * here; it is usually referred to as Fl, The lepton pair “+‘‘-can be produced from an intemlediate Z” or W+W- pair as well. This introduces new terms for which there is no analogue in b -+ sy, for heavy top quarks, say ml > Mw, they actually yield the dominant contribution (which is due to the coupling of the longitudinal Z or W bosons to the top quarks that appear in the loop ). 0.003 Putting these ingredients together one obtains (27) 0.002 0.000 I 3.5 x 1o-6 _*-- 0.001 m _ --50 __-- __-- __-- 1 6.4 x 1O-6 form, = { loo} 125 100 75 I 1.0x 1o.5 I50 GeV (6.30) I1501 mt( GeV) QCD radiative corrections treated in a leading log framework(28) enhance these numbers considerably, in particular for moderate values of mt: Fig. 13: The ratio r (b + sy) / r (b -+ CLV) with (solid line) and without (broken I 7.3 x 1o-6 1ine)QCD radiative corrections; from ref. 26. BRQcD (b --f s e’em)= ( 1.1 x 1o-5 for m, =( ( 1.4x 1o-5 A few observations should be added here: -62- PO 1 lm} I1501 GeV (6.31) (i) Theoretically this represents a truly lovely mode whose branching ratio increases very strongly with mt (the virtual photon contribution is of course absent here). For mt = 100 GeV one finds (30) (6.35) BR(b+svv)r2x10.5 The QCD corrections while considerable are not nearly as huge as the caseof b -+ sy. That is not surprising: it was pointed out before that the transition b -+ sy depends on a single form factor in a very restricted way and does represent the exception rather than the rule. In b -+ s “+“- on the other hand several short-distance contributions appear, as discussed before. (ii) Information on the underlying dynamics is contained not just in the branching ratio, but in the di-lepton mass distribution as well; details can be found in Ref. 29. (iii) The virtual photon has a definite preference to materialize in an e+e- rather than a p+j.t- pair. The rate for b + s p+p- is thus suppresssedrelative to b -+ which is twice the value of BR (b --f se+e-)for this mt. This should not come as a surprise since one sums over the three neutrino species (and the 2’ couples more strongly to neutrinos than charged leptons). Unfortunately it appears that the experimental signature for such decays, even for exclusive channels like B --f K’ v? is not sufficiently clean. s e+e- beyond the mere phase spacereduction; for details seeRef. 29. Exclusive decay modes exhibit a cleaner experimental signature, while introducing further theoretical uncertainties in the treatment of hadronization. Two channels have been studied in particular, namely B --f K e+e- and B + K* e+e- , (e) B + (S = 1) + glue On the one-loop level there are four types of quark processes in this category, namely b + sg, b?j+ sq, b -r sq?jand b + s gg. It is actually the latter two that dominate and altogether one obtains (3*) (6.36) BR(b-tsiglue,qq)-l-2% for which the following estimateshave been given (29) BR (B + K*e+e-) _ o.2 BR(b-tse+e-) (6.32) BR (B + K e’e-) _ o,05 BR(b+se+e-) (6.33) for mt 3.30 - 200 GeV, i.e. the branching ratio exhibits fairly little sensitivity to the top mass. There exists a second source for charm-less final states with strangeness, namely the KM and Cabibbo suppressed transition b --f uiis. A crude estimate yields V(ub) * (6.37) BR (b --f u iis ) - 2tg* 8, V(cb) s 1% I i where the factor two reflects the phase space advantage of b --f u over b-t c. combining these numbers with (6.31) we arrive finally at BR (B + K*e+e-) - [1.5, 2.2, 2.8) x 1O-6 The rates for these two reactions, namely the one-loop process b + s + glue and the tree-level process b + ulis , are therefore of a magnitude that is not very (6.34) BR (B + K e+e-) - [0.3, 0.6, 0.841 x 10e6 dissimilar. Not only is this interesting by itself, but it also creates very favourable conditions for the emergenceof CP asymmetries in this class of 6 decays. (32) for mt = [ 50, 100, 1501GeV. These are tiny numbers indeed, but not zero. And they could be enhanced quite considerably if there is a fourth family. CLEO has obtained the following upper bound: BR(B++K’e+e-)< Alas, we have to face up to the usual unpleasant business of hadronization. Gluon fragmentation 2%+ g&T.nri is “soft” thus transforming the original (virtual) masses of up to a few GeV into high hadronic multiplicities. It is therefore a multitude of exclusive channels that 5 ~10.~ builds up the not-so-small inclusive branching ratio given in (6.36). To make this (d) B-+fl+(S=-1) -63- ._, :- ..:. -..I .‘: ‘: .: -. : .: ‘- also add a short remark on light Higgs scenarios although they could be realized in the Standard Model as well. statement more quantitative we have at present to rely on phenomenological models. They tend to yield numbers like (33) BR (Bd+ K-x+) - few x 1O-5 (6.38a) BR(~d-fi?~)-fewx 1O-5 (a) Non-minimal Higgs sector with Natural Flavour Conservation The Standard Model contains one complex SU(2) doublet Higgs field. Three of its four degrees of freedom are transmogrified into the longitudinal (6.38b) A comparison of (6.38a) with (6.6) shows the considerable impact Penguin-like contributions can have even on the branching ratios. In particular the number components of the weak bosons while the fourth one emerges as the physical Ibggs field, which is neutral. quoted in (6.38a) is relatively close to the present experimental upper bound.We do not have a reliable method for gauging the theoretical uncertainties in these predictions, but we have to suspectthey are large, say a factor of three or so. For the same reason we have to conclude that the sensitivity to the presence of a fourth family is submerged in this “theoretical noise”, at least as far as exclusive decay modes are concerned Since flavour changing neutral currents are highly suppressedin nature one does not want to enlargen the Higgs sector in a reckless manner. Instead one introduces new Higgs doublets in such a way that they couple either to the up- or to the down-type quarks .(x6) For two doublets we are left with five physical Higgs fields, two of which are charged and three neutral. (CP invariance is still maintained; it is broken spontaneously if three Higgs doublets are introduced.) Even with this imposition of natural flavour conservarion we are dealing with a high-dimensional spaceof new parameters. To identify an interesting comer in this parameter spaceone can turn to B, - Bd mixing. C. One-looa AB = 1 Processeswith New Phvsics The predictions given so far for these one-loop B decays contain two types The ARGUS and CLEO findings do not establish a need yet for New Physics in the AB = 2 channel; on the other hand it cannot be ruled out that New Physics does of uncertainties: . The “embarrassing” uncertainties that enter into our estimates of branching ratios for exclusive modes in particular they are due to our less than satisfactory provide the dominant motor of B”-Bo mixing. It is thus legitimate to consider that part of the parameter spacewhere Higgs exchangesdominate AB = 2 dynamics and mastery of hadronization. The “good” uncertainties concerning parameters of the quark world, in particular the top mass. The unknown value of mt severely restricts the l then search for sizable enhancementsin AB = 1 reactions. Such an analysis has been undertaken in Ref. 37 numerical precision of our predictions; yet a measurement of the relevant branching ratios would produce a lower and an upper bound on mt. We have reason to entertain even bolder hopes, namely to searchfor the presence of imagination stretcherrather than a realistic dynamical scenario. New Physics in these B decays which represent classically forbidden processes. In the preceding discussion of subsection B I had already included one such scenario, namely the Standard Model with one additional, the fourth family. There we had encountered the one general impediment for such an analysis: due to the “embarrassing” uncertainties we can hope to perform a successful hunt only, if . . .,--. some big game is waiting for us out there, i.e., if the measured rate is considerabl\C h The authors’ conclusions for two quite different models with two Higgs doublets are summarized in Table IV. One should add here that model II serves as an than the expected rate. I will briefly review the situation with two other realizations of New Physics, namely a non-minimal Higgs sector and supersymmetry ( = SUSY); I will -64- Assuming transition BR[in %] Model II Model I EnhancementFactor I II b -+ sy few x 0.1 22 0 (10) 0 (100) ,, + s”+“- < few x 10e3 2 few x 10e2 0 (10) 0 uw b -+ s g(*) $4 5 100 (!) 2-4 0 (10) q 2 80GeV (6.40) as the raison d’&tre for a light Higgs one infers from the available limits on such B decays(41) (6.41) mH > 3.7 GeV There is still another window open, namely 0.3 GeV < rn~ c 2 GeV; it can be closed only by making more detailed theoretical assumptions on the relevant Higgs decay channels. Those can be checked (or challenged) by further Table N These numbers have to be taken with a grain of salt since radiative QCD corrections have not been included here. Yet even so they show how large a discovery potential there is in these uansitions. experimentation. D. Resume on Rare B Decays B physics is “full of promise”; there is tantalizing “poetry in beauty”! All of (b) Supersymmetry There is one feature of particular relevance here (38): gluino exchanges mediate flavour changing neunal currents with a strength of order a,, i.e. the this is of course a euphemism for saying that B physics has not reached the maturity level yet, neither experimentally nor theoretically. Experimentally: as a theorist one cannot help but complain that measurements of inclusive B decay rates have so far produced rough numbers only. Theoretically: - As far as inclusive decay rates are concerned there is still some homework to strong rather than the elecaoweak coupling. This enhancesthe rates for b --f sy and b -+ sg(*) by an order of magnitude for moderately heavy Susyons, i.e. if M l (gluino, squarks) - MW (39)! Again, QCD radiative corrections have not been fully included. l be done: QCD radiative corrections have to be included properly and comprehensively (42); more detailed thinking should be applied to the question of whether one can trust quark-hadron duality in B decays on the 10% or only on the 50% level. - More formidable tasks await our dedicated attention in exclusive B decays: most hadrunization prescriptions -- like potential models - are of untested reliability; trustworthy results from lattice Monte Carlo computations are still a few years away; it appearsthat an application and refinement of QCD sum rules (c) Light Higgs scenario It was already mentioned in Sect. III that an arbitrarily light Higgs boson can emerge in the presence of heavy quark fields Q, i.e. if MQ > 80 GeV. The decay b + sH is dominated by the loop diagram containing the top quark and is roughly proportional to rn: : one factor of mt enters through the Yukawa coupling of the Higgs, the other is produced by the chiral structure. Therefore (40) BR ( b + sH) = rn: a la the Blok-Shifman treatment of D decays is the best available technology. - As far as numbers are concerned one should keep in mind that the sxclusive branching ratios for these rare B decays are typically of order 10-6-10-5; the inclusivt transitions on the other hand command branching ratios that are & (6.39) by a factor lo-lOO! -65- ,_ ..: ., .:. -: .: . .. . :’ .. . In summary: if we apply the principles on which the Napoleonic campaigns were built i.e. employ large numbers, i.e. t 107 B’s, spend a small fortune (but get Aoaendix A: Long-distance dynamics in K-+ xvv others to pay for it) and, very importantly, rely on “fortune” in the French sense then we are faced with the prospect of guaranteeddiscoveries! The diagrams in Fig. 3 generate a local AS = I operator which - as stated in the text can then be related to the operator that underlies K 4 rrev decays. However there exists another mechanism which is of relevance, at least in principle, namely the two-step process VII - OUTLOOK We should keep in mind how much New Physics has been unearthed in K decays: parity violation, suppression of flavour changing neutral currents, CP violation and the existence of the internal quantum numbers strangenessand charm (and even top quarks). There is no reason to believe that the potential for indirect discoveries of New Physics has been exhausted in any way. Yet there are two K+ -+ “R+” + R+VV Since such states are not necessarily far off-shell, they can propagate over typical hadronic distances; the process (A.l) therefore represents long-distance dynamics and it is not included in the reference reaction K + rtev to the same degree(M) (it appearsthere as a radiative correction important lessons we should draw from the past: (1) A careful and continuous evaluation of our theoretical tools has to take place: lattice Monte Carlo computations will answer all these questions sometime in only). An analogous situation is encountered when one attempt@) to compute the longdistance contribution to K” the future; for now (and for some time to come) we have to rely on a judicious and detailed application of different theoretical technologies: ChPT for K mesons, QCD sum rules etc., for D and B mesons. (2) We have to pursue a comprehensive experimental program: for example the relevant quark mixing angles could be completely different for down-type quarks --like s and b -- than for up-type quarks -- like charm. Therefore one En mixing. Using similar arguments one estimates that the process (A. 1) could be numerically significant if top quarks are only moderately heavy, i.e., mt < M,. has to study also rare D decays in a dedicated fashion to obtain a complete picture even though one needs a gambler’s luck to find New Physics there. Dedicated searchesfor and studies of rare B decays are “assured” to yield a rich harvest. Yet even so one should view studies of rare K and rare B decays as perfectly complementary, a (A.11 R+ represents an intermediate state with S = 0: R = I, p, At,rcn, 3x, as competing. Acknowledgements I have benefitted from enjoyable discussions with G. Ecker, H. Galic, A. Pith, E. de Rafael, B. Stech and R. Willey. 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These would be supermassive (IOtb-1019 GeV/c*) and a density of only one per lo-10,000 km3 would be sufficient to account for the local dark matter around our galaxy. We have been operating a 1.3 m2 times 4n sr detector utilizing eight SQUIDS. It is the largest superconductive monopole detector. The second effort involves the development of large mass (-1 kg) elementary particle detectors capable of sensing weakly interacting particles. These utilize silicon crystals at temperatures below 1 K, have spatial resolution in three dimensions and would measure the total energy deposition. Such detectors will be used for direct dark matter searches and for neutrino experiments capable of setting better limits on the neutrino mass. @B. Cabrera 1988 -69- ._-_ .- PART SEARCH FOR MAGNETIC catalysis. It has been shown theoretically that the supermassive monopoles arising from many grand unification theories would catalyze nucleon decay processes. If the cross section for such events is of order the hadron cross section, as has been suggested,then all attempts a: direct detection of the monopoles from such theories may be doomed to failure. Arguments based on x-ray flux limits from galactic neutron stars, which assume a strong interaction cross section for proton decay catalysis, lead to an upper bound for magnetic panicle flux of about loo*’ cm-* ST’ s-l. There remain unanswered questions concerning the detailed theoretical understanding of the catalysis cross section and concerning the astrophysical arguments based on our incomplete understanding of neutron stars. In addition, proton decay has not yet been observed. Thus, from an experimental point of view more weight should be given to the less A: MONOPOLES IN THE COSMIC RAYS Introduction In 1931, P.A.M. Dirac proposed the existence of magnetically charged particles to explain the observed quantization of electric charge. He showed that only integer multiples of a fundamental magnetic charge g (Dirac charge) = hc/4se are consistent with quantum mechanics. Many years of experimental searches produced no convincing candidates. In 1974 ‘t Hooft and independently Polyakov showed that in all true unification theories (those based on simple or semi-simple compact groups) magnetically charged particles are necessarily present. The modem theory predicts the same long-range field and thus the same charge g as the Dirac solution; now, however, the near field is also specified leading to a calculable mass. The standard SU(5) model predicts a monopole mass of 10’6 GeV/c*, much heavier than had been considered in previous searches. More recent unification theories based on supersymmetry or Kaluza-Klein models yield even higher mass values up to the Planck mass of 1019 GeV/c2. Such supermassive magnetically charged particles would possess qualitatively different properties from those assumedin earlier searches. These include necessarily nonrelativistic velocities from which follow weak ionization and extreme penetration through matter. Thus such particles may very well have escaped detection in earlier starches based on heavy ionization of relativistic monopoles. Although GUTS theories are very clear in their prediction of the existence of monopoles, cosmological theories based on GUTS lead to impossibly high or unobservably low predictions for monopole particle flux limits with the latter results being exponentially model dependent. Thus, only astrophysical arguments provide guidance For the relevant detector sensing areas for experiments. An upper bound of 10 iT c& sr~’ s-1is obtained assuming an isotropic flux from arguments based on the existence of the 3 microgauss galactic magnetic field (Parker bound). The Parker bound becomes less severe linearly with monopole mass for masses above 10” GeV/cz. In addition, several authors have demonstrated that models incorporating monopole plasma oscillations would allow a much larger particle flux, approaching in some cases the local galactic dark mass limit. All of these bounds assume particle velocities in gravitational Gal equilibrium, i.e., very near 10.” Much more severe astrophysical limits can be obtained based on proton decay :: _’ : model dependent astrophysical limits. Superconductive technologies, many developed at Stanford LJniversity over the last decade, have led naturally to very sensitive detectors for magnetically charged particles. These superconductive detectors directly measure the magnetic charge independently of particle velocity, mass, electric charge and magnetic dipole moment [I]. In addition, the detector response is based on simple and fundamental theoretical arguments which are extremely convincing. Because of their velocity-independent response, these detectors are a natural choice in searches for a particle flux of supermassive (and therefore slow) magnetically charged particles. By far, the most definitive positive identification of a magnetic charge would be made with a superconductive detector. Other detectors, though larger, are less satisfactory for positive identification of monopoles since the interaction of monopoles with matter through ionization processesis less well understood [2] Detailed reviews of the theoretical, the experimental and the astrophysical work can be found in Magnetic Monopoles [R.A. Carrigan and W.P. Trower, eds., Plenum 19831 and Monopole ‘83 [J. Stone, ed., Plenum 19841. Operation of Three Loop Detector Between February, 1983 and March, 1986, we operated a three loop coincident superconducting magnetic monopole detector 131. The rms current noise levels in an effective noise bandwidth of = 0.16 Hz were 0.02 $JL in all three loops, less than 1% of the signal expected from Ihe passageof a Dirac magnetic charge through one of the two turn loops (4 $I&). The sensing area based on this low noise operation was 476 cm2 (7 1 cm2 loop area and 405 cm* near miss area) for events greater than 0.1 $& in C. -7o- :. at least two of the three loops. The data were extremely clean and no candidate events were seen. Based on the 1008 days of accumulated active running time, these data set an upper limit of 4.4 x 1O-t2cm-* sr-t s-I (90% C.L.) on any uniform flux of magnetic monopoles passing through the earth’s surface at any velocity [3]. -.:. I. . . .~,.,. _. New Large Area Octagonal Detector Our group at Stanford, consisting of B. Cabrera, M. Huber, M. Taber and R. Gardner, has designed, constructed, and brought into continuous operation an eight loop detector [4] with a cross section averaged over 47t sr of 1.3 m* for double coincident events and a signal-to-noise ratio of 30 for the passage of a single Dirac charge. This detector shown schematically in Fig. 1, is composed of eight planar superconducting detection coils arranged around a cylinder with an octagonal cross section. Each coil is a gradiometer 16 cm wide and 6 m long and is connected to a high sensitivity rf SQUID current sensor. The entire assembly is surrounded by a superconducting lead shield and housed in a dewar which is enclosed in a w-metal shield. This detector has a sensing area 30 times larger than that of the three loop detector. A very important design feature for the large scale use of superconducting coils as monopole detectors is the use of a gradiometer winding pattern [5,6]. The sensitivity of a gradiometer to external magnetic field changes is substantially reduced over that from a simple coil whereas the sensitivity to the passageof a magnetic charge remains high since the particle passesthrough only one element of the gradiometer pattern. We have utilized computer calculations to optimize our coil design under constraints from dewar size and minimum acceptable signal to noise ratio. The optimum pattern which we have used for our design is shown in Fig. 2. The conducting elements are NbTi ribbon, 2mm wide and 50 pm thick. It is a repeating rectangular pattern with an aspect ratio of 0.6 to 1.O. A further improvement was achieved by breaking the loop up into a number of parallel elements which are connected together to one SQUID. This technique reduces the coupling lossesto the SQUID from a l/L proportionality to l/c where L is the inductance of the single series loop [7]. The new 1.3 m2 monopole detector requires eight low-noise SQUID systems, T-*-l SUPERCONDUCTING -- SHIELD -- 7 :‘.:. ..,>,. .:,.. one for each panel of the detector array. We have chosen to use rf SQUIDS manufactured by Biomagnetic Technologies Inc. [B.T.i.], (formerly S.H.E. Corp.) together with rf electronics from Quantum Design. A shield of high magnetic permeability metal (p-metal) has been designed and constructed to shield the detector Fig. I. Schematicdiagram of octagonal detector. -71- from the earth’s magnetic field during the initial cooldown, as the inner superconducting lead shield goes through its transition temperature. The external shield consists of 0.038 inch-thick sheets of p-metal mounted on an aluminum frame. The shield provides an absolute field below 10 milligauss throughout most of its interior. We are utilizing a Model 1200 closed-cycle liquid helium refrigeration system from Koch with the new octagonal detector. We have modified the operation of the helium liquifier to maintain a constant dewar pressure relative to atmosphere. This modification eliminates SQUID signals resulting from the pressure variations of the original cooling-capacity control system. A very slow drift remains, caused by atmospheric pressure changes, but it is well below the bandwidth of our detection system and poses no degradation of our signal to noise ratio for monopoles. There are two significant advantages derived from using this system: lower long-term operating costs, and the virtual elimination of disturbances that are produced by liquid cryogen transfers. Now that the new system is cooled down and stabilized, we achieve essentially 100% live time. The geometry of our detector provides greater confidence in coincidence correlations for true monopole events than our earlier detectors. A monopole can intersect no more than two loops, and the only trajectories intersecting one loop are those passing through the detector ends (which are not covered by detector loops) or through small gaps between the panels. We thus exclude from consideration all signals appearing in one loop only or in three or more loops. The response of the detector is calculated from a numerical simulation of a uniform flux of cosmic ray monopoles. This response is shown in Fig. 3 for positive signals in both loops; it is symmetric in the other quadrants and includes trajectories which intersect one or two wires. A computer and strip-chart recorder collect data at 10 Hz and 0.1 Hz, respectively, from the SQUIDS, strain gauge, and other anti-coincidence instrumentation. The strain gauge sensesmechanical disturbances which sometimes induce spurious offsets. Also recorded are a line voltage monitor, ultrasonic motion detector, and flux-gate magnetometer in the anti-coincidence instrumentation. We also have added a wide-band radio frequency voltmeter for EM1 anti-coincidence. We began obtaining low noise data on May 5, 1987 [8]. Figure 4 shows typical filtered data (one point every 10 set) from the computer data acquisition system. Included is a calibration signal showing the signal to noise for a Dirac size magnetic charge. Figure 5 shows the high bandwidth data available around any events. This particular event was caused by a bump of the dewar system clearly seen in the strain \ \ 521.2cm ” -1 Fig. 2. Loop parameters for octagon01detector. -72- ; _., :.:.. ‘. ._ , ,-:: ., :’ - -1 - -E C41 T--------------N [%I 13 2 dl - - -1 - N z -I .-I:0 O ;/ : _.‘. 31-J’JL-87 gauge and external flux-gate magnetometer channels. As of July 14, 1988, we have accumulated 6,OCKlhours of live time. A preliminary analysis of these data [S] contain no candidate events and set a limit of 7.8 x lo-13 cm-2 srt s-1 (90% CL.) for any particle flux of magnetically charged particles passing through the surface of the earth. We intend to run the detector continuously for at least three years. > a a - Particle Flux Limits From Our Detector Exposures In Fig. 6 we summarize the current status of our research efforts with respect to astrophysical bounds. The Parker bound as modified to include supermassive monopoles has a mass independent floor at -10-1s cm-2 ST-ts-t and rises linearly with mass above -1017 GeV/c* until it intersects the local dark matter bound around the Planck mass (1019 GeV/c2 ). Since more recent unification theories suggest a monopole mass approaching the Planck mass, searches at a flux level of -lo-t3 cm-2 sr-t s-t are particularly important. Also shown in Fig. 6 are possible monopole particle I. . ’ ‘. ‘I’ &.-----------It I . , ‘. ” . flux levels 2 to 3 orders of magnitude above the Parker bound. These models are based upon monopole plasma oscillations within the galaxy. Detailed computer simulations performed by the Cornell group confirm the stability of such solutions and to my knowledge they are not ruled out by any galactic observations. The particle flux limit obtained from our three loop superconductive detector was 4.4 x lo-t2 cm-2 ST-t s-t at 90% C. L. Four other groups (Chicago-FermiLabMichigan; IBM, Yorktown Heights; Imperial College; and NBS, Boulder) had obtained similar limits, for a combined world limit of 1.4 x lo-12 cm-2 sr-t s-t at 90% C. L. In a preliminary analysis of 15 months of data from our new octagonal detector, we find no candidate events for the passage of a monopole through the detector and set an upper limit on such a particle flux of 7.8 x IO-13cm-2 ST-1s-t (90% C.L.). In addition, the IBM, Yorktown Heights group is operating a 1 m2 x 4tt sr sensing area detector and “1 -; has reported a similar preliminary result in slightly more run time. The combined world limit for velocity independent detectors is now - 3 x lo-13 cm-2 sr-1 s-t (90% CL.) and is shown in Fig. 6. Also shown is the limit our detector will achieve after three years of operation. These data effectively rule out the plasma oscillation models and approach the mass-dependentParker bound near the Planck mass. Fig. 5. High bandwidth data (twenty poirlts per xc) from trigger showing the eight SQUID channels, the strain gauge channel and the external flux-gate magnetometer channel. This disturbance was caused by a bump to the &war. -74- -_ Acknowledgements \ , Our group at Stanford has included 9. Cabrera, M. Huber, M. Taber and R. Gardner and J. Bourg. This research is funded in part by DOE Contract DE-AM03-76-SF00-326. 1982 (0.001 m2) , World Limit (Late 19881 I lOI I lOI 10IX 10IY I 102O I IO*’ Monopole Mass (CkV/c2) -_ .: __:.; ._ Fig. 6. Cosmic ray particle flux limitsfrom our superconductive detectors compared with varicw astrophysical limits. -75 i . . PART SILICON CRYSTAL ACOUSTIC The decay rates are very strongly dependent on phonon energy (=v5) and for wavelengths of several hundred lattice spacings further decays are entirely negligible. These longer wavelength phonons propagate throughout the crystal with little scattering and no dispersion. This mode has come to be called the the ballistic phonon mode II: DETECTORS FOR NEUTRINOS Introduction [121. Semiconductor diode particle detectors now provide the highest energy resolution (- 3 keV FWHM for 1 kg) and the lowest thresholds available (- 5 keV) for large mass detectors. In this energy range less than 30% of the deposition energy is converted directly into electron-hole pairs which produce the observed signal in the semiconductors, the rest forming phonons. The characteristic energies of these phonons is - 1 meV, 10s less than the excitation energy for an electron-hole pair in a semiconductor (- 1 eV). Thus in principle, energy resolutions over an order of magnitude better are possible if the phonon signal is used. Recent work on bolometers, which sense the thermal phonons, has demonstrated an improvement in energy resolution (most recently 17 eV, FWHM, by Moseley, McCammon, et al [9]) by measuring the temperature rise in a small ultra-low heat capacity sensor (- 10m5g of silicon). B. Cabrera, L. Krauss and F. Wilczek IlO] suggested scaling such bolometers up to a mass - 1 kg. Motivated by this suggestion, our group, now composed of B. Cabrera, B. Young and A. Lee at Stanford and B. Neuhauser at San Francisco State University, has proposed direct sensing of the ballistic phonons produced by an event in a large insulating single crystal [I 11. Since this wavefront carries information on the event total energy and location within these silicon crystal acoustic detectors (SiCADs), substantial improvements in background rejection are possible over detection schemes which measure total energy deposition only. A threshold of 1 keV or better is important for our primary interest in using SiCADs as neuuino detectors. For example, at power reactors all nuclear recoil signals from elastic neutrino scattering are below 10 keV with 60% above 1 keV, and a 1 kg SiCAD with a I keV threshold would register an event rate of - 100 events/day. An interesting and important aspect of ballistic phonon propagation is that strong focussing effects occur within the crystal, although the propagation is dispersionless. These focussing patterns, which have been well verified experimentally, permit three dimensional reconstruction of event locations within the crystal and can resolve tracks or multiple scattering events. We have performed Monte Carlo calculations on these effects [ll]. Figure 7a shows the result of such a calculation for a point energy deposition within a silicon cube with all faces cut along [loo] axes. The number of phonons used in the calculation is for a 1 keV energy deposition at a point within the crystal. It is clear that information on the event location as well as tracking information is available. We call such a detector a SiCAD (silicon crystal acoustic detector). We have considered several phonon sensor configurations for the surface readout. The most promising to date consists of parallel strips on each face and provides spatial resolution based on the intensity and arrival time profiles across the sensorson each face (Fig. 7b). The sensorson the front and back faces perpendicular to the x (y and z) axis have their sensorsparallel to the z (x and y) axis and thus can be used to determine the y (z and x) coordinate of the event location. As an example, the phonon energy flux intensities incident on each of the 384 strips for the event location in Fig. 7a is shown in Fig. 8. As can be seen, sharp peaks in each of the face intensity profiles locate the event to better than the width of a sensor and there is always at least one sensor with an intensity greater than - 2 % of the total energy in the event. To obtain a 1 keV energy threshold for event detection within a 1 kg SiCAD cube (for example to detect neutrino-nucleus elastic scattering at a reactor) then each parallel strip sensor must have an energy sensitivity of - 20 eV. Ballistic Superconducting Phonons from Point Events in Crystal Cubes For a deposition of energy in a well localized volume within a single crystal of silicon, a thermal-like spectral phonon distribution is generated with a characteristic .;....2 Phonon Sensors During this past year we have worked on two phonon sensor designs which utilize superconductivity. The first, called a transition edge sensor, is a simple single layer thin-film patterned into a series superconducting circuit and biased with a constant temperature of lo-20 K. This spectral distribunon arises from the rapid decay of electron-hole excitations to the band edge, first generating very short wavelength phonons, which quickly relax to longer wavelength phonons within less than -10 nsec. current. A phonon flux incident on the film will drive those portions normal where the phonon energy density has exceeded a critical phonon energy density. Then a voltage -76 ‘,. .‘__ : .. ._ II .:: : : .‘..Y. ‘.. la 0 20 40 CHANNEL mrrurr x on 2 ,rcrs 60 0 20 40 CHANNEL M~as”r. Y on x ‘ace* 60 0 20 40 60 CHANNEL Pleasure 2 on Y frcrs : :.:-. ,__ -_ ._ Fig. 7. (a) Calculatedphonon energy densip incident on silicon cube with [IOO] faces from point source within the crystal. (b) Arrangement of parallel xenon on crystal faces. Fig. 8. Simulated signals from 64 channels per face. Lower two rows correspond to time evolution of peak channel on eachface. -77- deposited on the surfaces of the silicon crystals and biased with a constant current. For currents below a latching critical current, self-terminating voltage pulses are observed. These pulses are caused by the heating of line segments above the superconducting transition temperature. Last year, we demonstrated this technique using aluminum films with alpha particle sources [13], and most recently we have obtained a factor of one hundred improvement in energy resolution and threshold using titanium films in x-ray experiments [ 141. These most recent sensors are made by depositing 40 nm of titanium on crystalline silicon wafers which are 1 mm thick. The polished wafer faces are perpendicular to the [ 1001 axis. The meander pattern, shown schematically in Fig. 9, was produced using conventional photolithographic techniques and consist of 299 parallel lines each 2 ttrn wide with 3 pm space between lines. The pattern is aligned parallel to the [I IO] crystalline axis of the wafer. The active Xcd of the pattern is 4.5 mm long and 1.5 mm wide. The normal resistance just above their superconducting transition temperature (T, = 312 mK) is - 18 kW per line. These films have sharp transition widths of 2 5 mK (from 10% to 90% of the resistive transition), indicating homogeneous properties across the film. A typical superconducting to normal resistive nansition for one of these patterns is shown in Fig. 10. Here we describe two recent x-ray experiments. These were performed by Betty Young with a 24 pC source of xt Am. The decay spectrum of z4tAm is dominated by two alpha particle energies at = 5.5 MeV. In addition to these two alphas are a nuclear gamma at 60 keV and two atomic x-rays at 14 and 18 keV. An appropriate absorber placed in front of the source readily stops all of the alphas and essentially all of the 14 and 18 keV x-rays before they reach the sensor; however the 60 keV gamma rays, being much more penetrating, pass through the absorber attenuated in number by - 0.5. We used ,005” (125 Frn) thick foils of Sn and Pb as absorbers. Using a cryopumped 3He refrigerator at 0.3 K (described below) we biased the is seen across the circuit providing a signal which is proportional to the length of the circuit driven normal. If the current is below a latching critical current, then self-extinguishing pulses are seen,otherwise the resistive heating of the normal state is sufficient to expand the normal region across the whole circuit. Such a system is straightforward to manufacture using photolithographic techniques, but the physics governing the response is non-linear and complicated. Below we discuss this point in more detail. A second device, the superconducting tunnel junction, possess the opposite properties. These are more difficult to manufacture, but the physics is more linear and simple. Such a device consists of two superconducting films separated by a thin oxide bartier (typically l-2 nm). This device is biased with a constant voltage given by A/e, where A is the superconducting energy gap. Phonons from an event within the crystal reach the surface and enter the superconducting film. Once inside the superconducting, those phonons with energies greater than 2A (most) are strongly absorbed by breaking Cooper pairs and forming electron-like excitations called quasiparticles. In fact for phonon energies well above threshold, several Cooper pairs will be broken. These quasiparticles will tunnel across the oxide barrier providing a signal if the tunneling times are short compared to the quasiparticle recombination time. This condition is satisfied for T < TJlO, where quasiparticle recombination with thermal quasiparticles is negligible. For these devices the tunneling current is proportional to the energy absorbed by the film as long as the quasiparticle density produced by the phonon flux remains dilute so that little self-recombination of the quasiparticles occurs prior to tunneling. Given the results of our experiments during this past year and calculated improvements, we now believe that transition edge detectors can be used successfully to construct SiCAD detectors capable of a 1 keV energy threshold. Such devices will become our central focus during this next year for our first generation detectors. However, we also believe that better ultimate resolution and thresholds will be obtained with tunnel junctions, and we will maintain a parallel effort to develop this more difficult technology over a longer time scale. As available, we will substitute the tunnel junction technology into future generationsof the SiCADs. Experiments with Titanium Transition Edge Sensors on Silicon titanium/silicon devices at the foot of the resistive transition in temperature and below the latching critical current in bias current, and we observe self-terminating voltage pulses when the film is bombarded by phonons produced by the interaction of an incident x-ray (or gamma ray) within the Si substrate. These pulses occur because enough phonon energy from the photoelectron in the silicon reaches the Ti film to drive portions of the film normal. To estimate the threshold energy density E, necessaryfor this superconducting to normal state transition, we integrate the heat capacity of the Wafers superconductor from the bias temperature to T,: Our first generation of SiCADs will utilize superconducting transition edge devices as phonon senors. These devices consist of thin superconducting lines -78- : -:. .,-. -.: -, -:- q . . . . . . . . .:: ‘, ,’ ‘. ‘, ‘G’,,~:, .’ .,, / .,:‘c:: E, = lTTc C,,(T)dT , where C,, is the electronic heat capacity below T, as given by the BCS theory. We assumethat the time constants are sufficiently long to allow quasi-thermal equilibrium. The asymptotic form near T, is: En = 5N(O) Aaz (l-T/T, ) , where Au is the gap at T = 0 and N(0) is the density of states at the Fermi surface in the normal metal. For our Ti films, N(0) = 4 x 10” cm-3 eV-1 and A a = 47 peV, yielding Et, = 22 eV/pms at T/r, = 0.95. In terms of the energy density per unit area of film, E, we get E, = (22 eV/pm3) x (40nm) = 0.88 eV/pm 2. We may also estimate the minimum detectable energy for a Ti sensor as follows. In our current experimental setup we use a cryogenic GaAs MESFET voltage-sensitive amplifier (described below) which introduces an ampiifier noise level of AV,, = 1 nV/@z at 1 MHz. At T/r, = 0.95 and a bias current (It,) of 60 nA we can detect a minimum sensor resistance of ARr,, =AV,, & = 17 R. At T ;: T, the resistance of our sensor is - 18 kfZ per 2 pm wide line 5 mm long, or 8.5 fi per 2 pm x 2 pm square of the Ti film. Therefore the area of film which corresponds to a normal area resistance of A& = 17 R is (17 n/8.5 Q) (2 pm x 2 pm) = 8 pm2. The minimum detectable energy deposited in the Ti sensor is then AE,, c: E, x Area- = (0.88 eV/pmz) x (8 pm2 ) = 7 eV. The inequality holds I...,....,.. 0 (a) 5 Tie ‘I...‘..“‘(.‘.( 10 15 (microsec) 20 x becauseJoule heating contributes to the actual area driven normal. Figure 1la shows (for I, = 120 nA and T = 286 mK) some typical single pulses, of - lo-15 psec duration, resulting from the interaction of 60 keV gamma rays (from 24tAm) in the Si substrate of a TE sensor. In Fig. 1lb (for I, = 60 nA and T = 299 mK), we have expanded the time scale to show the leading edge of each pulse with electronics-limited risetimes of - 140 nsec. We mounted the 24tAm source such that its active area faced the backside of the 299-line sensor, and investigated the effect on detector response when various absorbers were placed between the source and sensor. We chose two convenient absorber materials (Pb and Sn) and used appropriate thicknesses such that we could study the TE response primarily due to 60 keV g-a ray radiation with zero incident alpha-particle flux, and essentially zero 14 and 18 keV x-ray flux. The measured count rates for all spectra obtained, for various operating temperatures, bias currents and Fig. 11. (a) Individnal pulses from 60 and 25 keV x-rays. (b) Leading edges of pulses wirh 140 n.srise time. -8O- absorbers, were consistent with the calculated values. Figure 12a is a pulse height spectrum obtained for the case of a ,005” (125 pm) thick Pb absorber. The prominent peak towards the center of the spectrum is the photopeak due to interaction of 60 keV gamma rays in the Si subsnate of the detector. The sharp feature at 11 keV is consistent with the position of the Compton edge for 60 keV gamma rays in silicon. In Fig. 12b, we show a pulse height spectrum under similar running conditions, but with a ,005” Sn absorber. We note that the prominent features due to the 11 keV and 60 keV interactions appear, as expected, in the same positions as they did with the Pb absorber. Furthermore, in the Sn absorber spectrum, we observe an additional peak around 25 keV. This peak is readily recognized as that due to secondary emission of & x-rays from the Sn. We can qualitatively reproduce typical pulse height spectra (such as those shown in Figs. 12a and b) by applying Monte Carlo methods to a simple model of the detector response. We assume that an incident photon, if it interacts at all, interacts in the silicon substrate only once, and that this interaction is point-like. We imagine that, to first order, the phonon energy generated by such a scattering event spreads spherically outward through the crystal, producing heat spots on the surfaces. The energy density (per unit area) of such a heat spot is then given by F 10 Min Run 0 100 (a) 1 200 Channel Number EG (p.z) = z Ea /[4~(z*+p*)~~] where p is the radius of the heat spot, z is the perpendicular distance from the Si surface to the location of the scattering event, and Ea is the total energy of the heat spot. Defining E,, as the (minimum) critical energy density required to drive the detector film normal, we find that the areadriven normal is given by A(z) = x p* = z [(zErj4xE32fl-z2]= x ~2 [(z&$m- (z/z#] 0 100 200 (b) Channel Number where rc2 = Ee /(4 x E,,). The amplitude of the voltage pulse resulting from an interaction in the crystal is simply proportional to the amount of line driven normal, and the number of interactions producing pulses is proportional to (dA/dz)-1 for events uniformly distributed in z. For incident particles of given energies, we can then plot a theoretical pulse height spectrum for the Ti transition edge response -- as shown in Fig. 13a for the case of incident 30 Fig. 12. (a) Pulse height spectrum for z4/Am source using Pb absorber. (b) Pulse height spectrum for same source and geometry using Sn absorber. and 60 keV photons. -81- 22 8 4 , I 30 keV I I Another interesting and very useful plot is generated by graphing the calculated normal area A as a function of interaction depth z for incident particles of a given energy. By considering various initial particle energies, one obtains a family of curves as shown in Fig. 13b. Assuming this simple heat spot model is valid to first order (i.e. neglecting focussing effects), we can extract important spatial information about events by comparing such curves with those obtained experimentally. We are in the process of carrying out the more computer intensive calculations which fully include phonon focussing effects. We are currently working to fabricate 1 and 2 mm thick, double-sided (Ti I 10 Min Run meander patterns on both sides of the Si wafer) transition edge devices. These devices will enable us to do timing experiments and to obtain spatial information about each event occurring in the detector. We shall also be able to experimentally measure Fig. 13b and obtain an energy for each event. These improvements will take us one step closer towards our goal of developing a = 1 kg scale SiCAD. (a) Channel Number Cryopump 3He Test Probe We have performed these experiments using our laboratory-built fast-turn-around probe for device testing down to 250 mK and we are delighted with its performance. The probe was designed by Barbara Neuhauser, and we cannot overemphasize the importance of quick and inexpensive accessto ultra-low temperatures for the successful development of both transition edge and tunnel junction devices. Until a well characterized design is available, many devices are either defective or do not perform as designed. We are now able to rapidly test a range of different devices and we have significantly increased our rate of progress. This refrigerator is based on a sealed 3He and charcoal cryopump design. In a typical run we begin precooling in the morning and by early afternoon we can begin taking data at - 270 mK. The initial liquid 4He transfer (- 5 liquid liters) lasts twenty-four hours allowing more than twenty hours of data below 300 mK. /- . ..- 200 0 (b) Chazl Low Number Noise JFET Preamplifiers Operated Another important component for our recent progress has been the use of cryogenic preamplifiers in the titanium sensor SiCAD experiments ]15]. These were designed and constructed by Adrian Lee. The peak resistance of the titanium line, typically - 3 kR for 60 keV x-rays, would produce a large “RC” time constant if the fist stage of amplification were at room temperature. This time-constant can have two Fig. 13. (a) Monte Carlo generated puke height spectrum from simple model. (b) Pulse height versus distance from titanium sensor function used in Monte Carlo. -82- : Cryogenically ..:. : :.::::-L .. _- adverse effects. First if the rise-time is long compared to the signal duration, the signal will be truncated since the input pulse will start to decay bet-orethe output can reach its full Jlulse height. Second, a long time constant will make it harder to resolve the leading edge of the pulse. The spatial resolution of the detector will, in the future, depend on being able to resolve timing differences between different channels, which makes a long time constant undesirable. Mountmg the first stage of amplification down in the cryostat reduces the capacitance seen by the amplifier dramatically. The GaAs MESFET (Plessy P3S-IlOl), which we use, has the advantage of operation at 1.5 K and has very good noise above 100 kHz. The total power dissipation of this amplifier is about 14 mW. The bandwidth of the amplifier is IO MHz. but the rise-time is dominated by the RC time at the input. The gain of this device 1svery low, about 15 into SO0, which necessitatesa low noise room-temperature stage. We use a Trontech WSOATC instrumentation amplifier with a noise voltage of - 1.2 nV/&& and a bandwidth from 10 kHz to 50 MHz. Superconducting Tunnel .Junctions as Phonon - I5 pee were observed. In fact, this sensitivity is already sufficient for our detection threshold requirement of 1 keV in a 1 kg SiCAD. However, the area of each parallel strip sensor needs to be - 1 cm2, a factor of - 104 greater than used by the S.I.N. group. We are pursuing several techniques for obtaining comparable energy sensitivity in these much larger area tunnel junctions. Conclusions Ballistic phonon focussing effects greatly enhance the spatial resolution in silicon crystal acoustic detectors (SiCADs). Utilizing titanium superconducting transition edge devices as phonon sensorson the crystal surfaces, we believe that an energy threshold of - 1 keV can be achieved for a 1 kg SiCAD. Such a detector would be of great interest for a number of experiments including dark matter searches for weakly interacting neutral particle candidates and low energy neutrino experiments to set better limits on the neutrino mass. Detectors On a longer time scale, we believe that the most promising sensors for high Acknowledgements sensitivity phonon detection are superconducting tunnel junctions. For our proposed application as a SiCAD readout, we are beginning the development of aluminum junctions. These are formed by a - 200 nm thick aluminum film deposited directly onto the surface of the silicon crystal, followed by the formation of a thin oxide tunnel barrier (- 1-2 nm thick) and then deposition of a second aluminum upper film. Phonons from an event within the crystal reach the surface and enter the aluminum, which has an excellent acoustic match with silicon. Once inside the superconducting aluminum, most phonons have energies greater than 2A (where A is the superconducting energy gap) and are strongly absorbed by breaking Cooper pairs and forming electron-like excitntions called quasiplutxles. Tnfact for phonon energies well above threshold, several Cooper pairs will be dissociated. We have performed junction tests down to a temperature of 250 mK utilizing the sealed 3He system with a charcoal cryopump. Ultimately we intend to operate at T < T,/lO (-100 mK for aluminum), where quasipartxle recombination with thermal quasiparticles is negligible. Recently several European groups [ 16,171 have reported excellent energy sensitivities and resolutions for X-rays. The S.I.N. group [ 161in Zurich, Switzerland The work at Stanford has been performed by B. Cabrera, C. J. Martoff, A. T. Lee, and B. A. Young. Also, B. Neuhauser now at San Francisco State University has participated extensively. This work has been funded in part by a Research Corporation Grant, a Lockheed ResearchGrant and DOE Contract DE-AM03-76.SFO@326. has reported - 48 eV EWHM for the detection of low energy x-rays (- 6 keV) using a 100 pm x 100 pm area Sn Sn oxide - Sn junction at - 0.38 K. Pulse rise times of -83- :. :. -::, ._ ‘._ ,; . ‘. ::; ::, :: ., References [l] [2] [3] [4] IS] [6] [7] [S] [9] B. Cabrera, Phys. Rev. Left. 48, 1378 (1982). See the review article by D. E. Groom, Phys. Rep. 140, 323 (1986). B. Cabrera, M. Taber, R. Gardner and J. Bourg, Phys Rev Lerr. 51, 1933 (1983); and R. Gardner, B. Cabrera, M. Taber and M. Huber, to be submitted to Phys. Rev. D. R. D. Gardner, Ph. D. Thesis, Stanford University (1987); and M. E. Huber, Ph. D. Thesis, Stanford University (1988). S. Bermon, P. Chaudhari, C. C. Chi, C. D. Tesche, and C. C. Tsuei, Phys. Rev. Left. 55, 1850 (1985). J. Incandela, M. Campbell, H. Frisch, S. Somalwar, M. Kuchnir, and H. R. Gustafson, Phys. Rev. Left. 53, 2067 (1984). S. Somalwar, H. Ftisch, J. Incandela, and M. Kuchnir, Nucl. Insr. A226, 341 (1984). M.E. Huber, B. Cabrera, M.A. Taber and R.D. Gardner, Jap. J. of Appl. Phys. 26, 1687 (1987); and M.E. Huber, B. Cabrera, M.A. Taber and R.D. Gardner, Proceedings of Applied Superconductivity Conference, San Francisco, Aug., 1988, in press. S.H. Moseley, J.C. Mather and D. McCammon, J. Appl. Phys. 56, 1257 (1984); D. McCammon, S.H. Moseley, J.C. Mather and R.F. Mushotzky, J.Appl. Phys. 56, 1263 (1984). [lo] B. Cabrera, L. Krauss and F. Wilzcek, Phys. Rev. Lett. 55, 25 (1985). [ 1I] B. Cabrera, J. Martoff and B. Neuhauser, Stanford Preprint No. BC44-86. [12] See for example: Nonequilibrium Phonon Dynamics, ed. W.E. Bran, NATO AS1 Series B124, Plenum Press, N.Y., 1985. An excellent review of recent developments in phonon physics. [13] B. Neuhauser, 8. Cabrera, C.J. Martoff and B.A. Young, Jap. J. of Appf. Phys. 26, 1671 (1987). [14] B. A. Young, B. Cabrera, A. T. Lee and C. J. Martoff, Proceedings of Applied Superconductivity Conference, San Francisco, Aug., 1988, in press. [15] A. T. Lee, Stanford Preprint No. BC73-88. 1161 D. Twerenbold, Europhys. Lett. 1, 209 (1986). [17] H. Krauss, T. Peterreins, F. Probst, F.v. Feilitzsch, R.L. Mossbauer and E. Umlauf, Europhys. Lett. 1, 161 (1986). : .;, ., -84- . . ..,. :.... 1 .: : : ! Cosmic Relics F’rom The Big Bang Lawrence * J. Hall Department of Physics of California University and Theoretical Physics Physics Lawrence Berkeley 1 Cyclotron Berkeley, Group Division Laboratory Road Cal~omia 94720 Abstract A brief introduction given. Dark matter to the big bang picture is discussed; particularly tary particle physics. A classification of the early universe is its implications for elemen- scheme for dark matter relics is given. ;.. ‘This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DEAC03-76SF00098 and in part by the National Science Foundation under grant PHY8$15857. @L.J. -85- Hall 1988 ..::. .:I. ..- Table remarkably of Contents about (I) The Importance (II) A Brief (III) Dark of Cosmic Relics Introduction to the Big Bang. electric Perhaps we even learnt per century Scheme for Cosmic charge, Relics. placed from Importance Of Cosmic It is probable that physics will come from unexpected particles accelerator described There experiments. are two clear examples. the origin physics: of electroweak and the discovery Accelerator symmelry breakdown. evidence; is crucial It will also shed that of searching masses are typical done for other What reasons: the next major and cosmology. the questions as supernova the most exciting What of galaxies, form clusters thing have their about However, in these lectures hope to learn about I want to take a more limited particle For example, free paths its surface, of various scalar could be emitted so the existence the best example SN1987A[l]. astrophysical particles with unanswered viewpoint; matter: questions. ments containing powerful deal of evidcuce [3,4]. It is worth A new experimental form: of its const,it,ucnts. “surely” for example, A mass st,ars in the local in our and other spiral in the whole universe, galaxies, it does Since we have not detected dynamics, it is completely this we call it dark matter. no constraint the nature at 01~ then asks more, unobserved see it, surely it could be anything.” which restrict looking field is opening, be sure of its foundation. stable system or whether clouds that a system will be observat.ionnlly and even for galaxies the word constraints of dark matter the eye. I will not discuss this guess that there is virludly “if we cannot have now m&s by means other than this gravitational You might is what can we objects open. We can certainly to place limits a mass of less than from the entire volume of these particles is the supernova Although For a particle and cosmology it can be on the nature As with false. of dark most state- We have thrcv very of dark mat.tcr: physics from astrophysics? In fact this still leaves a wealth of possibilities understanding matter We on the qu&ion seem that a great deal of extra mass is required. clustering limits is a great [5], and we shoukl hydrogen l&Lime backgrounds. it. For a. great many systems; galaxies a supernova If I,, is heavy There the mass and velocities of our galaxy, hot gas in elliptic why do they have the of galaxies? to determine neighborhood How did the than has the following this is a gravitationally is needed to stabilize is own intrinsic triggered astrophysics that there seems to be an endless succession of interesting whether physics and cosmology and quasars? of the universe come about? size they do, and why do they themselves in particle Most astrophysics why are there so many varieties perhaps advance being addressed is the nature of such objects observed mass distribution into galaxies, that plrysics. for dark matter I,,. [2]. it over for yourself. piece of evidence with case very st,ringcnt there are now several books on the subject the evidence and thinking analyzed possible the gala.xy currents. v,. Since we are now we now know that on X and r-ray there is much more to the universe of new physics for particle of 11,: its and right-handed v, than we did about in these decade old limits and its implications possibilities: at the very least we can learn how fermion will come from astrophysics physicist are many of particle at the TeV scale. It is also quite worth. in our understanding decay modes of Ii, D, B, p, r, Z particles on flavor limits mixing a supernova is populating observational we (lid learn a. great &al about other propertics I will reduce my scope again, and concentrate the next leap forward at high energies in unravelling light Relics from y or e *; in either decay giving espcriments, We lcnrnt moment, more about in our galaxy great confidence (1) The magnetic sure of the size of v emission MaLter. A Classification physics from SN1987A. lifetime, could (IV) close t,o that from la.boratory particle which the mass limit dark matter on new particles. a keV and long mean 2.‘We of a star, and not just form is severely constrained. went off in a nearby or ve from 1. We know the location use our galaxy this event turned of the dark matter. in locations know that it is dark. in the local neighborhood. Perhaps mass m it is raining last year, and we just cannot out to be -86- This is especially important If the dark mat,ter down on us with see it. (Of course there could also be other than those we have st,udied.) for the dark ma&r is composed of particles a flux of N 107/(m,/GeV)cm-2s-’ of ,, ._ :: . . . ., .. 3. Dark matter start should result from a reasonable the big bang off with they typically with annihilate the observed big bang cosmology. a given set of particles and do not survive abundance until with today. is a very powerful dR is the usual element of solid angle, t the proper time at any location If you given interactions and r is a dimensionless Requiring at TA and r~ at time t is given by constraint survival coordinate. The proper distance of fixed r, between fluid elements : _, -.-..: ;I:. : -,ry:....: (24 object. To implement the third constraint, it is necessary of the hot big bang model of the early universe. this picture, 3’K which emerges uniquely microwave SU(3) x SU(2) background to have an understanding In the next section from three cornerstones: the general radiation, x U(1) gauge interactions of relativity of the elementary on the experimental baryonic or whether stable objects, In Section and finally Why a classification and experimental particles. have I chosen to orient that we have for particle A Brief The cosmology on ideas rather A simple cessional expanding stituents the standard Big Many references, cal. Although could be and isotropic temperature for species i pz(T). of the plasma of the 3’K candidates and with 1/2~ZhSl. of cosmic relics? plasma. T(t), of the big bang details in terms of the Robertson-Walker d? scale factor microwave at will be = dt2 - R(t)’ galaxy radiation an early which then H = n/t picture is helpful. at time has been measured to be H;’ (2.3) sets the scale for the age of the universe. and to = nH;’ is given by some power law N nh-‘lO’Oyr. of the expanding Cornmoving tA with universe coordinates wavelength tA and as the surface of an inflating are fixed to the surface of the balloon. XA will have a stretched Th e red-shift received at TV is defined to be (Xn - X,)/X, wavelength at some of a photon emitted and for tn >> ta this just becomes R(&)/R(t,). re- dynamics general relativity of the expansion applied is given to the metric by Einsteiu’s of equation field equations for (2.1) is that (2.4) at where G is the Newtonian of the con- gravitational sity at any point in the homogeneous itself is described equation appears in the metric: expansion is inspired + da’) by Newtonian of a small spherical nate radius r << & it is frequently era of a hot can be described from a knowledge The expansion R(t) If if k = 0 it is criti- of the universe of the universe later time tn given by XB/XA = R(te)/R(ta). will be omitted Emphasis law for distant This system Th ese are determined In many cosmologies The simple its pressure p = p(p), and the chemical and their interactions. behavior parameter suppose the expansion R = &(l/to)“, balloon [6,7,8]. from vanishes or has unit magnitude. it is open, while H,, = 1OOh km s-~,,,,-~ for dark matter. The and has evolved for the future being the spa- early times and can be set to zero. The present value of the Hubble A photon red-shift k either H = h/R I will scale the coordinate are the best evidence the framework important constant parameter. is closed, if k = -1 k is crucial during from this, with Hubble exotic model. elsewhere of the Hubble is expanding homogeneous the dimensionless unimportant Bang is to present and of the isotropy universe any era by the plasma potentials In Section directly but time dependent k = +1 the universe than formalism. interpretation velocities the present with at the question and dark non-baryonic, and brief way. together T so that I give a few to include law, ci = Hd, follows constant For example these lecture To The of this section in a simple and can be found and its implications scheme for dark matter physics beyond Introduction purpose physics of the and the the dark matter of particle tially signatures. Cosmic relics, both visible baryonic (II) I discuss whether I consider inflation IV I introduce give examples results, it requires an extension Hubble’s we discuss the isotropy theory III I discuss three general points which have to do with dark matter. remarks :. on any relic constant, and p is the total energy den- fluid at time t. A useful mnemonic ideas as depicted cornmoving I. The sum of its kinetic in Figure the region with a unit test mass at coordiand potential where A4 is the mass enclosed in the unit sphere, is just -a7- for this 1. Imagine energies d’/2 -k/2. - GM/R, Thus if k = -1 ;_ :‘.. ‘: -.:,... : : the total energy is positive not correct from general relativity. mology However, is flat, k = 0, equation today I like to interpret of the universe I I I J (r,is) \ \ is driven in driving by energy the driving the expansion density today; \ I------+ I I content of the universe cosmological constant). to the critical we know that Defining O(lO-‘). When during a previous era: that of Hubble’s today it is probably density mnemonic dominated so the expansion We do not term. EM components: i.e. the electro- microwave radiation, and V to vacuum of density energy If 00 is larger v ie. a in any component galaxies (2.6) and for very light neutrinos law which is dependent observations R, = we see them as and where t,hey were when the detected photons left them. on the deceleration measurements This leads parameter of qo lead to CL,S2. Hence that 10-%noS2. of k/R If Gp, the invisible has various baryons, by the 3’K 0, = pi PC Rvs = O(lO-*) 1 for interpretation R-’ curvature. only through today is visible to dark matter = Ro12. Experimental we know from very direct Newtonian than R; to be the ratio we observe distant qo = -RR/k*It, rather density OEM N 0(10-5), to a violation Figure DM (2.4) as the terms which Gp >> it could be the curvature of ~0. The energy refer to massless neutrinos, i relative If the (2.5) side of equation po = pvs + PEM + py + PDM + pv (VB ,--. f ,(rvc4) // of big bang cos- at any time. N 10-5GeVn-3. the right-hand or dark components / --\ is (2.4) can be solved to give p 0: HZ. This critical At early times we know that know what dominates magnetic equation is expanding picture as it follows is drive the expansion. dominates The Newtonian (2.4) is correct It is about the most important pc = &Hi 77 / is open. equations since it tells you how fast the universe universe density and the universe for the whole system. than CLVB the difference is predominately (2.7) due to the presence of dark matter. At early times during number densities to maintain the big bang the temperature thermal equilibrium rate to be fast enough to maintain than the expansion -88- was high so that particle in the plasma were large enough to give reaction between many species of particle. thermal rate of the universe, equilibrium rates sufficient For a reaction it should basically be faster that is the mean free time for interactions .I... should be less than the age of the universe example, for a reaction time t requires at the era under AB -+ X to keep particle the reaction consideration. A in thermal era: t - M,,/T2. For equilibrium The constant of proportionality does have a weak dependence on T. Near an MeV: at (2.12) rate How does this hot plasma at T > eV evolve into the universe rastx = %+AE-XUAE) > r,,,(t) = H(t) = At first where R,,J,(~) thermally are particle averaged perature T(C). member cross section In thermal densities times at time t and (cr,.~~+xu~s) relative equilibrium speed for this process the particle number densities of spin states of particle and 3~1 refers to fermions ij’ + mf. and bosons. Useful order of magnitude i,p,(T) The particle approximations mass ni is perfectly are given enters inhomogeneous reaction does the expansion via E2 = electromagnetic are temperature prevent - 573 (2.10a) n!“(T * << m,) N (,,qq+‘-“‘v~. (2SOb) only relativistic hot big bang model p is dominated species (with there is a plasma which about 1 eV. Although long-lived exotic T >> m;, so n; - T’s) for virtually is thermally coupled; era is a very important or with periods one. During have p - T4, so that Einstein’s k/R of inflation, scattering which cosmologies with heavy that calculate T, we exotic The calculation particle (2.11) This is equivalent (one which grows as R3) being constant. most circumstances, with which (2.11) allows for a solution in a cornmoving The gas is expanding so that RT = constant only when there is a mechanism gether to the entropy Using k/R for T(t) the radiation = -T/T growth. clustering, it can and stars, are we see should particles abundance particles contain into What in the universe determines today? Is it p, e, y in the observed ratios? theories of particle physics can we in the universe? of these abundances is very simple [9]. n,(T) of the last such reaction will be given by equation since the i particles Consider changes the number equilibrium, (for example from the hot plasma to the (2.9). Suppose Ti, is to be in thermal equilibrium. do not decay and assuming by the decay of some other a stable of i particles they are species) we have n,(t) N to the temperature T;J. (R(t)lR(t,))3n~“‘(t,) wh ere t, is the time corresponding After freezeout the remaining i particles are just diluted by the volume expansion. under and is violated creates entropy. during volume adiabatically holds more generally, once the gravitational that we must address. temperature not produced era the relationship about the evolution the freezeout and R(t). is that RT is constant. there is some Furthermore, such as galaxies is in thermal ship between dominated out”. of the resulting species i. As long ss a process which At lower temperatures the radiation of the plasma for each reaction systems, universe stable their present expands it does work and hence cools; there must be a relationDuring picture stable the universe When the universe T(t) so that of all the stable fundamental If we introduce dominated - T=IM,. As the temperature - n < ou > fall much more rapidly in the plasma from undergoing cold, inhomogeneous reasonable has the form - (Gp)“’ it evolve into a processes freeze out, there is no longer any pressure to stop once gravitationally the abundance above this era, since n - T3 and < E; >- equation we 6ee a we have come to realize that it is “frozen we are far from a complete observed all times for which the radiation hot-spots, formed. from that is for all temperatures this is not the case for non-standard particles by contributions universe. rate I’,,(T), There is a very basic question In the standard local also it is grossly inhomogeneous However, rates I’,q(T) beneath mass perturbations Although from that the plasma of the hot big bang should cold, non-interacting, than apart interactions, drops all the particle critical >> m.)1 different: with few particle reasonable potential nI”(T they seem very on all scales up to at least 50 Mpc. at tem- is the chemical sight very cold universe is the (2.9) where g; is the number we see today? ; Since R - T-i to- dominated -89- it is convenient n,/T3 which become independent which is still relativistic to consider of at freezeout t “reduced” after freezeout. (m; < Tq), ny)(Tf) number densities Note that k(t) = for a particle is given by (2.10a) so that the relic abundance at freezeout which rzp’(Tf) can reflect and mi >> f, N 1. However, is given by (2.10b) an enormous Boltzman process, which be seen by numerical particle I for which Ignoring a possible n, The physical integration since freezeout ideas are correct of the rate equation. for small chemical the rate equation potential p* as a as can consider a process to freeze out is xz + is < c7AtJ >zp+.,. (12 - nq has be en numerically This is treated however For example, changing is shown in Figure abundance - m,)/Tif) at freezeout the last z number = 12~ = n. behavior suppression are approximate it is not. dn 3k’ - = ----1xdt R where was non-relativistic TX,. The above relic abundances sudden if the particle so that f; N (F)s”exp((/l; 2. A useful analytic (2.13) integrated and the freezeout approximation for the freezeout is (2.14) where 2 = m&~(u~v), the freezeout temperature T, ‘Y nz.~ / in Z and the result is valid for large 2. For very large 2, fxf N Z-l, so that R, N (m,f,r/Tof,~)R, or Q,-b&&&T This result has one astounding if XF annihilation ~53 proceeds on dimensional consequence via strong interactions grounds. Hence 0,X2 I sible to have a stable fundamental is encouraging, possible if the dark matter to push their particle increasing which is rarely with nz,S103TcV. cannot only be avoided by having a phase transition by < ~Aav > than 10”Z’eV. particles small. i It is not pos- mass larger be made arbitrarily Z Even of fundamental high, and consequently sity and flux at the earth mentioned. it will be bounded implies is composed mass arbitrarily (2.15) their number This This m it is not bound denFigure could give a mass to z after it has already Schematic frozen out at a low abundance. What are the relic abundances we believe to be stable? ,f, = O(l), Photons we have observed. The photons of the four known particles (I/, y, e,p) which are massless and have relativistic are the only relics which were relativistic They play a crucial 2 role in determining freezeout at freezeout which the age of the universe. -9o- illustration of particle abundance freezeout behavior We believe the observed of the hot big bang. they maintain universal These photons a thermal expansion: distribution relativistic roughly with T(t) wavelength temperature stretched which equation describes light but need this: 1OsTs N 30eV they would %(nz, give &(m, the then gives the age domain of p with If m, relativistic freezeout of a heavy neutrino < a~v >- p. Although trons to write of the universe mean that To obtain accurate). MeV, then to other about This is excluded v, must be unstable. astrophysical 30eV. implications. Equat,ion annihilation occurs At temperatures applies is completed picture number to any neutral and the baryon get trapped for baryon number typically lead to be less than fermion Such a particle whose dominant with mass in the interacting is carried int.o quark predominantly supercooling nuggets t,he baryon for example.) are in of p and I, vanishes, {LB = 0, then the freezeout abundance (2.14), and fin is given by (2.15). Since < oav >- is given by equations this gives R,3 - lo-*s. We conclude /LB # 0, i.e. it requires a cosmological that the standard potential for lepton asymmetries carried it is necessary, just before the QCD phase transition, (n, - ni;)/ np = 0(10-s). big bang framework should be. The asymmetry all anti-protons initial Although today is enormous come across a proton small it is of crucial somewhere. condition The imporhow big and obvious to annihilate. However It also implies the nature ..) is pure speculation that processes occurred of the phase transition interactions. that particle physics at some gauge symmetry of the main events in the hot big by the SU(3) x SU(2) asymmetry x U(1) model of pai-tick gauge 3. This model should be good up GeV so this is where we begin. the cosmic baryon an at the moment. These even& are shown in Figure to a few hundred during phase transitions (inflation, and a randomly in a non- thermal because it implies additional I will end this section with a brief summary as inspired it is not just it must have been generated This is fascinating model. importance: Assuming to the universe, environment. the standard ‘bang cosmology -91- asymmetry. it is non-zero effect. have come from breaking baryoii excess to be present, by T = 50 MeV. The absence of antimatter in a billion early era, although big bang scenario requires pr, = pn, since by neutrinos. it was a one part beyond m;s number does not early on in the big bang it would not have been very obvious, such as potential such in clec- This is that it allows us to calculate equilibrium by p and n. (The Reactions domains incorporating implies that the cosmic asymmetry era of the universe when CP and B violating particles If the chemical such enormous cosmology tance of the standard it must could take place or baryon distributions. could produce This over-annihilation cosmic baryon adjusted u,d and s quarks Way symmetric today would lead us to expect a non-zero because essentially cosmological lepton asymmetry such an asymmetry assume that by T = 50 McV the phase transition number therm&e < 35 for the dark matter. could be much more complicated; could m,, with the eight gluons, and these strongly For simplicity @ --t n(rr) ra.pidly I expect < m, have very exciting above the QCD phase transition equilibrium are all relativistic. would via W and Z exchange. range l-10 GeV is a good candidate thermal problems: to the contrary (2.16) If 1 MeV In this case the decay products or cosmological Evidence (2.15) and (2.16) are not numer- for a stable heavy vr. could be baryon at least for a closed universe. the chemical 0~ = 0(10-s) to have a quark ically in the and some anti-baryonic. down a complete in protons, there could be additional factors of 4~ equations universe some baryonic an era of inflation is equal to that necessarily (2.15) gives (Since we have dropped that we would anywhere a scheme. For the non- G$mZ, and equation anti-matter in the cluster of galaxies of which our Milky domains, it has not been possible = O(1). This could also be true non-relativistically. about the nature must have existed at T - 50 MeV to prevent structure Charge neutrality I,, would freezeout assumpt,ions argue that it was obvious The only way that the entire is if there are enormous of the that they also were tau neutrino. is above 1 MeV, You might we do not see any evidence of primordial is a member. = 0) = O( 10e5), If their mass were = 30eV) by more complicated solar system or indeed anywhere fy - 1. If they are stable and massless they contribute at decoupling: is not altered of the QCD phase transition. by the Of the neutrinos to be sufficiently This conclusion relic to any plasma, being of To = 3’1;. v, and vP are known is the photon coupled from Einstein’s the observation the same to ps as do photons: for a light radiation are no longer distribution Knowing to from model, background X 0: R, so the effective T cc R-r. of the universe standard 3°K microwave It is likely, but not necessary, exists even at this high temperature. At a ::-’ :. temperature dam.?) near 250 GeV there is a phase transition acquire a mass as well as all the quarks is light considerable phase transition. supercooling (but cosmological consequences below Mz, Mw, mb, m,, and m, they freezeout. footprints. so the baryon to the plasma rather than a miniscule is possible at this of this pbsse transition which As the temperature are depleted essentially asymmetry. so that every anti-baryon in reducing the neutron energies are O(MeV) mediately is as given decay becomes number density it also becomes possible photodisassociated and ‘Li. The abundance from a variety important ratio. experimental for T < 1 TeV. support cess has important is especially for deviations Hence the interacting tons in the ration 1 : 1 : O(lO’), plasma to cool until as the reverse photodisintegration plasma dark He, in the stan abundance inferred success; there is direct big bang and could the light now contains T = O(eV). matter electrons, process freezes out. the photons decouple just the electron protons the heavy nuclei. At this point be baryonic, neutrinos down to essentially and also contains by a factor of E 3000 until At all temperatures -92- primordial At O(MeV) the plasma ceases to be interacting, red-shifted which escape ending up in *ff: from the standard to the issue of whether and e+e- --+ yy depletes the charged leptons formed binding for the big bang model back to times of 0(1 EC). The succonsequences important continues (2.12). are not im- by nucleosynthesis with energy an MeV Since nuclear This is a very important as we will discuss in the next section. excess. beneath Most of the neutrons of these nuclei predicted of observations. radiation in equation to form nuclei which by the plasma. dard hot big bang are in good agreement events in the hot big bang cosmology if This era, like the pre- by relativistic relation neutron to proton driven decay are processed into 4He nuclei, with trace quantities Important annihi- component which could effect primordial events take place. rate k/R the time-temperature Since m, - mP = O(MeV) 3 until no observable The QCD phase transition inhomogeneities At the MeV era many important Figure drops by annihilation decays, again leaving ;,;. i: : : ;) ,:. :_ ‘. ., of the light elements. vious ones, has the expansion density, boson inflation) excess now becomes an important it is first order may lead to density abundance rapidly the QCD phase transition a baryon If the lliggs today. particles these Any relic abundance After lates with or attribute the W, Z bosons leptons. insignificant I know of no feature leads to observable at which and charged ep -t Hy Once neutral and phoThis dilute takes place hydrogen now free-stream is and are the present era. smaller than O(lOMeV) we havepB = n~rn~ - 10-9T3mn :- :. ,: :, :’ ‘: and p-, = n, < E, >- T4. At T = lMeV,p., p7 = ,DB when T - 10-9m~ drops until an era when R/R RT = constant, is driven by the hydrogen Einstein’s equation, nated era. If k = 0 this behavior curvature dominated The plasma continues radiation mogeneities last scatter in the baryon stars must have evolved present a late phase transitions structure which cosmological critically distribution during this energy density so it is sensible sentially identical native classification underlying (III) particle Dark together galaxy many aspects: energy density Elementary of the universe, as to its nature. of the dark matter particle active candidates which scheme for dark matter; one which is motivated that one component universe of dark matter [3,4,5]. may be fairly should be given u(r) The form of this dark matter particles, such as monopoles, chunks of solid material, etc. configuration, visible = GM/r’ where From the and it is frequently about dark matter be cool stars on distributed over the of particle onic density particular burnt examples be in clouds provide only the rotation speed mass. In fact constant Thus one values of n(r) to a spiral galaxy, that of as r out to very large distances, the first Examples or perhaps not revolutionary. thought. is related planetary it would larger of how such objects option are formed are, to varying be interesting (4He,‘Li) to ask would of cold for particle mean that the baryonic asymmetry, simply is larger because we do not is a mistake: formation of so the nudeosynthesis [ll]. As the bary- reaction rates are (2H,3 He) since they are more fully whose abundances range of Rn from a comparison :A.. .:;: degrees, not understood. on Qn comes from big bang nucleosynthesis mass nuclei question dark matter sided lumps to the cosmic baryon To ignore the baryonic at the MeV era is increased to the higher important of baryonic It would simply This depletes the low mass nuclei crease. The preferred -93- physics low luminosities abundance,which One constraint increased. from the should that the halo mass is an order of magnitude all types of stars and galaxies It could be a Since the galaxy out to very large P (up to 100 kpc). If this were the dark matter but certainly have an understanding energy, topological The H clouds distant component increasing is: is it baryonic? with than previously These mass. From the viewpoint into have M(r) estimated center and of the spiral arms. M is the galactic This has not been seen. It should limit mass of the galaxy, the dark halo. that near the galactic and since these distant to the total by u’/r axis. and since more by the and each of these classes has many spiral galaxy. the symmetry for many spiral galaxies an alter- different they yield masses in the range of 10” - lOi* there is an additional evidence vacuum about the visible This suggests for dark matter is not known. beyond 4. Together cx r-i/s. than the visible are many 15 kpc from the component have been observed give es- There such as our own. areas of solely from its gravi- smootldy galaxy depends and indirect ..‘ :; it is the lo arms of stars; the sun is in such an arm about center rotate freezeout to groups of galaxies, is of most importance. There is also a spheroid in Figure solid material. There is direct evidence as our own galaxy is the disk con- clouds, which extend physics, is inferred interest of dark matter There a small contribution by Matter gas of elementary center. which to a spiral a stable gravitational physics. whose existence with galaxies of quite differI will make a few comments detection expects can be divided hot, warm and cold. In the next section I introduce the spiral galactic need be known, candidates for example. of direct times the solar mass for a typical and in baryons the clustering taining are sketched of the universe. produced components hydrogen Hence the inho- fluctuations is associated and spirals, the viewpoint density visible galactic of this background perturbations and from cal dark matter We know this galaxies elliptic, . is spiral once the peculiar clusters, dwarf, on the case of spiral galaxies [lo], which is of particular domi- the origin of this large scale those dark matter effects is called dark matter. defects ent types: if R < 1 then a Lo have is one of the most only a few properties all scales from the solar neighborhood entire today, or large density of the dominant Any form of energy density tational The photons could be small density It is a field with behavior. three such groups: However to be isotropic for. seen at T = O(eV) to group There is evidence that dark matter enters - Ts12 and to a very high degree. is dark there are only speculations of clustering DC T and this matter this last factor of 3000 in redshift we see the universe on the nature viewpoint until today. at T < 1eV. Understanding research. Since fi t*13in at the era when T = O(eV). The seeds for this inhomogeneity or dark matter rest mass. background has been accounted have their p-,/p~ IeV the universe (2.4), gives R - at 1eV was homogeneous of the earth pn, however Beneath R - t is reached. era with because we see the 3OK microwave motion >> = IeV. consequently of big bang nucleosynthesis in- ,, .I,‘,.’ - with the observationally inferred are many uncertainties and consequently known one cannot dark matter It is widely believed underwent produce that process history which There increase (d/R)’ presumably :. to many times Gp dominates initial condition amount of entropy I will cosmologists. describe for the rate of expansion Direct observations also and reheats the way in which of the universe; today era) while R-’ by an enormous incrcnscs amount. for evolution it has the tell us that the curvature times p increases first as T3 (matter required scale factor era would problem. equation dominated : reasons ie to why this quite bizarre term cannot be larger than about ten times the energy density As we go to earlier : than the This era is ended by some very non- releases a stupendous - Gp - l/R’. T4 (radiation that all the larger [12, 131. This inflationary (RT = const.). solves the “flatness” Recall Einstein’s form at some temperature, are several theoretical is attractive inflation there observations, began an era when the Robertsor1-Walker very rapid cooling adiabatic However, of the various use this alone to rule out the possibility a very rapid the universe. is a few percent. (RD,~~ 1: .l) is in fact baryonic. weak scale, the universe R(t) abundances to do with the interpretation term: l/RZ~lOGp. dominated era) then a~ only as T*. Thus at very early In fact at t,he Planck to reach the present universe scale the is (3.1) Figure 4 A much more natural Schematic that view of spiral galaxy. case the universe R = t. Furthermore Since p - Thus universe is reached open universes might the l/R2 RT = constant, P/G at a time to avoid This is avoiding term negligible initial would be for this ratio to be unity. become curvature - - - 10-l’ this problem just implies = l/R This In or 7’ N t-‘. in this universe n(7’) t.cmperaturc - of the implies this is not our universe. set k = 0 (I took k = -1 that, You in the h- = 0 is the same fine tune as making wit.11 Gp. is sketched in Figure at T - MP. A curvature takes place, but long before the present, era, the l/R2 -94- condition sec. Naturalness certainly to this problem Gp - l/R’ lOem. R. the issue: putt.ing solution condition l?/R the initial to N T&’ compared dominated: 12”p’P we find that become cold very quickly, The inflationary natural condition when T = To = 3”K, argue that above). with II” and pC - T2/Mz. initial will rapidly curvature 5. There is a dominated era then term is made very : :_ : ‘-: :. -.: -:. . small by inflation: recall that inflation since T drops rapidly during inflation p is dominated It is true that the radiation of inflation After than R-’ GP I I percent. c: energy density. drops faster a fine tune. Hence inflation Known gives dark matter In view of the theoretical it seems to be a small step to assume that further particle nucleosynthesis physics this is the crucial too small. cosmological problems new particle physics step: standard since the deuterium Inflation beyond the standard which contribute perhaps tic scales (I’ll call this the diffuse dark matter physics which is responsible it not only There should component). solves considerable be new exotic 90% to R and are not clustered for the vacuum is of allows 0~ = .I, but it dictates model. stable objects dark matter is then three orders exciting: problem contri- motivation from the viewpoint abundance is tremendously such as the flatness a new idea which plays the role of inflation In this case there is no need for the diffuse Figure ,_ ,_. ,. we are now in the era when they are It is also clear that we should tread very carefully: t t, Inflation that However, > to t1 to radiation out there and that R is really very close to unity. the particle :. is constant. on galac- There must also be energy which drives the inflation. R-2 I I pv which Gp subsequently to R are a few percent. but 0~ = 1 really is excluded I I that i.e. it gives R = 1. give an R of ten to twenty of magnitude think is not correct; pv - ‘P does drop, however at the end because pv is converted The visible contributions from inflation, That energy density indeed this would itself constitute Rm2 today, butions increases R. You might Gp is much larger than Rm2. While there is no reason to expect comparable, Gp >> by vacuum energy density it is replenished inflation rapidly p would also decrease catastrophically. 5 solves the flatness problem. R = 1. component of dark matter. In this dark matter. exotic, for. It is also worth and both forms are worth Both theory issues. dark matter homogeneities created of observation theoretical question nucleosynthesis era with are predicted sufficient homogeneity it seems that in a small region of parameter with the standard currently size to radically assuming model. stressing under or that the of nucleosynthesis. have many interesting at the QCD phase transition dances which It could be baryonic also relies on our understanding and interpretation An important searching invents does not require case there is still the issue of the clustered case for exotic -95- suppose somebody but which study unresolved is whether in- could have persisted to the alter the conventional abun- [14]. This is not yet resolved; space s1B = 1 might yet be consistent :, .. : A more radical element question abundance is whether dances for 2H,3 Hq4 He and ‘Li particle decaying is rekindled during the keV era to produce ble exotic particle or exotic. it is important Such late decaying sLi than the standard It is possible complicates model, that over an unstable a higher The clumped in gauge theories I will divide their typical contribute about .l to R. They components contribution be something If there could be baryonic to R is certainly like relativistic is a dark matter in the earth? how stars form in a galaxy. occurs only because the components gravitational molecular kinetic potential collisions energy is radiated gravitational the earth collapse to dissipate particles this kinetic the galaxy. by dissipating for example) their are sufficiently Presumably energy, they have no option particles particles, gas cloud is in the halo, 7~. This allows a cross section from baryons as large as a millibar*, a few simple estimates of event rates which of our halo is composed of particles curves of our galaxy and other observations, of halo dark matter to try and observe from is .3 GeV cm-‘. the nuclei this enormous of the detector, Thus with speeds of Suppose flux. that If the dark matter of mass mu, of detector of mass the best estimate at the earth is N 107n-2s-‘(GeV/nz~). cross sections are non-relativistic and only build For example is crucial the rates could experimental with with some cross is be enormous. challenge. (3.2) However, detect- Since the dark matter p = 10e3, their kinetic of this will appear for any been performed approximate excluded Most interesting is that the that they are unable orbits with energies are low background necessary annihilation -96- 1 < mn this region Ge detectors is to Searches have which have mssses of < 10 GeV, which is so interesting can be read from such as a Dirac neutrino, equation (2.15). Q is a known 6. has not yet been is straightforward. cross section oA for a cosmic relic to survive R E .I today candidates, The challenge of O(keV). designed to search for double beta decay. The is the region The reason that interesting recoil. region in the mn, os,~~ plane is shown in Figure excluded. and contribute Since they are dark, these particles as nuclear which can measure energy depositions O(11Cg) and which were originally the reason why but to move on bound a fraction detectors already on de-excitation: of dark matter weakly interacting This is quite reasonable. For large enough can sink in the energy. This dissipation quantities :‘ this it is useful to of a pre-stellar modes which give photons enormous dissipation particle (g$) =(2.1~:m2) (g) (Z). it should of exotic To understand (HZ molecules away from the cloud. scatter with ing the events is a considerable composed A condensation of a dark matter os,~, then the event rate per kilogram which energy. to form a stable dense object. and sun do not contain halo dark matter around of the cloud excite rotational The components To avoid clumping halo in our galaxy why do we not see these particles remember or vacuum cross sections for these particles for a halo stable against scattering if the dark matter a detector particles section velocity particles the flux expected up to R = 1. Such a large, not baryonic. particles infall requirement : escaping from the galaxy. or exotic. scales could contribute on that the scattering this section From rotation we build are elementary this is the typical The clumped on galactic are clumped weakly . . . .: be longer than the age of the galaxy, for the local density into two their interaction a weak cross section. lo-sc Faster speeds would lead to the particles smooth mn. which could survive If these components speeds will be O(10e3)c, should could be expected we know Presumably they are often called WIMPS: that the mean free time for collisions I will finish certainly these components into a galaxy. are not clumped This to think A sufficient < afi > for dark matter of and those which do not. components U(@,). hardly but it is not unreasonable: scales and hence are non-relativistic. particles I?‘, is baryonic abundance has several components. formation, the big bang and would be dark today. galactic primordial and this can be searched for [lS]. the dark matter clump It is a mistake simply interactions. of the weak interactions; massive particles. is really one. Form the viewpoint or not the dark matter is that interacting it is not clear that a sta- schemes predict which arise quite naturally classes, those which physics, have strong or electromagnetic strength abun- have an exotic to know whether issues such as galaxy of many objects acceptable showers in which nucleosynthesis of particle should be preferred cannot the main era of light to reproduce with Rg = 1 in schemes which [15]. From the viewpoint of observation we have identified in the big bang. It is possible The the big bang For several function of nn -. :-: ::: :‘. c. ._: : . and hence one can predict mn and it turns out to lie in this region of a few GeV. Furthermore, if the annihilation by a crossing relation nucleus N : US,N. Putting the event the dark matter depositions large. (3.3). to directly Typically The problem Future and will explore explanations. detectors Figure 6 with seeing these events can be this crucial Excluded responsible region region in the mn/as,o. corresponds overburden. plane assuming for the local dark mass. The upper to the cross section The plot is taken from of a double beta decay Ge spectrometer. a Dirac neutrino with conventional for scattering Ref. 22 the particle is Scheme For relics can be classified on the earth can have a variety from of the remaining the rock and results from use The curve labelled vn is for transitions the signal is too feeble. Cosmic according Relics to the way in which equilibrium and they underwent three classes were produced and were never in thermal and the classification they are pro until today. (IV.l) Plasma relics are elementary couple. no - That All relics of photon is still relativistic plasma relics which for dark matter, is excluded Plasma today. greatly thus destroying they cannot relics which and would clump. could therefore are relativistic density is no Z’,” so no - is the best illustration - when they deTz, and today 10-s. The three of a plasma relic If the masses for v, are less than L?” they are also are relativistic Hence although not be clustered, We discuss each class in turn which number background since they would cleosynthesis. today particles their today. unless there were O(10”) of nucleosynthesis, Relics in the table at the end. mass is less than To then p0 - degree microwave which equilibrium. process. events such as phase Relics is at decoupling 7’2. If their a freezeout in catastrophic scheme is summarized Plasma weak interactions. -97- of I am aware fall into one of six classes. For three of these classes the relics were once in thermal edge of the shaded energy of to such low energy region. detect dark matter duced in the big bang and the way in which they survive which -+ QQ, then cross section from it is either that os,~ is too small, nan is so large that the A Classification Cosmic eg 00 will be sensitive event rate is too low, or mn is so small that (IV) matter, the scattering The lower value of mn decreases the kinetic particle. Our failure to calculate these values of mn and QS,N into (3.2) one finds that rates are quite seen from equation process is to ordinary it is possible Such plasma such species. increase relics are not important This bizarre p and therefore the successful predictions k/R of primordial plasma relics which are still relativistic contribute today nuwill much to R. have masses larger than 7’s would Any of the three neutrinos make an important possibility at the time contributions be non-relativistic could have such masses and to R. : .: (IV.2) Freezeout This important are particles were made recently Relic case was discussed the reactions which contribution change their a freezeout as Dirac neutrinos Consider baryons into a bound Although these candidates, . with neutrinos shadow QED. carrying shadow arises with l/A”. energy of shadow quarks These baryons If nb is the mass of the shadow Asymmetric Asymmetric greatly number Dark matter would reason that the visible matter abundance In particular, of the surviving way below what of the antiprotons would produced abundance asymmetry. Protons that the dark matter a cosmic asymmetry solution have survived until today for precisely while the chemical potential major the minor component, have survived with seen in cosmic rays survived directly initially component zero chemical which are initiated does this oscillaton directly be an interesting which temperature while signature the rest; ‘00 = nm. expands None aho from the big bang, they If 4 has strong V. easily, so the equation is strongly damped. the equation of motion In the limit that -98- physically? governing On the other it rolls to couplings the damping represents Of course, equation density hand, if 4 has only particles (4.1) would survive These oscillatons until Because the oscillatons a uniform carries had only a small contribution today. no momentum. correct: gets diluted However, What are the same at distribution (4.1) is not quite due to the expansion. and the can be neglected the field 4 creates. of these particles it t.he evolution will have small damping it is a mode of the field which in the oscillaton the number which by the phase transition has a time dependence relativistic in for for this field at the phase transition 4 = g everywhere. represent locations energy density is annihi- potential. I$ = 0 everywhere, of the potential where m is the mass of the quanta a chem- determines would How- (now much higher c$(Z, t) = 0 + (b@P the same including which the solar opacity. neutrinos relic buildup To a phase transition will be oscillatory. all spatial calculation in changing in high energy a freezeout will prevent Relic is in baryon did. [9] freezeout While potential very weak interactions has been [17]. temperature the high energy solar by the sun, xz + to be important can radiat,e the energy density asymmetry the central in Fig. 7. then at some critical the minimum that it has done the same for some other quantum It is fun to redo the Lee-Weinberg ical potential. anti-particle It is very plausible we know native B, so it is reasonable number. relics whose survival because of a cosmic particle relic: lepton will occur: particle so that R,, N .l problem the con- relics could a scalar field d(?, t). If the zero temperature of 4 has a solution are the best examples. an asymmetric zero shatlow the lightest an/m:, Relic relics are freezeout enhanced and electrons electron, charge, then e’Z’ -+ y’y’ has < ~AZ) >z is as sketched does not deplete produces ....:--_ -_. relic candidates. Oscillaton Consider U(1) gauge group: the solar neutrino than usual solar neutrinos) (IV.4) rate which them up in the sun, masses such bound of the sun, decreasing may itself result some freezeout can annihi- could have built t,hat for certain opacity is au asymmetric by scattering Over the age of the sun sig- relics so that sz + the reaction concentration particles the sun. particles can also be trapped ever, IZ -+ . If A’ N 300 TeV these shadow a world with a new unbroken m,, 2 a’300 TeV, again taking (IV.3) thus solving (no asymmetry) which has an asymptotically mass O(A’). < ~AV >- one could imagine to the thermal of a sufficient shadow &CD, of dark matter It has been found contribute such bind dark matter as they pass through of the sun and decreasing they are not arises if the halo dark matter they are asymmetric centration. so that R, N .1 are quite plausible, orbit concentrations providing dependence possibility The sun can gravitationally nificant the would give R N .l even if there were no cosmic D’ asymmetry. Similarly lated Their relic. 5’ which acquire + x’ relic. t,han lo” TeV. For which gets strong at A’ causing confinement q’ into shadow baryons 1at.e int,o r’ : Ui? to be lighter photinos a new version of &CD, free gauge coupling freeze out. cross section < ~Az) >E G$mz results with mz N O(GeV). freezeout densities A very intriguing relics when Since < gnu > ZZl/n22 even for a strongly or supersymmetric the only possible number relic is expected with a weak annihilation for halo dark matter Freezeout (2.15) f or any such species z. Although cross section. particle, a particle sections. and are non-relativistic in R,, their is almost always implicit nxass does not appear explicitly via the annihilat,ion equilibrium comoving to R is given by equation interacting in the previous which were once in thermal in high energy collisions. The of 4 quanta at as the universe n - l/P, so do even if these non- to p at the phase transition ., :::..: ‘_ po(T,) << ~(2’~) they could easily dominate by today era. This is illustrated 8. The most well know example dominated an oscillaton is the axion. Goldstone boson the potential parameter results symmetry, for the symmetry they from the breaking at some scale f. of a global The QCD U(1) result of breaking, from V, is f. symmetry However, breaking with symmetry, interactions 7, V, - A4 where A is the QCD parameter, of Fig. frequently; if T, falls in the radiation In the absence of QCD the axion is in fact a massless which the Peccei-Quinn in Figure i’ :. :.-._-- and the order oscillatons a weakly :. ._ ._ produce occur coupled very scalar, and are much more general than the axiom (IV.5) Secondary Relics So far we have assumed that relics are stable, or at least that their lifetimes sre longer than so far could the age of the universe. have lifetimes stable decay products for obtaining I will call secondary Sl = 1 in a smooth None of the first relativistic, today potential for an oscillaton via small today which is bot.h relic could be primary. The inflaton gets suppressed by exp(-l?t). example, is an oscillaton. How- because it is unstable In this sense, everything to t.he decays of inflatons to R. they clump. violating interactions. which plasma photons radiation the majority which theories although One example, relics. e* and demonstrate The e* lose energy However, electromagnetic supersymmetric 9. This gives e*, v as secondary from the background background consider we take to be the photino, of the relativistic significantly -99- interest size clumping. a secondary its oscillation R parity the evolution (< IO-‘). matter to describe which t,rated in Fig. relic galactic of secondaries. As another Typical cosmologically is a sec- reheat.ed t,he after inflation. superpartner, 7 without even if it came from a non-relativistic relic, we owe our existence universe Figure distribution Their They are of particular (4.1) is insufficient so the oscillaton ondary relics. and gives R = 1. However, There are many examples ever equation any of the relics considered few classes of relic lead to dark unclumped relativistic However, less than the age the universe. today X and y rays observations rapidly where the lightest long lived does decay ? + e+e-L/, is illus- In this case we can follow that they cannot by inverse Compt.on contribute scattering ey -+ cy. Once the e’ are non-relativistic of the photino rest mass has ended up in would be ,Y and y rays. We know from that R in these components are very small As usual, one finds that the big bang is a tightly constrained frame- :.-. :. .’ .,_ .:. .; ‘\ ‘A e- e violates Lad RG\ < Figure Figure Temperature baryons. evolution The oscillatons 8 of p in oxillatons are produced Photino and p in radiation at T,. At ‘I&, decay via lepton ” 9 and R parity violation. and prodiot,m and phrva are equal. -_ :: .. .I -lOO- .,.~ . work. The majority do not work. of new particle (N.6) Soliton By “soliton” Relics has a potential stable defects: consider V(4) = X(4’ field 4 takes on a vacuum - 2). the minima. This domain wall contains made complex and the theory J~(m’4 - 2’)‘. In this case a pattern configuration 8(c). as shown in Fig. to be localized in the monopole A simple a potential example The calculation in particle is a theory the U(1) V($) Suppose that while at ‘I’, 4 makes a transition where it vanishes. length the horizon there will typically The subsequent However, E3 under for domain where rapidly density p today evolution certain is n,o(T,) is dominated as shown in Fig. conditions by domain other contributions one-dimensional which has to I$1 = o everywhere of 4 is random except on scales of Hence, as an order of magnitude volume less than at T,. of defects can be very intricate. pnw - R-l, p. N R-’ I know of no complete walls or cosmic strings. Cosmic strings and PM N cosmologies Domain walls quite unlike our which 10 stable defects ( a ) a two-dimensional string the arrows represent for a phase transition to p and lead to universes own, unless they can be made to disappear. Topologically - 2). N Ce3. Since C is certainly of the collection walls, strings and monopoles. overwhelm at a point be many defects per horizon simplified A group defects is not straightforward The direction f, of the phase transition. the defect number be gauged. at T > Z’,,I$ = 0 in each of the above examples, the correlation Figure of this field symmetry Simple estimates near the defects estimate should = in a internal = A(& rates for vacuum of V(4) result of three real scalar fields ($iv2(ps) or in the big bang. in the big bang can be made. then In fact for the energy invariance: B, then If the 4 is now field configurations when a non-Abelian of production collisions phase invariance case the defect occurs which has an SO(3) near region a U(1) 8(b). degenerate 4 is not at either field energy. of vacuum which takes place such that the wall at which on the line defect arises in gauge theories is broken, has two discrete localized processes [I& a real scalar field 4(Z,t) This potential by a domain Some s&ton and monopoles value +o near region A and -g will be separated monopole and which is produced walls, strings 10(a), if a phase transition these regions string domain a theory which contains As shown in Fig. t,opological localized This is not the same as other uses of the term. relics are topologically 191. For example cosmic relics simply quite unlike our own. I mean energy which is spatially at a phase transition. minima. physics ideas for creating They lead to universes self-intersect -lOl- S (c) a point monopole the direction domain wall (b) a M. In csses (b) and of the scalar field in internal (c) space. “. and produce loops which be problematic. one finds R,Xu/Mp. provide can then disappear by gravitational radiation may not At any era p. then scales the same way with R as pror,.+n. For o of 10’s GeV it is possible that the string the inhomogenities If monopoles about which galaxy clustering first are made at a very early phase transition must be depleted by a subsequent era of inflation may density the universe will not with magnetic charge and mass near the grand unification scale is depleted just enough to be the dark matter a flux of monopoles today. This would been experimentally monopole which produce excluded. carries It is possible have become topological stabilized solitions and which logically nuggets I describe In Fig. assuming matter There are regions nuggets. nearly that the picture medium the QCD phase transitions phase transition it is first order, as indicate phase are nucleated Since the vacuum would by lattice equal numbers Tc,ns of quarks and antiquarks, However, and antiquarks II(b). c << at T, is maintained. When the phase boundary be swept along with although if the critical must annihilate N np z (Tc.mg)wP-~= equilibrium bubbles 11(a). quark phase. plasma because in the hadron transport / had The cosmological hadron phase at The q?j annihilation quark can excess tends to number across the boundary energy must be found to create the baryon degree it is therefore energetically for the quark excess to remain 11 QCD phase transition (a) nucleated bubbles of into the quark plasma (b) shrinking bubbles of phase. :. .:I .. :.: _. .. the quark excess. This is because for baryon phase expand Figure :( energy over large distances Now imagine following favorable Subwithin is say 100 MeV moves into the quark fluid the quark the boundary. The bubbles there was a quark ex- temperature T,” (see 2.10). 9’ @ is lower are collapsing The original At homogenous half of space is filled by the hadronic as shown in Fig. cosmo- calculations. energy of these hadronic occur to vv via the Z, and since neutrinos thermal proceed in the previously is that regions of quark phase which cess of one part per billion. the many quarks 9/ H 63 These non H how the QCD and coalesce until the hadronic of false vacuum or charge. than in the quark phase the bubbles expand as shown in Fig. sequently, has be a The most well known exam- which could arise during of hadronic quark gluon plasma. will collide which could below [20]. 11 I sketch first small bubbles relics. by the presence of matter I will call false vacuum ple is that of quark at the earth the dark -: Z” . some other charge. There is a second class of &ton which that .A:. ‘.il :, ‘j .k., : occurs. their number otherwise evolve to the one we see. It is not possible that a monopole Today network to go mass. To some in the -102- y. ” .., quark plasma. If this e&t shown in Fig. 11(b) will eventually pressure of the quark at temperature is quite powerful excess inside the bubble. just even if quark possible category eflect of the baryons. were formed However, at zero evolution from Jecoupled 7, to T = 0, rather nugget of another phase transition n > T,, they it is the universe issues. which the need for a cosmic would The standard we observe. Most additions to the standard the correct restrictions an enormous the Table. Plasma particle of candidate and freezeout equilibrium which relics. P, e CI’ violation Abundance UD New quantum asymmetry and there is Oscillation Very weakly cou- pled scalar description New phase I3ifficult transition. \Neakly couplet 1. relics have been proposed. these cosmic relics, An approximate jion ,Other symmetry 1llcts (including asymmetric) with the plasma of the hot big bang. techniques Oscillatons and solitons are directly associated field theory, and occur in a surprising in the Table, understanding are planned turning there for the future. point particle Soliton in which are many variety with in cosmology. physics beyond Defects from phase Domain New phase Direct sear& transitions walls transition Gravitational with localized energy. Secondary phase Strings ing Monopoles Gravitational NugRets ation of forms. ways to search for the various Several searches have been done for many years and new ones with be a major y, X ray signs. Is. I have introduced relics are particles The discovery It would the standard TABLE novel A cla.ssiIication scheme for cosmological of any of these relics would also give us solid guidance decay prod- of X1 may giv e Nevertheless and it is summarized as 4xion to y colnver- of 0.1 N R N 2 places conthe relics. I direct detectic number give cosmic relics do not give which generate of I by cosmological arise from the decay of any of these three types of pri- in the quantum As indicated model which The requirement scheme to describe relics are particles relics. m > To determined physics does not lead to The cosmological detectio 11cts physics gave rise to an era of inflation, on the interactions were once in thermal transitions abundance. number a classification mary if particle P I 1etection grew very rapidly. them with siderable apparently I Cect ,veak scale sun or halo. a simple and elegant is the need for baryogenesis relic to be the dark matter. also be more acceptable when R(t) gauge theory There VW physics at f mm annihilati Summary on cosmological IVM.D contributes in which to study the effects of various gauge models of particle as low Bosons Ion-relativistic Lsymmetric provides I )ifhcult e “. : : froze out while to the dark matter. The hot big bang model of the early universe %z,v light >articles eg ;oldstone that it seems that quark nuggets are not the dark matter, some false vacuum I temperature, it has been argued I )ctection ‘ossible mplications at Z’, and even if they were stable at T = 0, the cosmological [21]. While framework 1Examples A quark nugget has been formed such nuggets would be stable decay to ordinary nuggets that 7- Zharacteristics n < T, they do not survive evaporate by the stabilizing T,. We do not know whether they might then the collapse of a quark bubble be prevented in model. -103- relics. S lensrad- 16. L. Brown References 1. L. Okun, Proceedings of Neutrino ‘88 Conference, Boston 17. W. Press and D. Spergel, MA, MIT-CTP- 1606 (1988). 2. S. Falk and D. Schrarnm, 3. J. Kormendy and J. Knapp, 117 (1987); Universe, J. BahcaIl, Jerusalem 4. J. Binney Phys. Lctt. 79B, 511 (1978). Dark Matter T. Piran Winter In The Universe, and S. Weinberg, School Volume and S. Tremaine, Gala&i 4 (1987). Dynamics, IAU Symposium Dark Matter World Ch. and D. N. Schramm, Fermilab-Pub-88/20-A. Astrophys. J. 296, 679 (1985). 18. T. Kibble, J. Whys. A9, 1387 (1976). 19. J. Preskill, Phys. Rev. Lett. 43, 1365 (1979). 20. E. Witten, Phys. Rev. D30, 272 (1984). In The 21. C. Alcock Scientific. 10, Princeton and E. Farhi, 2.2. D. Caldwell Univer- et al., Phys. Phys. Rev. D32, 1273 (1985). Rev. Lett. 61, 510 (1988). sity Press, 1987. 5. Proceedings fo the Workshop 1988, Ed. E. Norman, 6. S. Weinberg, Gravitation 7. M. Turner, Proceedings mond and R. Stora, 8. E.W. Kolb, Cruz, Wiley Proceedings School, 1985, Ed. P. Ra- Holland. of the TASI in Elementary 9. B. Lee and S. Weinberg, Dec. (1972). of Les Houches Summer North Berkeley, Scientific. and Cosmoloa, 1986. Ed. H. Haber, 10. V. Rubin, on Particle-Astrophysics, World World Particle Physics, Santa Scientific. Plays. &v. Lett. 39, 169 (1977) Science 220, 1339 (1983). 11. R.V. Wagoner, W.A. Yang, M.S. Turner, Fowler and F. Hoyle, Astrophys. G. Steigman, D.N. Schramm J. 148, 3 (1967); J. and K. Olive, Asrophys. J. 281, 493 (1984). 12. A. Guth, Phys. Rev. D23, 347 (1981). ; 13. L. Abbott and S. -Y. Pi, Inflationary Cosmology, World Scientific, 1986. .: ._ . ., :. 14. J. Applegate 15. S. Dimopoulos, and C. Hogan, Ploys. Rev., D31, R. Esmailzadeh, 3037 (1985). L. Hall and G. Starkman, Phys. Rev. Lett. 60, 7 (1988). -104- ... -SOI- -9OI- -_ -. . . . _. 1 ‘lapour pr~pue$s aql puohaq qshqd plno~ sluauxa+bal 9108 ‘sseu~ seq ouynau aqg 30 hysgay hq hluo paysyzs aq aq$3! h[qeJou tsour ‘smsrueq3aru 30 laqurnu 8 hq paysyzs aq uw luauraz!nbal s!q~, ‘I- h[l>vxa aq louue3 ouynau ayl ‘uog!ppe ul .sal3!ged eue~o[eyy ale sougnau 3! a[q!ssod s! qyq.+t ‘suo~dalye pay+osse ou q?!~ palr+!rrraare suo$da[ OM$aau!s ‘panlasuo:, aq lou gsntu JaquInu uo$daT ‘~n330 o$ “Odd ~03 s?uauraIybal OM~ azv alagL .slualln:, papuqq-@y pu-2 ‘%u!x!ux pue sasswn ouynau ‘uogaaIasuo3 JaquInu uolda[ arz heap vlaq aiqnop ssa[ougnau u! sanss! ss!shqd luellodur! 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Introduction The ueutriuo only is distinguished weak interactions. decays. Like other v,,, and I+ associated type of neutrino are concerned concerning neutrinos with is known neutrino addition it is quite electroweak massive ably providing with theoretical it clear that theoretical natural as one introduces the dark physics matter discussed sources, in particular, In the first lecture seriously evidence 2. Mass the gauge theory is that on theoretical Terms do not interact links by SU(2) proportional ativistic all fermions invariance. Conversely to the SU(2)-breaking, transform fermions field theory the right-handed The existence particles embodied fields $~(z). particles of left-handed particles by fundamental in the CPT theorem. The usual Dirac principles of rel- One can similarly field G(z) is related by try (2) flux In conceivHall. A techuical Also point of importance from the charge-conjugate is that one can define a right-handed field of +L of neutrinos the sun. ideas and then I will turn mass. will be gauge theory; are introduced and so must antiparticles. of right-handed left-handed the minimal by Prof. gauge theory. and so must. transform the left-handed quantum Here br, annihilates neutrino in Gauge Th.eories discussion the existence 5 ev- on new physics. from neutrino A crucial fernlions as doublets. as singlets. to the right-handed This is the field which, when expanded, and creates left-handed particles. and T is transpose; the particular in partic- the correct trausformation feature emphasize that alternative way of writing as massless chiral The reason for this, of course, is that left-handed which implies evidence in cosmology, change the detected x U(1) electroweak dard weak SU(2) interactions bidden window in the lectures concerning of our theoretical SU(2) term and di creates right-handed We we will beyond as a small mass. Thus neutrino the neutrinos I will concentrate and prospective ular, the standard acquire could be of great importance from astrophysical fernlions where the sum is over momentum Each experimental However, physics as a possible mass could fields. vc, partner. in favor of a non-zero are massless. model that neutrinos in particle neutrinos The framework “flavors” ideas and experimental argument fields may be expanded it has e, IL, and T respectively. there is no defmitive all neutrinos effects of neutrino t.o available to exist in three chiral of weak write by making mass is of interest leptons in that as a result mass. It may well be that standard are believed the charged idence and no compelling to show that fermions in the laboratory to be much less massive than its charged in these lectures I must start mass. from other elementary It is produced fermions The free left-handed of (Weyl) Lorentz right-handed anuil~ilates right-handed anti-particles (Here C is the Dirac charge conjugation way this is written property.) fernlions Note guarantees matrix that 4; I use the subscript are annihilated, but in fact 4; +!I;. In the same way an alternative has R to is just an to v& is have the stan- d$ = C(4dT. Right.-handed The usual mass fernlions is for- the mass of all the usual fernlions is It. is asual t.o imroduce a set of fields in, introduce however, interactions, and anti-particles or weak, scale. 110 $Rj -126- without we don’t and another set. $~,(r). know the difference so we could (and sometimes loss of genera1it.y. (36) Before we between do) start only with particle a set $~i and .:,-_ I -. ::.p.:. ,_.:: _. -. Let me first acquire their handed singlets review mass. how the other The fernlion ferulions, quarks and charged fields are the left-hauded doublets leptons, and Z becoming and right- the fermions massive. One also introduces ) , (2) Y = (Doublet where i = 1,2,3 charged lepton, associated is the generation and Vi, D, are the quarks. SU(3) of QCD.) will be discussed in detail The interactions are dictated The question neutriuo (We ignore throughout of whether The Yukawa the original interaction chi- is SU(2) @)r(Duubld FL)z(Singlet FR). (8) and Considering color and the to inlroduce fields. only the coupling involving the neutral a0 we have the fields NiR later. of the fermious with the four gauge bosom by the gauge principle weak interactions. IV, aud Li represent index, Dirac between invariant (4) F -kyUiR,DiR interaction and the Higgs bosons as a means of converting ral massless fields into massive (:f a Yukawa In particular c of SU(2) x U(1) and lead to the usual electromagnetic the charged g WA current ‘%;r. TX D,L interactions where the sunl over repeated indices is implied. Using Eq. (7) and setting and have the form (5) + h.c. we have 1 The fields of Eq. (4) defuse the weak eigenst.ates, be the mass eigenstates. leading to the standard assignment To make a sensible the standard bosom version The right-handed theory fields of electric it is necessary of the standard which ss we shall see may not have only U(1) interactions to introduce the Higgs bosons. model a single complex doublets In of Higgs Here ‘p represents is introduced tion with /m+\ (64 The antiparticles Comment: also form a doublet IIiggs boson 0” acquires a vacuum expectation x U(1) symmetry (124 breaks down to the electromagnetic the physical Higgs boson field and Y(q) the fermion for the quarks interac- and the charged Weyl In Eq. fields. (12) the fermion Considering fields the leptons, are actually for example, Dirac fields rather one obtains directly ., I, ..: : . : r., ,. ; - the aid of Eq. (2) value (VEV) <w>=v the SU(2) A4c = h,jvLiLj. ‘p. The A& are now the mass terms from Eq. (9) with the neutral (126) 1eptons. than When A4u = g*j*UiUj charge. (7) U(1) with provided W without -127- the matrix h is hennitean. loss of generality In fact one can always choose h,j hermitean by redefining the basis for the right-handed fields. they are required D, = (v,)jdt in many extensions of the standard to give neutrinos a mass term completely and quarks (12) ) (Eq. equivalent Uj = (Vu)jt% ._ : :. ;.: + This is referred When we Eqs. (14) into Eq. (5) we find to construct WA~LjYXujrdL.r to as a Dirac can be combined term. mass term since, as discussed to form the four-component a mass term We ca.n coustruct Dirac where U is the famous Note that in the case of neutrinos here as hermitean), thus 18 arbitrary these end up as observables: (three in its gauge sector and ugly in its Yukawa (16) d (KM) two arbitrary parameters quark 3x3 matrices for the quarks, Notice The standard model which (only two coupling constants) mixing (chosen vation for the other violate the total lepton number but only 10 of sector. For the charged leptons is so economical becomes with and extravagant we have similarly where the l’, are the usual e, p, 7. Because the neutrinos standard model we can redefine them by operating the lepton (or degenerate analogue massive) Let me return model we never On the other the doublets the lepton now to the neutrino. them. introduce on the original of U is just the unit matrix. neutrinos the fields hand the symmetry remain mixing Therefore, way the Majorana mass called weak isospin matrix with leptons of Eq. (4) may suggest that there really and quarks should to lepton by one unit This term - N(L+)). does However, charge since it is not associated of neutrino number mass the fundamental violation. (since it annihilates to MD which violates a Majorana - N(N) changes the by charge conser- for neutrinos. + N(L-) like electric and therefore be forbidden weak isospin The term or creates by f unit. ML two NL It is also mass term from NR f h.c. V, so Characteristics massless of the standard N,R since we have no essential between to construct (N(N) ME = /L:ITRiNij V, is unobservable. In the usual presentation is related 1s = f) in contrast + NLNL would In most theories also violates + h.c. but is conceivable number” symmetry. NiNi Such a term fermions “lepton introduced massless in the N;L with proportional by two. L is not sacrosanct a gauged possible Lj = (Ve)ji& number” new physics with that that this is really “particle the six quark masses and the four KM parameters angles and one phase). elegant contains above, Nr, and NR There is another (15) 3x3 Cabibbo-Kobayashi-Makawa the Lagrangian field. a mass term using only NL ML = pijNLtN;11 matrix. (18) 11.~. (14b) where d, = (d, s, b) and u; = (IL, c, t) are the usual “mass eigenstates.” u = v’vu It is then possible (14a) MD = m,j~~,Nnj substitute model. to those for charged leptons need for as seen in be NOR and indeed -128- of those three types of mass terms are summarized in Table 1. _._.‘.. -.._ If we have only t.he Majorana will be massive particles. In their rest frame these particles the anti-particles and Majorana are identical mass terms. set of t,wo-component viewed simply obtained from IELSS term, say hf~, but still have only two components. MR. More terms can be found It is possible In this case in general details neutrinos solution from formulation those of neutrino mass beyond the standard the NJQ so as to get the Dirac the simplest While conceptually considered as the sole origin the smallness of neutriuo 2. Do not, include to leptons. 1. a four-component Majorana, The reason is that neutrinos h&city part neutrinos (whether in general (E >> requires almost m). observations distinction is that all models we can imagine the Dirac “standard model” with suppressed neutrino discussed (18). While not of neutrino mass because it provides :. : >...I. .: ., .: .. : no insight, into NR~ but add a Higgs triplet a Higgs mechanism that has a Yukawa for producing coupling the Majorana version is the Gelmin-Roncadelli mass model3 Dirac viulation from which of lepton number we will pursue at a large mass scale M, in particular which results in Majorana lriplet mass terms. the It is this idea in most detail. The basic idea of the Gelmini-Roncadelli and this An important moment effects of new physics (GR) model is the addition of the will1 the charge states pLv but in and so very smaIl. T = (To, T+, T++) In the . Bohr coupling of T to the product of two lepton doublets is (21) magnetas is much too small to be detected. An indirect, but very sensitive, come from the observation a change of lepton Witherell the virtual The amplitude rather indication of neutrinoless number As discussed exchange of a Majorana is proportional of a Majorana double beta-decay, by two units. to the diagonal neutrino element where $1~ is the leplon mass for V, could doublet from Eq. (4). Looking just at neutrinos a process involving in the lectures yT of Prof. could induce this process. pee of the Majorana When To acquires mass IV; a vacuum - k&;NL,T” expectation (22) + h.c. value VT Eq. (22) yields the mass term of Eq. (19) with than to a mass eigenvalue. 3. Models In the standard vided of Eq. mass, it is usually mass solely due to film one finds2 I‘” = 3. lo-‘9 m,(ev) matrix neutrino below. The gauge invariant which ways to get a mass. This provides 3. Consider left-handed $$) (m/E)‘. can have a magnetic to m, from a of the right-handed the anti-particle by a factor pL, is proportional a neutrino with to distinguish the character $n or just The indistinguishable. completely In order one needs to determine it is the new particle is very different they are practically are produced and at high energies Majorana Dirac neutrino experimentally mass term way t.0 get a non-zero term of Eq. (19). The most interesting two-component model. ,.: will be a iV1~ with is uo physics 1. Include this provides term in this case may be obtained on the general in Reference and (3) there 11011-zero m, are: to have both Dirac the final The Dirac particles. the Majorana particles have the usual t,wo spin states and to the particles. Majorana as mixing then the final These are called Majorana SU(2) of Neutrzno x U(1) gauge theory (1) there is no NR, (2) there are no IIiggs P t, = k, L’T. Mass the neutrinos are massless pro- Note that bosons other thai quantum the doublet, -129- given its charge structure number of T) the triplet (corresponding to the choice of the U(1) does not couple to the quarks. The smalhress .:.., ., of neutrino mass is “explained” constrained by astrophysical The Yukawa interaction nunll,er by or related argumeuts4 ton nmnlxx theorem there results a massless spin-zero usual Higgs boson this boson remains uumber is not a gauge symmetry. are many interesting emission of a majoron discussed boson (essentially This particle One of these is the possibility Let me now turn to the idea that interactions Sucli interactions that typically uot renormalizable Of interest and ax Indeed mass arises from There the neutriiio particles of the nortnal handed the major to be used ady in lowest-order interaction tlmt nornml Equation (23) violates -. .>.. :-: . . ., __ :.I..: -.,.::_.. lepton this is due to the new physics at because the larger M the smaller comes in theories NR~. One assumes that. these neutrinos mass given assume that singlet by Eq. (20) with the plj the magnitude of fife acquire a very large M z). Because of order >> defines the scale M at which We now assume that in addition magnitude with right- there is no reason for the @Ij to be of order (similar to quarks Then the form of the mass matrix of new physics there is a Dirac and charged leptons) v and we lepton number mass term MD of but keep ML = 0. is of M. particles NL Ni N; 0 MD NR Q MD Mn with interactions perturbation f of the see-saw formula as au efTective four- Such effective ouly Al’= and it is presumed realization fifR is an SU(2) new physics The mass. neutrinos Majorana see-saw fonnula.7 arises because, as shown in Table 1, ML requires SU(2) x U(1) variety. cm be described I.0 [m (iv)]-‘.) to us here is the effective virtual to v2 necessarily The simplest with to some power Gell-M~ln-Ramotld-Slansky-Yallagida by t,wo units is broken. involving Mr. of Eq. (19) with mass scale M. This is called a see-saw formula to fine tune V(T, @) proportional arise out of diagrams proportional double x U(1) scale the consequences (At a lower mass scale the weak interaction interaction uumber because leptm are so much fum5 The main disad- neut.rim mass term A? = 1 whereas < @” >= v provides the beta-decay are inversely masses of the order M but external fernlion unlike of neutrimless lectures. proport.ionalily sun11 value of (VT/W). at a large scale M. At the SU(2) are effective Imp); particle and it is necessary the Majoram This is the famous when To ac- such a massless of the GR model is that majorons is t.bat it has lit.tle motivation lep- By Gold&me’s is called the Majoron. Witherell’s we obtain T has a leptoll co*~sequeuces of having in Prof. in order to create the necessary broken. &s a true physical l~lieiioi~ienological particle. advantage provided V(@, 2’) also conserves value, L is spontaneously is in the GR model. A s a consequence L (there is no t.erm of the form cP9T). expectation of VT/V, which 1V7 I+ conserves lepton number of two, In the GR model the IIiggs potential quires its vacuum vantage to the smallness to be less than are Diagonalizing theory. particles t.llis we find for AiD <i characterized by nii, and light n,f~ that neutrinos there are heavy with a mass matrix Majoram given by of the forn16 (26) Mu = DTM;‘D. . . ‘...C. Note this is part of a gauge invariant bined to form a triplet a t.riplet. When together a0 acquires term made of two fennion wit11 two Higgs doublets a vacmun expectation value dorlblets also combined (Eqs. corn-to form where m.~ is the Dirac (7) alld (10) ) A,JR were zero. -130- mass, that Since rn~ conxs is, the mass the rleutriuo from expressions like Eq. would have had if (la), it follows that :_. _ :: .- Eq. A ssuming (27) has the general form of Eq. (24). as the mm lhe factor of a quark or a lepton we see that mg is of the sane order the neutrino mass is reduced (31)) the fields e;, etc., are really the charge conjugates by to the present (ma/M). showing discussion up in the form the 16 of SO(10) Ni. contains The conjugate of Ed, etc. Of importance both NL and NR, the Iatter fields 416 transform under SO(10) . . The motivation quarks which mass term standard for this suggests sinlilar approach there should to that of other is the symmetry be NR and that fernlions. model is a weak phenomenon, and the mass of the charged leptons the NR are completely it becomes SU(2) that possible breaking scale that the large ratio large ratio neutral with respect that electromagnetic x U(1). A disadvantage introduces in SU(3) The Yukawa is not equivalent to 16 (just as 3 and 3 are not ). -7. ::.f:..:. interaction :. ._. 2, : :_ : involves so interwhich t,ransforms as 16 x 16 which As a consequence mass much larger M and Y is t~echnically is needed in any theory in the of SU(2), the NR and all other fermions; to SU(2) rn~. equivalent be a Dirac 13, which to their strong interactions a Majorala determines between should and mass generation to their between for NR to acquire leptous with the breaking is unrelated There is, of course, a difference there Note that associated that the mass of quarks does not appear to be related action. between as the representation however, new physics representations 16x16=10+120+126. than the of this approach uxznatural; breaks down to irreducible is Higgs bosons that such a we can write can couple the Yukawa to fernlions interaction are thus &lo, &o, and 4126 so that of SO( 10) in the form at a large mass scale. The original idea for t.he see-saw formula of (25) comes from the SO(10) in which down down to U(1). different to SU(3) parts are different x SU(2) The weak, conlpouents The simplest GUT on SU(5) 16-dimensional Ill one starts x U(1) just fermion (GUT). with SU(5) 11xre eventually interactions Similarly quarks that breaks are just two are no NR.) different (A simpler representat.ions, The fernlions The Dirac the bottom; are united GUT mass terms the Majorana based The Higgs field ~$10contains which normal in SO( 10) form mass terms &s well as Dirac terms can arise when the Higgs bosons acquire vacuum values. of a single generation Eq. (28) into Eq. (29) one can see t,hat Majorana By substituting and leptons field. is based on the group SO(10). into (29) GUTS are models’ x U(1) and strong in which all the fernlions divided of mass matrix a single gauge group as SU(2) gauge interactions. of a grand has the fermions ululatural. theory electromagnetic, of the original in a single representation Seellls grand unified at a high mass scale lLf~u~ breaks and for the form Higgs while mass matrix a expectation (28) couples to mass terms when Nr. couples to itself or N,” to itself. two SU(2) doublets &20 contains schematically arise when t.he top row of Eq. an SU(2) 0, that can play the role of the triplet T aud a singlet S. Thus the ;. .. . :: :.~.:.I”...z .: -:. .. :..: ._,. __ _-’ take the form representation (28) which reduces where a is the color index. We show only left-handed fields, but as shown in Eq. to the form (25) i f we, some&at arbitrarily, value of < S > and thus of M can be equal to the GUT -131- set < T >= 0. The scale (2 1015 Gev) but In fact the SO(10) model with only two mass scales ~JG~T and could be smaller. v tends to have the failures of SU(5) in predict,ing 1.00 fast. a rate for proton and too low a value of sin’ Bw. Thus there may be an argument at, a value more like 10” -1 Ta.hle decay for choosing M Gev. 2 - Limits on Neut,rino Mass ..: .;.:::.- ‘. Because Yukawa the SO(10) interaction has such a large munber and its Higgs potential However, most analyses’ followiilg qualitative 1. model The neutrinos there are no definitive that fit t,he quark and charged conclusions of parameters concerning lepton .,, in its to those of the other together) m(v,) ii=1 : m(vJ analogy : m(r+) = d(U) : d(c) : d(t) with interactions flavor the quark expressed eigenstates mixing are mixt.ures described in mass eigenstates of the mass eigenstates by Eqs. (14). As a result the limit assumptions (31) or 2. 2. The neut.rino in detected it is possible preceding the main of neutrinos resenting mixing mixing angles of the neutrinos in Ue are all small (f7= - 0.2) with particularly The most direct between on Neutrino way to study neutrino mass from the kinematics to that of the order small mixing 4. Limits missing relative of the KM of the charged of the Cabibbo the first and lhird a non-zero confirmed by other mass of v, arolmd experiments. 30 ev, hut It is unlikely that this Present mass experiments an earlier of the which limits lifetime Detailed which supernova is m(ve) supernova produces 5 15ev, similar with to more neutrinos burst (a pulse of V. of neutrinos) it is possible that analysis maSses can also be obtained the observed time when the universe density t, of the universe as a function by the Hubble 10’ times and other evidence. of the number of and thus determine It is then possible of the neutrino Ho. Assuming Ho > 50 km se,-’ a density have a mass of several ev they down. constant arguis a relic The same the- all space with is about of the universe is slowing cosmological background and denser. filling Thus if the neutrinos expansion specified This number from microwave was hotter also be relic neutrinos the energy the universal from radiochemical -132- and could detect a large range of V~ or vT masses reviews are found in Ref. 10. SN and IMB analysis all flavors Mpc-’ the rate at to calculate mass and the present rate If the neutrino large the value t, will turn out too small to be consistent can be the supernova statistical of the neutronization emission cosmology in the universe. of expansion has not, been any of these limits a study 110 cmm3 for each generation. baryous has persist.ently result reduced by more than a factor of three in the foreseeable future. of neutrino ory says there should masses is by the determination are shown in Table 2. In t,he case of 3H decay one experiment indicated from The dominate neutrinos. on neutrino In the standard leptons. generation. con&&u down to 2 ev or less. Furthermore rep- Masses of decays involving that from (19 in Kamiokande on t.he particular 3H decay. i;br a future from a future Limits angle depends thermal matrix, mixing interval of neutrinos 100 ev and 100 kev. ments. analogue limits from time of neutrinos used. I believe a reasonable could provide the weak have the form and U’ is the lepton in a short obtained obtained (32) ~j = (z+,v~,I/~) arriving the limit between where energies 19S7a. Because of the small number fermioils with on the mass of V, can be obtained I1 from the observation A limit of different analogous ::. - predictions. masses yield the neutrinos: have a mass hierarchy __,.) ..::. -..: mass is t.oo wit.11 t,imes determined ..‘... .: I>, ‘-. -. :: -, t, > 10 109 y7-s A beam that is originally 1 u(t) >= rn(V,) +m(v,) This limit does not bold if neutrinos an earlier time in tile history decay mechanism constraints. that satisfies + m(v,) decay rapidly will annihilate (33) enough of the universe. It is hard cosmological, astrophysical, In the GR model the limit into nmssless nlajorons of the order of the neutrino < 80ev. and so disappear m(v,) which of the universe in Table m(vw) 2. If we further < 1 ev, and m(l/c) requires neutrino << oscillation energy needed to satisfy conditions on m(v,,) demity of Eq. (31) then m(v,) of the universe; that limits to probe small neutrino < VP 1 v(t) The prohabilit,y such small nmsses Ppe =I< 25 and 50 ev could provide is, provide : The basic idea of neutrino v&, may be written << p’. v, because of the change in the relative projection >= the dark masses using neutriiio of neutrino oscillations oscillatioiis is not too small. of an oscillation vp (u(t) its mixtures of t.lle mass eigenstates (38) into vp is then given by >12= 2sin2%~os2%x[1-Cos2(_2__1 m2- m2 2p )t] = sin’ Z%sin’(nz/!) (39) oscillation length c = c, = -aL m;-m; pro- is given by = 2.5 meters ~(Mea) Am2(ev2) to express the oscillation . (40) These It is convenient using just two gen- The flavor eigenstates on the state V~ given by matter masses. can be illustrated to three is straightforward. phase - sin 89cos %e--IELt + cm 9 sin %emiEzt. Formulation mass diITerence and t.be mixing are met in most theories the extension (37) = (m; - mf) < 80 ev, the time evolution erations; An? and has a non-zero where the characteristic Oscillations ._ : _ -.:..:.: . and R = 1. vided there is a signilirant. (36) The state (35) is 110 longer purely than the direct 1 ev. The only way to explore 5. Neutrirro It is possible more stringent ~nass between (35) EZ - E, Y cm; - 7$)/2P studies. We note in passing that a neutrino the critical (33) we have a constraint accept the hierarchy > is the kij are not too small. is many orders of magnitude sin % 1 * assuming and experimental when the temperature result eCElt cos 9 1 y > +eCEzt to find a theoretical of its two compomnts If we accept the cosmology of time where at (33) can be evaded because the neutrinos nmss provided ve becomes as a function vp components. for what follows of a two-component vector in flavor pheimn~enoii space v(t) with as I+ and Then v, and vy and * (41) The 2 x 2 matrix h4’ is given by M;” (34) -133- = $L’ - Am2 cos 2%“) (42~) _ ._ _. ‘_Z. :. : :.. .. M;, = ;(P’ is easy to see that (42b) -t Am2 cos 2%,,) iIm since substituting where %, is the mixing Pauli notation angle (subscript this matrix v is for vacuum) and $ = no: + mi. (45) this into (43) gives exp[-Ncrz/2] tion of the amplitude In p(n - 1) = iNa/ due to the absorption which cross section represents V. the deple- Combining (44) and (45) one obtains has the form CT= 4iThf(O)/p (46) M2 ~~21+Am2(-cos2%,~,+sin2%,a,). which is found in many books. of the iudex of refraction. Neglecting the unit matrix precession of a spin -4 axis. Neutrino To probe must magnet oscillations the same folm in a magnetic oscillations from Eqs. passing through cases one must take into consideration to the material medium. the phases of the flavor as a precession over very large distances. of neutrinos in flavor space. In practice adding the sum of the forward mitted wave; a succinct assumption about the target atoms. of the oscillations neutrinos effective due and cme source - l)s] . wave packet; oplical scat.tering theorem of the neutrino to the spacing are limitations in applications Physics.‘3 nor does it make any related of to the these limitations are current both n and f(0) must be considered model f(0) is diagonal (W boson exchange) in flavor. as matrices in flavor If we consider the weak cme f~ids for V, scattering from electrons = -xh’Gp/2n is given by the opt,ical theorem PC" - I) = --di~N, of scatterers amplit~ude. per unit I1 is customary volume and f( 0) is t.he roberent. at. this point. t.0 note that can be found in any book on quant~um mechanics. this is not the case. A number (47) (44) where forward notes on Nuclear of targets effect there to the trans- (43) P(” - 1)= 257W(O)lP where N is the number a lattice of the neu- by coherently important. f(0) The index of refraction the absorpl.ion waves from all the targets is given in Fermi’s Like any coherent in the real part (44) may be derived the ratio of the wave-length space. In the standard charged e+p[ip(n derivation does not require For our example term Equation scattered size of the neutrino not generally have to do with negligible. the result leads to of the propagating this is completely Note that here, however, For the prol~lenis of interest trinos the earth or the sun. In such point is that oscillations of change in phase is the index of refraction of the (39) and (40) t,hat one the modification The essential components as the problem field at an angle 28, to the spin may be considered small values of AILS it follows look for oscillations studying this is exactly We are interested of books give t.he imaginary the current; Unfort,unately part of Eel. (44). N, is number reve&ed. muons. It however, -134- of elect,rons per unit, volume. Of course, I,,, do not scatler lhey scalter elastically There is also scattering iron, elasl ically muons For ce 1.he sign must from electrons but normal of u, and v,, via the neutral media be via I he charged do not contain current this is the same for all flavors aud so only adds an overall (Z exchange); phase (not a relative phase) to the propagating factor r/(t). We cau uow take account (43) by using Eq. (41) but replacing Mze = ;(p’ Note that iu obtaiuiug (37) the ueutriuos of the phase - Am2cos20,) the eigeustates + 2hGN,y. (48) esseutially with the velocity replaced by e,, value of N,, oscillations are described of the suu) the upper the resouauce where deusity of light. by Eq. (39) with 0,e the upper the upper = siu20,/(cos20, - state which Iu this case 1. At large densit,y is primarily v, (&, by the mixing term vP. If the density cau be used, which As a result is now primarily M$. variation meaus that the original At the levels Finally at zero is not too rapid no transitiou v, remains vP. The probability (such near 900). the two levels come close together; state is primarily the eigenstates. state, to zero density. that takes primarily ve is still I+ is Pee = cos’ 0, cos2 B,, + sin2 0, sin2 fIti = i( 1 + cos 20, cos 20,) e,, = c,p 2(e,/e,) - k-0= 27r/diGNe co5 ze, + = (1.6 x 107/p,) meters where 0, is the original (51) not included where pe is the electron number value C, defines a characteristic order of the earth’s &, >> 6, oscillations which radius. density length in units in matter; For e,, << are highly C,, and e, are ~~~~prable. 6, suppressed; of Avogadro’s for uormal matter effects of particular In particular, (54) (50) (ev/eo)2]-f nun~ber. matter The interest rapidly it is of the can be ignored; meam oscillating Pe, that (Note that a complete conversion in deriving are three important (54) we have siuce this is a For 8, uear n/2 aud 8, small we of v, to v+. l?or values of 0, too small (this (B,, = 45O) and the adiabatic the adiabatic Eq. the ~1 and vs components term and averages to zero.) go beyoud There (52) between is small by Eq. (42~) ) tl ie mass eigenstat.es M$ the resonance for value of B,,. any interference have almost for in the case iu e, = e,cos20, in given by (49) ev/e,) = 4Y f& approximat.ion place between etn tal128, corresponds chauge as showu in Figure as the center the adiabat,ic For a fixed in matter would cross but they are “held apart” Eq. (45) we have set z = t, since with the approximaliou are moving 45“ down to 0,” = 8, which through Eq. (42a) by get too close together approximation approximation cases in which fails. Formulas at for are given in Refs. 14 and 15. matter effects play an important role: 8,, becon~s 45O. The importance of ibis case was discovered Sniirnov who refer to it as the resonant matter. For the case of Y., G@ the sign of the right-hand reversed, effectively be satisfied chauging for v, if m(v,) amplification the sign of C,. Thus < m(vP) 1XI t not for 4. by Miklraeyev of neutriuo side of Eq. the resonance and oscillations (1) Neutrinos by rays and passing in t.he atmosphere a major condition (2) Neutrinos cau For small values of 0, Rq. (3) Neutrinos For most applications = 6.S x 10~Am2(euz). the value of N, varies. as the density decreases, 8, passing (53) Of particular decreases from interest a value as a result of collisions of the earth of cosmic before being detected. originating uear the ceuter of the sun aud traversing is the near a radius of the sun. through originating 90° -135- iu the core of a collapsing star (supernova) and the dense out,er layers. 6. Ned-ino case in which, portion (47) is (52) gives E,(Meu)p, originat.ing through We first summarize tory neutrino oscilld.ion briefly Oscrllations our preseut experiments. : Erpe~iments knowledge We distinguish obtained from labora- two types of experiments. Appearance experiment~s new flavor (like Uisup~ewawx measure quantities v,~) a.ppears in a beam experiments measure like PPe of Eq. originally quantities (39) in which a different flavor like Pee of Eg. (like a v.). (54) in which . one measures the flux of a given flavor some distance from the source. In the .. ..‘-: case of only two flavors Pp. + Pee = 1. However, in general, the original lation flavor experiments disappearance experiments to any new flavor. probabilities only a correlated amples for which most information oscillations. Our prejudices t.o note that production this important v,, disappearance +Ne iment it also provides result was simply at CERN.17 limits and 8, so that these quantities. The exand V, -v,, may he very small; is summarized in Figure For the larger experiment The lower branch experiment (39) the oscil- An? are vP - V, oscillations two experiments. an emulsion by neutrinos. between is available Eq. from are the most diffGzult to probe experimentally. shown come from E531, limit on both of vP - v,. oscillations Our present, knowledge Ihey come from x depend suggest that. I+ - I+ oscillations in any case ye - r+ oscillations The results are sensit.ive t.o oscillations As can be seen from at a given distance provide at Fermilab.” a byproduct 2. values of Am2 It is interesting of a study of charm of the curve comes from the CDHS Since this was a disappearance on 9 - V, oscillations; however, better experlimits are r- Figure 1 of electron Eigenvalues density N, of of the M2 matrix or distance I the sun as from a function the center available in that case. If we assume I3 in this case equals or is greater Cabibbo angle (indicated (assrmihg m.(v,) << constraint on m(q). by t.he dashed m(vT)). As we have noted be of enormous int.erest involving J+ are certainly worthwhile. There by Koshiba. is also shown a value of m(v,) 2 a dashed Further cross that data on atmospheric ward and downward neutrinos be required. so it is necessary than the m(q) < lev if sin’ 28 < 10e2 there is no If the effect were as large as indicated vu and ve or vP and V, would -136- then we conclude had for cosmology. in Figure of the preliminary line) On tl le other ev would interpret&xi . -: between efforts large mixing The effect on oscillations represents neutrinos appears 25 and 50 a possible presented here angles between for both to assume a vacuum up oscillation ‘_ -_ .; .: .I length short negligible enough with There is a mwb best present the solid greater laboratory body limits line in Fig. disappearance apply to affect the downward neutrinos. 3. of knowledge on Am2 For large on vP - V~ oscillations. mixing angles the best limits t.0 L,~- V, oscillations. These disappearance experiments to values of sin’ 20 less than 0.1. The remaining of V, in vP beams at the CERN occasional with experiments the acquisit.ion Reference Our theoretical 3 that very little I data. prejudices by : ./: .. : come from of course also are not sensitive come from looking PS and the Brookhaven For a review they for the AGS. While have disappeared of accelerator experiment.s discussed from above suggest m( vP) < lev with with sin’ 20 of the order IO-‘. of this paramet.er laboratory abstracted discussed Am2 < lev’ 3 are indications by future i limits have seen signs of oscillations of better The see 19. much less so that Fig. effects are and sin’ 28 are shown schematically using iie from reactors. l8 These limits, experiments appearance Thus matter this solution. range has been explored. of discovery possibilities or limits experiments of the type already various by Koshiba) conference but there is no assurance that Fig. The dashed lines in that could be achieved done. These have been and proposals reports’8~2” m( ve) We see from (including those the experiments will be done in the near future. To go further 0.5 1.0 sources sin*20 using listed one needs to go to still at the end of Section atmospheric Ii t tie da&dot neut,rinos large Hz0 with those coming would Cerenkov from above. be a large enhancement Future neutrinos. gone different distances distances through and we turn has already the earth; comparing For neutrino this is shown of neutrino vw and V, arriving energies oscillat,ions to the been obtained around by the group using from below 300 Mev there inside t.he e&h because satisfied. large det,ectors In principle larger One result 3. The resrdt 2’ comes from the IMB detector Eq. (53) is approximately -137- passing curve in Figure their 5. can further because explore neutrinos and t,hrough the oscillations coming different ill different amounts of earth of at.mospheric directions have these experi- .’ ,..’ _ I . IO nieuts cau explore uncertainties Figure I a wide range of parameters. in the incident 3 is a schematic lo-’ flux as well as by statistics. indication of the possible smaller by exploiting earth Super Kamiokande mixing 10” ;’ \ . \ Since the matter \ way around) \ ampliftcation. detecting The dotted values that would nuclear by curve in be explored ..._.*37Ci - - -4:; - - -c:“_.-..-. .-. a.... 7 \ \ \ _--- -l ---\\ c\ \ \ 12 \ \ \ 7’G\a\, \ 16' \ \ should Icy3 I 1o-2 of the energy a way of probing be able to dist.inguish in the form . .\ \ \ 3 with flux comes from the weak pp reaction the calculated \ neutrino This relative that the resultant the other to solar neutrinos. The in the sun give off The study of these neutrinos reactions fluxes. over distances yielding While makes them larger neutrinos are the predominant is the first step in nuclear difficult a very low flux but the high energy of these neutrinos introduction be nnrons. burning to detect. of t.he very rare PI’111 chain of reactions For the standard to the can practically energy oscillations of these neutrinos sI3 is t.he product easier to detect. \ :. of what goes on in the solar interior The three major shown in Table produces \ of neutrinos. a way of exploring the size of the earth. In contrast _ .’ :‘-:“ .::. n+ from p-. we must turn for providing our understanding iu the suu, the lower energy \ exists” from Eq. (53) applied up to 10 Gev. and then detecting are responsible provides than and so make them much to these reactions see Reference 23. \ \ I that a portion and also provides / // \ the possibility effect holds only for V~ (and not i?p or conceivably the detector reactions In principle However, neutrinos To go to values of Am.’ below 10w4ev2 Am2 16" lCiE is limited angles for values of Am2 of the order 10m2 to 10-3ev2 the resonant this requires detector. done only by using rock as the target lci5 sensitivity ‘.. by the proposed to explore 16" Their \I I 10-l 1 I Table 3 - Sources Maior ENERGY of SPECTRUM Solar Neutrinos RELATIVE FLUX : SIN2 28 Figure future 3 Existing experiments limits on vu-ve 1 ~ and possible oscillations The hrst (aud for more than 15 years only) attempt was carried -138- out by Ray Davis using 37C1 as the target to detect solar neutrinos mat.erial. The 37C1 is . converted to 37A by the reaction time dependence. sunspots, ~e+~~Cl-+e-+~~A. The experiment produced requires per month. detecting the production Very elegant radiochemical for this purpose. The threshold ppv and ahnost too high for ‘Bev. given in SNU (solar neutrino 37C1 detector units, In contrast of which (SSM). etc.) varied In Figure for the Am2 experiment carried are taken the present from laboratory of the opacity dances. Fundamental The calculations from the out from radius, the boundary luminosity, measurements due to complex of nuclear atoms, dance with calculations their uncertainties. (special understood. The major (such might be wrong. temperature as neglect the input Excluding exotic question of diffusion approximatelyz4 would not support Iaws of physics mixing sensitive it. However, the experiment at the Baltimore APS meeting with oscillations the high-energy ergy neulrinos unlikely cannot are well iu its infinite a new source of support in 1987 and the result for that is 5 + 1 SNU. Davis believes Davis, now at part be in the sin’ &, a factor by the neutrino effect). hypothesis the SSM. One is a study Neutrino in general traversed the oscillation with of two or solar neutrino values of 0” is due to the en- medium oscillations the spectrum flux. of the is modified For example, is depleted from are an energy- of ‘Bv This is because the resonance if for Am2 - but the lower en- condition of Eq. (53) unchanged. differeut in flux. to distinguish if the threshold electrons from even for a fixed v, energy. t,hat detects electrons that consists of a distorted sB spectnun in the Am2 - sin’ 26 space that give the It is possiblez6 because the detected detector The delection regions like Kamiokande for t.he Gran Sasso Tunuel -139- of about of the ‘B spectrum There are at least two proposals this could be a real it cannot and less ‘B exists in the sun the total flux is reduced elecCronic .h : for low values of E, even near the center of the sun. In con- remains energy spectrum year reported is wrong neutrinos. Thus ._ _, away from but the spectrum dilIi;rult wisdom, however, is trast if the SSM is wrong same reduction on solar neutrinos. small are the cause of a reduced would also distinguish central be a reduction of detecting get through. be satisfied 1120 Jet,ector euded in 1985 because Brookhaven, Penn, continued phenomenon. 10-4ev2 in accor- deviations 3’CZ encloses the region by the material something The result the SSM prediction. would of the ‘B neutrino in the solar interior) reported that above 10 Mev. uncertainty, we at leas.1 two way of distinguish;ng from approximations to the calculated there here by out using the Kamiokande and three standard the center of the sun (MSW spectrum dependent with with As discussed flux of I+ in the Davis or the Kamiokande abun- as TJ*. In the last year there have been t,wo new results The Davis experiulent involving some reasonable or convective The sB flux is ext,remely T,, varying possibilities the relewwt is whether energy rates, calculations were varied onIy to ‘Bv and theoretical The possibility the assumpt,ion parameters all the values obtained parameters There radius, of solar element has been carried is sensitive of the oscillations as it emerges from the sun (initial Input reaction and observation kinds 25 of WIMPS) new particles made in which to describe conditions etc. are fit. The range of values given above includes one thousand plane for which experiments. are based on the standard laws of physics are applied for this is known. 3 the dashed curve labeled more in the detected small amounts detection to disagree 0.9 to 1.3 SNU for ‘Be Y, and 5.3 to hancement of 4.5 x 10’ years with until This experiment (This includes of the Davis How serious is this discrepancy? solar model detector. said definitively 19’70 to 1985 was 2.1 f 0.3 SNU. over the period the first electronic zero. Given the experimental the neutrinos is irrelevant) Koshiba explanation equal to 0.45 times the SSM prediction have been developed ratez4 of detected the definition the result 30 argon atoms (55) is too high to detect The calculated is 3.9 to 8.4 SNU for ‘Bv, cycle). of less than methods of the reaction 10.5 SNU for the sum over all neutrinos. CNO (55) His data for the last ten years show an anti-correlation but no reasonable different can be reduced; spectra however, in an it is v, + F --t v, + e have a continuous It. would from be much Iwtter inverse aim at this. of a large liquid beta react.ions One called ICARUS argon detector.27 to have an like (55). planned The other - ., . . .. L: : is a large Da0 ” d&ector planned The second possibi1it.y nos oscillate. electrons In principle in detectors for scattering from on nucleons from via their However, current.) via the charged which One possibility the disintegration only current). with is the DzO detector Detailed A more difficult found cur- if one can detect the Of great importance is the detection uses “Ga Gran out in the early tions indicate GO tons in the Soviet 1990’s. that It should (26%) sin’ 8, that would detected be emphasized (- nz(r+) << in greater conclusion for exploring m(v,)). Resulls that should the theoretical in the be coming thau a factor The major of two reduction between This range is of great interest to nexuses M in t.he see-saw formula lo-’ (with emerging the supernova from 10 *l to lOI (> IO9 gq’cc the outer portion of t,he neutrino equal mixture neutrino layers of to those of the sun. oscillations coming flux of all flavors of have no effect. from the supernova only Ver the neutronization and 0 were within burst. Since the the region labeled 3’C1 burst would explore neutrinosphere ). Indeed pass through as seeu from small values of 0 is almost Fig. impossible onre agaiu the great impor(.ance of detectors for seeing t,he ueulrinos from the very limit.ed tion burst, at their is much larger very small values of 8) up to 1000 eu2 or more since the V, the first. event observed provide can be experhents to those *B v hxxn the suu, most of these would In spite of a huge number and 10m4 ev (assuming since it corresponds from a variety in the V. flu experiinents the major that the very first neutrinos if the values of Am’ This emphasizes at Fig. 3 is that. for reasonable angle, solar neutrino values of m(vl,) however, are similar of an approximately Thus in the first, approximation 10-4eu2 with other regions 3 t.he region to explore of establishing of very high of Am’ above in any other way. a progranl with from the next supernova. of papers on the subject observations no conclusions can be of SN 1987a. It, is quite possible in t.he Kamiokande br:t those who draw statist.ical detect,or inferences came from from that the neutroniza- a single event do so own peril. 7. CmcllLsion roughly Gev. Of course, the solar Neutrinos -140- ,. ‘.. ;... effect could also take and passing through t.!lis is that consists values of Am2 drawn to be reached by staring from a supernova of a short pulse ccmtaining density calcula- in 71C:a are due to ppv so 15%) in the prediction. of V, to v,, or uT due to the MSW in detecting a supernova be transfornxd3z detector. values 0, of the order of the C!abibbo the possibility Union. 30 tons of gallium effect for solar neutrinos for solar neut.rino in Fig. 3. In fact a study of this neutronization for this purpose is the ‘Be V. We also show in Fig. 3 the values of Am2 and result in the gallium The major with only 54% of the events expected that. there is still scmle uncertainty contribution experiment of the MSW of 1mxpert.s energies of t,hese ye are similar of the pp,pvsince their flux can he calcu- in place of 37C!1 It is being planned Sasso and with for this purpose. Thus we may be massless. : -: .:. I., The problem It is expected, A radiochemical and 10m4 ev can also be explored. star where the densi1.y conditions from We that lllost Gev. the exploding consist lated to a high degree of accuracy. A discussion place for V, emerging using reaction has also been proposedz9 lo-’ thoUgl1 Even it is possible Ref. 31. in neutrinos. using “B 30. The transformation flux v+d--tv+n+p. A special detector between Ye and V, to be smaller results of calcula(iolls in Ref. given for all flavors. the flux of V, nwasured are also sensit,ive to ue - VT oscillations. angle betwren cm get. close to values of M of lOI 0.15 give the total the mixing of the range of nz(v,) from about experiments expect the neutri- be via neutral flux in this way should ncut,rino this cross section have the same cross section to be compared Ontario. scattering is of det~ecting vP or V, would of t.he neutrino of oscillations or ICARUS. (due to the neutral also scatters inverse beta reactions. neutron be detected method Thus a measurement independent of the vP or V, into which uw or V, could electrons more dist.inctive reut. interactions is the de&lion like Kamiokande t,inws that. of V, (which but to be placed in a mine in Sudbwy, Nevertheless the search for a non-zero mass is _’ ..: exciting for many reasons. would be new physics might he explored The most reasonal~le explanation at a large mass scale M. Values in this way. A mass of the heaviest of 25 to 50 ev would mean that close the universe. Neutrino from theories grand unified observation and prediction Arguments from our attention angles. could explain combined enough consisten1 an apparelit of the solar neutrino cosmology neutrino, provide nmsses and mixings on relatively From this point interesting relic neutrinos experiments. be carried dark matter to 4. D. Dearborn Phys. et al, Phys. L&t., In particular, large accessil& the light.est neutrino effect) provide in no other to do experiments focus way. Nieuwenheieen Proc. over longer and reactors et al, Nut. there ~a.11lx a large enlrancement due to the effect of the solar maberial. neutrino experiment calculated flux. Only a concerted yield some definite gallium conclusions. experiment, possibilities must lx qlmlified is abollt of possible effort using a variety KEK At least one new experiment., to get ul~derway (1986), numlm Workshop 1566 (1979); Phys. and R. Slansky, in North Rev., m, in Supergravit,y Holland (1979), 1694 (eds. P. van 317; T. Yanagida (eds. A. Sawada and A. Sugimoto), Phys. KEK (1979), 185 (1981) and references Reports,“Z, et al, Phys. Neutrinos in p. 95. therein. Rev., E, 2597 (1988) and references 86 (eds. 0. Fackler and J. J. Van) Editions therein. Front&es (MSW any one solar 12. J. Bernstein in the and J. N. Bahcall, Phys. L&t., Bx, 366 (1988) E, 39 (1981). and therein. 13. E. Fermi, and G. Feinlerg, Nuclear Physics, Phys. Lett., University of Chicago (1950), Lett., 57-, 1271 (1986); p. 201. detect~ors can 14. W. C. Haxtoa, of other exciting of Energy Phys. Rev. S. J. Parke, Phys. Rev. Let.t., 57, 1275 (1986). 15. S. T. Petcov, in part. by the 1J.S. Departments 5, pp. 441-584. references the radiochemical and a number et al, L. M. Krause 297 (1981). Lett., P. Ramond, 11. D. N. Spergel if v, is rmcertail&s of different Rev. and D. Freedman) 9. M. Gronau have been proposed This work was supported contract lwcanse from M. Fukugita a large I,ecause of the oscillation Conclusions 5G, 26 (1986); Rev. DZ6, 1840 (1982); Phys., m, Phys. 8. P. Langacker, neutrinos. to study is possil& 411 (1981). will of t,en vr more. oppoxtunity This E, 391(19843. 7. M. Gel1 Mann, mixing oscillation solar, or supernova a unique Lett., Phys. Lett. (1980). of (.he range of by neutrino values of Am2 ~UWII I,y a factor solar mutrims radlge of values e, Phys. Rev. 42, 1522 (1982), 5. II. Georgi between theory very at accelerat.ors one must use af~mosplmic, et al, Phys. Rev. L&t., 10. Massive To go much fimther and M. Roncadelli, expectations ideas from part,icle the range it is necessary out to explore 3. G. B. Gelulitli 6. S. Weinberg, of view we find that only a small portion To extend L+, with masses a.nd llot and we hope t,llat new experiments presumal~ly disagreement values of Am2 and sin’ 28 have been explored distarlces mass flux. with mm11 wutrino of a non-zero of M up to 1Ol5 Gev 16. N. Ushida under DE-AC02-76ER03066. 17. F. Dydak Phys. Lett., et al, Phys. et al, Phys. z, 373 (1988) and references Rev. Lett., 47, 1694 (1981). L&t., 34 (1984). c, therein ,. rtrfe7.P71(.E9 18. 1. S. M. 13ilenky and S. 7’. P c t COY, Hcv. Mod. 2. K. Fujikawa I-eferwces and R. E. Shmck, I’hys. Rev. F’llys.. “, liTI (19%‘). Lett., 42, 963 (1980) Scientific and F. Boelm~, (1986), 148.176. -141- 86 (T. Kitagaki au(l II. Yuta. eds.) World p. 135. 19. M. Shaevitz therein. in Neutrino in Reference 10, p. 259 or Neutrino 86 (Reference 18); pp. 1 20. hoc. National BNL Neutrino Laboratory Workshop 21. J. Lo Secco et al, Phys. L&t., 22. G. Auriemma, et al., Pllys. 23. D. 0. Clayton, Principles Graw Hill) (M. J. Murtaugh, Brookhaven m, 305 (1987). Rev. D37, 605 (1988). of Slelh Evolution and Nucleosynthesis (Mc- 1968, pp. 366-390. 24. J. N. Bahcall and R. K. Ulrich, Rev. Mod. Pllys., 25. W. H. Press and D. N. Spergel, Al,. J., 22, R. L. Gilliland, Ap. 679 (1985); J. M. Gelb and S. P. Rosen, Phys. 27. J. N. B&call et al, Phys. 28. G. Aardanm et al, Phys. 29. R. S. Rsghavan L&t., Let., et al, Phys. E, J. Faulkner and Phys. Rev. Rev., m, 2976 (1987). 324 (1986). l94, 321 (1987). Rev. L&t., 57, 1801 (1986). 30. S. P. Rosen and J. M. Gelb, PlyI s. Rev., B, aud T. P. Walker, 60, 297 (1988). J., 299, 994 (1985). 26. J. N. B&call, Lett., ed.) (1987). Lett.,z, 2322 (1986); 969 (1986); S. J. Parke M. Cribier et al, Phys. 182, 891 (1986). 31. J. N. Bahcall, 32. T. P. Walker R. Davis, and L. Wolfenstein, and D. N. Schramn, Pllys. to be published Lett., e, in Nature. 331 (1987). .:;. :._ .-.: : :‘.--.’ :; . -142- I 3 ,,:;,, .,.(“‘,’ .‘, a ,: ,,:, ;::: .;, ,’ I bI ‘,.; .,, .2., ‘.‘. ,,:,j: ,,: ., :. :, .:, ‘, ,’ ” A.J.S Smith "Experimental Paper was Searches not 147 submitted for Rare Decaysll . : .. ‘. ‘. ;. ,: ,: _ : ,: : ,. “gL 8g-lzz (6101 I)1 I I 6fO-LQ60ZfI 0001 008 009 006 02 002 0 0 002 3 3 m OOP za Y SLN3.43 ,3AISn?CIX3, E’E z 009 2 z 2 008 - 0001 Number of Events / 4 MeV Number of Events / IO MeV ,’ I, .’ ,’ ,I, I’ : Photons / 3% bin Energy / 3 % Energy Photons bin ‘:‘::.. ,, , ww3) -091- 800’0 121’0 L60’0 11’0 ZSO’O 90’0 , Eg 3 :g:a :@a + &*a - IZ’O LIO’O LPZ’O ,g”a a3 oz.0 280’0 p :ap%I p’:fIp’“g ZZ’O 11‘0 + p:8P’“8 SSO’O I(d) I xv P’“fy’“8 ssw w .:., _. .‘. 2’1 I 0’1 I 8’01 9’01 2’2 tr’z zu SL .-.-.s9 ss ....‘....’ I 2’1 I 1 1 0’1 I Sb ----I 8’01 Ii ’I II j[ ? m 8’2 < c-l 9’2 (4 \j . t 9’01 I 2’2 9.2 : m 8’2 50 < G 9’2 jz(Z!m - I!& ,d”J? - z~&fl + (%’ 1 + I?JAJ) - - M) uJ’ikZ zM]/' = 'd = us O’E i..: ...~. -. .;. .‘i’ 2 *c -191- (AV) 09’S I SS’E OS’S I I uD’q3 SC’S Ob’S I I SE’S OE’S I I XI-E SZ’E DSC SL’E OO’t 3 g P SZ’C OS’f SL’C OO’S -, ‘: ,‘,,..’ Pholonr / 3% Photons Energy bins / 3% bins Photons 13% Energy bins :: 1. ‘8: ., ‘:’ -,. ‘/ ‘. _~ -E91- 1. -:. * 4 pt . ., - ‘, , ,’ -: __: .:>.. -. _’ ,.,(,. ., ,:;:: .,: :., ,. ‘, ) ., ,’ ., ,) .; ; ‘. ; ., ‘, : ,’ :. -891- .. ‘, ._ : .__. .:. .;:.. ,: ... 5’8, 0313 sn3xv .&I+01 9E z(dL.0) + &Cd #Z.‘[) + d5.0) &Qz.o) + &‘o) IS+OI+& (a/~.a3 u; d ‘yJ s1aKq apouy ,($) 30 # L8‘ 03’13 (“/ATT u!d’%)‘,(dgz.o) + ,(L’o) = z;i;? 0d Charged Tracks 1.4<p<2.4 Mean of Lowest 50% GeV/c :.’ (. -. _’ ‘. ‘.’ ! ; ., .‘, , “( ‘,’ ,(/ -ILI- .. .:, .‘. : ^ 0-s d 0’9 q -7+7--j -n 4 - -0 0’6 (,I,,,.z, coo-ee90soo I Combinations/2.5 * -- .- --7--* ..- R MeV -ELI- (/WI) OOC'S SLZ'S SSDfl OSZ'S SZZ'S I""""""""" OOZ'S I 0 os-I ‘(cp.o = (-8+ET)N + hm?)N k18)N ., P’Z 8'2 8’1 Z’I Z’I E’I 1’1 S-Z L’I L'I 8'2 P'8 9.t E’E O'E 6'11 LOI) (-‘+tid+-,&)a I 1 1 --‘++rN ,Vo*N --,N++:N &.N .JL++v ,yov (3*3 snoav) lo --*- N++V lo ,&oV ‘-Ad o,Nd ‘-Ed ‘,vd_ d pue d ‘“~=!IIW urn~uau~om MOI 3-s @IO d qw.zas .a3eds aseqd, (r-01) (-x&J+---g)8 doiN -I oz 1 200-8e90500 I E EO r-71 I 0 b I x x X II b 0 b t.- 0 b I MeV 0 VI b b 1+-+-J”‘I”“I”“I Combinations/2.5 0 b cn b ‘: ” ,:.. : :I Combinations/2.5 MeV ::,, ‘. ‘.,_’ .‘,. .I :.’ -: : 1 ,(x+a+-oah _ ~ (x-a+&TAJ N (o&ST) ‘(,&a)N + @7,,tT)N = ’ : ‘I ,‘. .’ ,I I;, ,, I/N, dN,/dp, IGeV/c) X II ,I L .: ,, ,, ~‘.; ., ‘, ‘,.. .; (, ,,.,, .’ (.’ ‘. ,..‘, , .’ : .,’ “,: i’,.,. : ._ L, __, /. .. . : .. ,- v -H . . : : .- T .’ ” /’ ,’ 6’6 F L‘ZE P’Z 9’Z Z’O C’O Z’O 6’0 -L81- ydures (SP)J aq1 (3) u: s?uaAa -JV 103 s”o!vq!w!p -+wp urnnm?uor, Smpuodsalloa aq& aq? (p) pm -0 am&~ I”RL sP”QqaP!s v s”o~~x?Ja~“~ v+xJ sKwap f~f sKmap K~repuom~ suo~sGauo~ suoldal avd spuno&fmg PP’ZX 8 6’S urnnu!-+uo3 (SPb” 21 E. x 3‘ -681- : : ,a .; ‘. 0’0 0’01 lf=il -ii- E -06’t- ._ 0‘01 h=w s N ‘\ _s. ‘. ..:;,,’ ’ .:: 01 LPOO'O 6'0 =F 8'0 T I'Z L LZO'O 01‘0 =F &I'0 T IE'O 9 EEOO'O 6‘OF Z‘I TZ'Z P> ZZO'O 13 %06 ?e E'O > dq pa=Yqo syuaha -da pun i.3/rm r : -&a 103 uoynqysrp ‘puvqap!s punox%yxg 0 8 %u!sn ‘8 a~n%a S-M 92s OE3 1 P2'S 923 1 1,’ 02'S 22'S I 00 0’01 0.02 L AW I==% s N _. ~.- : ,. _: .:. .. -1. I :: g-01 x OX > *-Ol X E'8 > p-01 x 17 > ?-Ol X 2'8 > *-Ol X 6'Z > p-01 x P'Z > (73 %06) 43 1'6 > LL(08Ll):,Y‘-fl P'9 > ~(om),ZX+a P'P > qooPT)~x+-8 P'E > L(z68)+*x*+8 6'E > ~(Z68)o*Xtoa I'P > ~L(zssLxw? apour Kwaa ('I3 %OS)S?Ua*3 /” (ooPl)Tx - t7 :apom %upw01103aql us paw%lsa.wr uaaq seq +I = af q~!.m aaueuosa~ (oopl)~fl aql oy suosam g 30 Kmap ayl ‘uog!ppe *I ‘a3=*e=osal(08L1):z~ w =o (ot31):x aq? ‘(z68Lx a97 09 sJa3= .>I -v Events / 5 MeV I.... 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I I “Y . EVENTS/DAY . .* l . W”. . a .*I I . l I - ” ,n -. 60 N 0 ? E P 0 P EVENTS/DAY/BIN ? l? 0 ? W : .. . .- .. :: : .aA-dA 40 leyl JaAo uo!~e~pso LA-‘A 40 83JaJCqaJd :aq E’O 40 BZzU!S Pue z(Aa) E-OL 01 z-ot 40 zwv 40 a6UeJ JalaweJed aiq!suodsaJ aql ‘uo!leueldxa 4! Inq apew 6u!aq s! luaw!Jadxa awes aql 40 elep $0 lU!l/ E q$!M ‘JEI6JlZl JO plnohf uo!le~~!3so ou!Jlnau 13aJJoO au1 aJaM s!ql ti 6U!O6-PJeMdn aql -ql!~ yOaq3 huals!suoO ayl (Lz’AIIJOqS Jeadde II!M au!1 S!ql 6uOle S!Shleue IIn4 aql pue ‘Jalyzw u! Jo/pue enOeA u! ‘uo!lejl!Oso ou!Jinau ayl u! i46nos aq ue0 hllewoue paAJasqo syl 40 suo!leueldxa 6u!s!woJd ayl 40 au0 ‘13a44a OS e ‘(60’OT9S’0)‘~3’W(a ayl aye1 am ‘sou!Jlnau aLj1 40 p!J la6 01 JapJO ‘IBWJOU al!nb al!qM 40 ‘ON/If 40 ‘ON)pea(a ayi 40 ‘ON/d 40 ‘ON) :u!elqo pue sjuaha 40 sadhl 0~1 au1 40 o!jeJ O!Jaydsowle 40 xnl4 IleJaho aql u! h$u!elJaOun %oZ LII ‘9 ‘6!j U! hlleOydeJ6 UMOL(S ale suos!JedwoO ayl S! qO!L/M (gt’()TZt’t) =‘O’W(a :loa44a Dg e ‘(~gO’OT6S~O) :s! IlnsaJ -rl aql 01 2.0 luaJJn3 MEN =‘3)‘w(Ti .hua!O!44a y&6 ‘a6Jel a41 pue II!M ‘. ,1 : Jayia6ol KeOap-v eel pue asneOaq (Z ~WI 001 a~/‘A sem %(ZTLL) palzadxa a-d-u pawnsse ayl sluaha ayl s! aql Gu!waas UoJlOala pau!e~uoO (lews uo!le3!4yuap! ‘%(LOT ‘u I#M d~l saA!6 o!leJ II!M SllnsaJ ske3ap aql leu!4 l! uaqm ‘I(6Jaua OU!J)naN aql JaleOs JO~ tit S!ql pue ‘tit a41 u! aOuaJa44!p UO ‘lah IlnSatj pue ayl aA,!l!SOd se lu!eJlsuoO JO4 ISZ-E :Aag ‘eA JaleOs u! suo!baJ ssew ou ‘At saiy6 6u!pJe6aJs!p JO PJ!H ‘8 ou!loyd Jo4 :09-c papnl3xa lo4 pue ‘1.3 0Z o/O06 a uns 01 papaau SeM 19) pa-sqo aql alnf!p q6noql a-d o!leJ aq II!M ayl u! salO!lJed ‘saOJnos lu!od Ja6Jel apnl!u6ew Oyat] AAeaH JO4 yOJeas .L UJOJ~ souylnau h6Jaua q6!4 a41 1Oalap 40 SJapJO eaJe aA!l!slras 40 sJol3alap aql leql ‘JaAamoq ‘Jea13 s! 11 wieJowii0~ 3aNv)1oIwvy acll Aq hl~o~ paqs!lqnd aq 111~ sllnsaJ leu!4 ayl pue hJeu!w!laJd 11~s a18 Sanleh asaql Jo4 OL’O ‘EEPSS Jo4 ‘P-X-3Wl Jo4 9Z’O Pue ‘C-X-‘la/\ Jo4 PE’O “ua3’lK3 gzj.0 ‘ebu!wag JO4 Eg.0 ‘qeJ3 JO4 99‘0 ‘t-X-‘JaH JO4 pp’t ‘E-X -,6h3 JO4 135’0 ‘eLg6tNS JO4 Z’t : I.sz.w3cL.ot 40 sl!un U! aJe sa3Jnos alq!ssod 40 UO!lOaJ -!p aql ~0~4 s,ri 6u!o6-pJeMdn PaOnpOJd-Ou!JlnaU .sllnsaJ aA,!lebau l!w!l Jaddn ‘1’3 %06 ayl SaOJnos lu!od ~04 y3Jeas atQ seh? apew oslt/ apew SeM eLg6tNS 40 uo!lOaJ!p sluaha aqi (,,sou!JlnaN WOJj h6JaUs aql ~04 pau!elqo saxnl4 u!ebe L#M s’A h6Jaua 46!y 40 .Je4 OS s$lnsaJ aA!lebau L#M AbJaua SdA y6!H y6!y 40 sa3Jnog JO4 yOJeas lu!od ayl Jo4 q3JeaS ‘9 Buowtj y pue apow 6u!~01 U! 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JO$Oalap AoyuaJaa Jalem a6Jel e ‘8WI pue 3aNV)1OjWV)1 qlOq ‘UO!leJadO 40 Shp I(iJea aql WOJA (,;sllnsaJ 6u!lsaJalu! awos paieaAaJ 2aNVyoIWvx hq sou!Jlnau O!JaqdSOwie aql 40 s!sAleue In4aJeO e I(lluaOat] UO!$e]l!3SO Jeadde “A JaleOs JO4 IS< “A :sz-P ‘A OeJ!a ~04 :gL< ‘A eueJo!eW 3luaAa rl aql aJe TaNV)(o[Wvy kq pau!elqo Je4 OS sl[nsaJ AJeu!wllaJd aql 6u!o6-pJeMdn ayl u! se IlaM se sluaha pau!eluoO aql u! apew uaaq ahey uns aql 40 uo!lOaJ!p ay ~0~4 sleub!s ou!Jlnau alq!ssod ~04 yOJeas aql elea(T( 40 ‘ON) sem (zz.kllJOqS we -0t 40 ‘ON)/ eleO(a 40 ‘ON) 40 ‘ON)/ q1!M apew .rl e ~0 uoJlOala ue s! LJepuoOas au1 JaylayM az/(leue pue ‘O/Aasg’Z ‘sluaAa pau!eluo:, 6u!J-alBu!s 40 aldwes a41 le yool snql am .sluaAa pa6JeqO O!lsela-opnasd ayl u! alq!s!A I(lalnOe aJow aq II!M lOa44a au uww AawZi’L u-q w w-ww uwwp a-41 am-w 3aNvyoiWvy u! hlle!Oadsa hlay!lun osje s! (Z hl!q!ssod a41 pue aAoqe pau!eldxa se Alay!lun hJaA s! (L &!i!q!ssod aql .sO!sQd Jo4-palunoOOeun-1aA -se awos (& JO ‘palew!lsaJaAo suoJlOala &Oap a-T( 40 huay44a uo!lOalap lOa44a s!ql -104 ayi PaAJasqo pue pue %(tFpc) s!y$ ;: c_ :. llenba bu!yOueJq I( 40 uO!lOnpOJd I(eOap SnLQ aA 40 Jaqwnu 3,rl uoJ$Oaja olu! AeOap-)1 ayl ‘puey Jay10 a41 uo aql saop OS pue leqruawos tf as!eJ II!M uo!ieJap!suoO s!ql all1 40 aseaJOu! paheOapun o!leJ II!M 40 aOuals!xa AdJaua aql ‘at ~I!M .Jalua:, O!lOele6 aql 40 hl!uyh ayl u! peq haA aq ~83 yO!y~ aw!i 40 uo!lOun4 13a!qo ayl 40 hl!l!q!S!A leO!ldo aql uo puadap 1OU saop Se wnJ]DadS ouylnau 40 UO!l&?AJaSqO luanbasqns ay$ leyi kIeJn33e 40 saaJ6 -Jaluas qpele6 ayl $e uo!iOaJ!p aql lu!od o$ q6noua s! s!yl -apz Yl!M eAOUJadnS e ~04 OOZ lnoqe aq plnoM SW ot $SJ!4 aql u! ‘6u!JalleOs O!lSela I 30 0 IO I5 2 20 p 40 50 0 Fig. 8 observed momentum spectra of e-events, 1000 0 MOMENTUM by KAMIOKANDE. The 500 (a) and of ( MeWc) ,,,, as ‘., > ..: ‘, ., .’ ,A,: (b) 1000 Events m-events, 500 Muon-like ‘aOe4~ns ayl uo Jayd!llnwoloqd @WOOS alfiu!s e Aq paJaAO3 sJa!ld!ynuJoloqd )cu30~ q3ea 1UaSaJdaJ aq 0~ eaJe aql s! s pue ‘OSSeS-UI?Js-VN3-l 40 Ma!A Ino-in3 qzuraq3s aql 6 ‘6!3 qeho pws aql ‘i’s’)3 UJOOOZ le ~a,,o~ aq I~!M skew-l 40 EJaua ploysaJy1 ayl .aaJ6 ‘SJaMOyS -ap 1 ueql Jallaq s! 1uawaJnseaur JI?lnbUe aq u! kxJn33e ayl UOJpEq h?J 3!LUSOO 40 punoJ6yOeq 6L+J~aqMJaAO aS!MJal#O aq$ UJOJ4 pa$eJ -edas AluealO S,heJd h6Jaua q6y aql lOa$ap UKI JoPalap Uonw ayl se ~01 -0alap Jauu! aL# hq dn-yOeq alaldluo0 ayl L#M pue SJolOalap ~014 h6Jaua ~006 aJe ‘sa!pnls Jay10 ~04 SJajUnO3-!$Ue atil se 1Oe qO!qM ‘salnpoLu Jakl ‘shel-L A6JaUa q6!4 40 SaOJnos lu!od aql ~04 y3Jeag doi au ki) ‘4!1!9 -edeO abeluehpe uO!~eU$U!JOS!p Gu!ye$ a-ri hq uns ayl aql ~J!M Jaqla601 u! salO!lJed 1uawaJnseaLu ~eln6ue aq1 .zw e L#M hOUOJ$Se ou!J$nau A6Jaua po1 y6!y O!lau sseu~ le!Onp!4 I(AeaH uole6aw ~04 43JeaS auo 40 (9) .aaJ6ap 1 ueql Jafaq s! 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JO~~alap aql 40 1Jed S!ql 01 u~op aA!l!suas 1~ ayew 01 s,lWd aJow qI!M awnloh yOot lsowJauu! aql d!nba ue3 aM ‘lUe6eAeJlXa aJOw l!q a[ll!l e aq 01 lUeM aM 41 CL) 40 luaw$Jed 40 aaua!Ds 3aNv)101WvH ~04 lloddns e s! 11 ‘e!UeAlkUUad 40 ahoqe pue le uoysodwoz AeJ 3!wSO3 hJew!Jd aqi 40 ApnlS ‘Aa (9) .: .: :_ .: 'Ot q3Jefl pUE ‘886t pue JadJEg '8861 :le ia pauJea1 '9.r '88 -&Pg-tts-Hn 'lu!JdaJd !!eMeH 40 .r\!un y3JEfl ‘PtP/Hd/(-JVW ‘lu!JdaJd U!SUOC’S!M 40 ‘A!Un :lUEUS!L#,rj ‘)( ‘A :oqe aas ‘(8861) ‘ohyol 40 .A!un ‘s!sayl ‘a‘qd :evyel ‘4~4 (LZ ‘91P 'PO9Z '8tl (L861) (L861) x-5 pue 'ueder (886t) 166 (9861) "=eAol m ?E '3lai "llal 'AaH '98,NV803l/Il~OM 'sh4d 'shd fle la QeJ!H :ie ia eweho YlL '3oJd :eY'slol 'S'Y ‘gt-88# ‘SOZ (9861) 'ss1 (0861) m .Aat] pU’I2 _-: ._ : 0-z-a uo 'O~yOl (~61) (986L) zz m 40 h!sJaA!un ‘TJS "I' ‘?a’./1 “shd wr4 'dv ‘a’lld ‘IanN 'Aatl :Jau!llel :OleS ~AOYeY’ki :ie ia uewaw 'W'r pue ‘N (ZZ ‘V’A 'z.a sMoJJ"El (LZ (oz 'V (6L .sAydoJlsV ‘UOJlSV .AaH ‘UUV :JaAEaM ‘V’l pUE AalSOOM "hau awa!3S aDedS :olouJoN ')1 pue o$our!bnS 'a (81 :JasauaM UO!lnlOAg '3 JellCIlS 's&d 40 lU!JdaJd s3!shydoJ~sV IE3~aJOayl EUOZ!JV :SMOJJnfl ‘V "shyd 'I3nN :wweJq3S 'N'a 'amelsu! Jo4 aas 'luaha pue sc+l(qd alD!lJed uo 'suo!$e3!lduJ! ayl ~oj (Q E8 z g a3ua!3S 'le la atjp!qJna "AaH (9Z 'A (SZ 'A (PZ ‘EUOZ!Jkj Al!sJaA!Un ‘OSIV ‘LLP (8861) S!ql 40 's3!s~qdoJPe .(886L) t LE (286 t) m .f9t '8L1 '3's 52x (L86t) 'pow 'r pue fosle 40 Japuelpa!Jj '9 'amew! we 6961 we JO4 aas 09f (Lt 'LPS (LS61) 6t "shYd '(8961) II!H-MeJ33W 's!saqwAsoamN :UOl~el3 .a.CI ‘aDuelsu! Jo4 aaS (91 aaS Sap!XI!Jd 'PE9Z ‘.. ‘. .. (8L61) 7-m .f+tj 'shd :u!alsua4ioM (6L61) '1 (Sl -‘: ‘LL (986L)'i;-j oway3 OAonN :AOUJ!WS ‘S6P (696L) pue Aoq!Jg '/\ lp86 (8961) ?i?-? ‘d13r 'A 'V pue AaAwi!w 981 'llal +d "'OS 'sAlld 'd.S (PL :oAJo3aluod 'oAJo3aluod '8 '8 (Et _. PPL3 ?VNd 1= tlIlIBH3 30 NOIL3n(IOXd ONIKLfl3N /. -9IC- ;. .. - .. :. X 0 1 -. I L 0 \ (x).mqsx -(X)JWPX X E (x)s* -- (x)px --- 005 .. oat ooc 002 001 0 : I . -. ‘-. : .-.: ..:.:. : : : 1 ,,(z - -7-----??--- l)(z)pON uo!ynpodd = (z)6 = t5k uoncqp u%!s-a>!soddoJo lapo~ 'm ---- .-.- _.. ,(? - f - I)2 I = (z)a ; :,:):::‘,, .; ,, ., / ‘, ., 1,:,: ‘, (,.’ N 0 63 0 0, 0 ;P 0 I :I - - I - - - -4 +-k ! t ?..I tEi+ I I Jz- dN/dz t-2 g 0 z 0 r: 0 0 dN/dz :. ’ -22c- AW 009 ‘“3 002 OOP 0 00'0 \I *-tb+~- ,. 2 10'0 -----IA - mopaaq 30 saa&lp 11 ‘03 1;‘6 = zx %O’I T Z’OI = “8 g’p = D 009 900’0 + 110’0 + 890’0 = *!A - OOP f \ 9 + 20'0 002 00’0 r 10’0 ZO’O I. xir 0 iv 0 0 0 0 cn 0 dN/dx dN/dx 0 - 0 cr’ E 0 g dN,‘dx -PZE- I 002 1I 00% . : -LZE- : . : SNO;Ld3’IICl NVA-‘IT3lTCI 60 SXV3A AiLN3M;C -_ ‘_ : ooz . 00s v oot7 n .:._.::. . _. ::..f^- .: ‘. SLl’OQl S’Z- S’6E S’*Q’Z osz l’+B‘Z OS1 t’+E’Z 082 OS1 EE’+ZZ’Z LE’+Gt’z szz t’+OL’Z t6I l’+e’z Z’+Zl’+St’Z E’+s’+l’E L’l- SZT @It EQ’W=p OOP &‘+Q’l EQ’PP=S’+ Z’+Q’l L’L oar M--U M-*lL v--u M-J-L M--u (L860.1~ f40 PIeUOaw (0861).me ?a (6L60 (S861). (‘360 . I= v (0861) (98) ’ ,* UOPJO) o?e’q le 70 ~‘W=W I = -30 00 I “=Vl (E861)‘l’V m-d’d_ m-d_ ‘+d-d d-d d-d Je!P=a I” ?a ‘@!PW 30 S!Z’JUOSSI3”“V (S86I)‘l’ (IQ)‘,” ‘W Jo!P’il qe S!,W”O~J”O] (1861) 19 W ‘=~S-J?uV M-d (186T)‘le ?d-d 10 W!‘S (7861) ’ le W 0’41 -6X- dI3 7330~0 11-v ! I q.l ‘-3 OWN d> “Yl 8’EZ=W P’6L=W’ V 13 8823 EVN EVN SRWV EVN S38VV dNWH) MJNW SXI ,: .” BEAM .DlJMP in the M-East 40 at Fermilab. COUNTER BANK I 50 Meters ELECTRON HADRON CALORIMETERS MUON PROPORTIONAL .. DRIFT CHAMBER _ PROF~RTI~NAL ~HAMI~R beamline ----- -. -.- 2’0 3’0 ELEVATION SECTION E-605 Fig 3. E605 spectrometer IO I azzd STEEL MULTISTEP PROPORTIONAL WIRE CHAMBER ~~~~.~~~~~ PLAN VIEW E-605 SM3 -,, $,,.. ,,‘:, ,’ R P 0 L P b 4 e r 0 :: do s Liz&I,-I Ol ki (cm’Gev’/nucl) 0 u 0 ifi ., ;.‘ .: ,‘.’ ;’ ,“. ,, -El&- ssm “31” i I ,’ ,: . ..‘, .,. ,’ ‘,’ ‘: :, ,:. ,‘(. ; 1’1, ‘, : . I -9w :-, ,: ... ;, (9) +(I (INY ;a 3H.L 60 SAV33CI NOId 33XH.L ‘I s S I / 3 ‘+-M . . ._ : .paqsgqnd uaaq Kpeaqs axq ,sKwap ..‘.. I I 0 I I II Events/(O.l Events/(10 $ I 1 GeV2/c4) E MeV/c') I KJ 0 P P / 3 3 :ii 7Pn (0) (T3 9406) 610'0 > (?I3 X06) 6Z'0 > 100'0 T 900'0 + 800'0 200'0 T LOO‘0'f LZO'O EOO'OF LOO'0F 5x0'0 EO'OT 01'0 7 82'0 ("I.3 x06) 80.0 > EO'OT 60'0 i 62'0 PO'0 F 01'0 T PP'O +u+kx + +y+cw + +X+=-H+ +4 + +J+ + p9 + +@ + +a +a +a +“a !a +“a fa +r+r.-r+~a +- +a +~+K~+JL-Y+ ;a +uod+- +a ?Y+Y+Y-JL)+ +a +y+~-= + +a +~4 + Ia +x+x-y + +“a : S F P 3 $6 A 7 ZXLI~&X~ OMJaql uaaM$aq asuala3laly aaynwap JO uo!lou aqt svod -dns K[~ea~ssdmap +a passalddns-oqq!qas 30 sadd? OM~a~? JO uos!radmoD aq& . go.o ~ +a 81.0 = P(+x-x+x)-+aPw ‘a.rq aM sapn$![dmo parcmbs 30 oye~ aql IO,J ‘XXX .I .:.. aqt ~J!M par-zdmoa ST Ayers uo!d aalq$ aql 103 azzds aseqd atom aa~gl JO ~o~~e3 e s! azaql alaH XXI ~ueuosa~uou ar(l ‘03 uos!mdmo:, ayl ayem ospz 1183a& . ‘sKmap lo?>ah-Ie[wsopnasd passalddns-oqq!qoD JO sadd? OM?aq$203 ~o!yz~BuyDuwq JO -OV&- : .: .. :’ 1%(z~o T 2.0i ~‘0)= (~fi+=V+uqC + +a) a _ > 1 I 8 I I (GeV/c2 1 EVENTS IO.02 (GeV/c2) 8 EVENTS IO.02 ., ,’ ,. 8 I : ” .’ CTI s;o y ‘p- -ZPF- 1” _. -UK- .’ : .:‘. 001 002 001 002 OOE OOP 009 009 :’ 1693 - : I 0 Es Events Events iz / 5 MeV E / 20 MeV I, :. 1 ,,,I. !j /. ^ .,: ” ., -:. ;., ..‘. 09 \ CL 0 08 OOT 1693 L -9tc- j8861) 8SO-88 .^ i; -LbE- _. ., :: “. .__ ;.. .._ .,.,,, /, ., : ,,’ :,,:‘I, ‘_I Fig. 2. Plan view of the E777 spectrometer 3- 1 3 3 3 3 I W’O ‘/O-O _--- _----- L-OF% __-. 1-JJO.l _----- L -OlXZ> ril.0 ------ 1;-0V8 t/l’0 10’0 L-OFQ> > laJ3TluaPI ll ---- ‘/6’0 86’0 S6’0 ---- 08’0 ---- ‘~6.0 .lar372uap1 -leaoJ, ---- -_-_ -a SB -d ZOO’0 ZOO’ 0 SO’0 < LO’0 CO’0 20’0 co-0 +I! se +a “)UaPJsTW 66’0 66’0 96.0 66’0 66’0 06’0 06’0 86’0 L6’O 66’0 < 23 - -6b&- +ri se +u +ri sv +a -a sa -!I 200’0 ___ 13 200’0 ___ 13 ‘il.0 __ lanoqS 66’0 - ,anoqS ___ 66’0 r, +J -a +fl +u 13 -I - LOO -. -3 - -2 - -1 - 0 I 100 ‘1 t 200 400 ‘1 I so0 r b) longitudinal and y=O. 0 LOO ‘1 200 along the beam (z) direction -1oa ,,,,,, of the PWC’s. (kGauss) -2 t I-- field at x=0 and y=ZO cm. field at x=0 are the positions a) vertical indicated I t 60’ Fig. 3. The field profile ?l ,,L!r 300 1.5 2 (cm). 300 ?a:,,,; 1, Also 400 ‘J 500 L 600 I4 I - - - publ. run) >ffspring(sI E777 wssibLe for estimate (1988 at ready hand data or E777 8XP.5. previous 1,: : ,’ ‘. .: I... . ;:‘,; , ,J::‘, with 2700 HZ limits m(e+a-) ClR / on ? and C2R study detailed study some OVBP ekn. of quantitative scalar vector matrix Overview pi+e+e- (E051) in +-0.1 +-0.2 +-0.4 2.7*-0.5 low 700 -> Ea*10**7 K+ III: /also: 200 41 evts Table with O? O? 0 0 evts K+ E777 -> Past, *10**-9 two-stage 10**-11 2.*10**-10 1.1*10**-9 5. beam SR 90% C.L. pi+mu+e- Physics: 500 200 N 150 50 h N N 4 14 evts -> -> K+ K+ Present Future. 0**7 the fast optimization resolution end with events events events -II- -_- 2+2-1 1,+-3 m*, *+e+e-"" rnu+e+*-"" and (E151) e+e- 7 the PWC so --- 1.2 events (90% 1.7+-0.7 2.2+2.4-1 Ee*10**7 -> of beam 0 59 9 evts pi0 CL) .I .’ .” .I “, .” .. (” .; _.. .. :,.... ii!. 1.. *, . . .. * : i .,’ -ESE- -’ ., :_. 09s 02s . . 08P *. * # : .: : : ‘, .. . .-:., .‘, 1.:;. ,1 _-. .: . :.,‘.. : s 9 R m * P I” In % P a P & z b . ,’ f 0’ m .I., :.. (. .,’ ‘, *8 4 A 9:: s5 Fig. 1. plan view vertical of the scales. 0 5 5 .? E780 detector. Note Lead Glass the different horizontal Range and Stack c3 E ,..,“ ;. ‘, Fig. ‘, 2. 10 I 470 M 490 TT+TT-n” .+.--7J I, ,h (hleV) 510 G I (b) 12.5 Distributions of (a) effective mass, (b) T+TI-~~ y the square of the events with 6' < mr -4 , and (c) angle for events within MeV/c* of the R mass. % (MeV) (a) F m 6 :: effective target 0 5 (:nrad2) mass for reconstruction o-’ (C) :: ‘_ ,: ,: Z L L 0 ozc 00s 08 (q> :( I P R R Events/bin ,’ .:., .’ ,’ ’ ,’ : I, ‘, G “T1 cd k n %I Fig. Fig. 5. . .- . . .a . 6. -, Scatter target Scatter target 460 o-“‘$;.i *. I nOe+eangle. I effective . . mass SO0 I (Mew I e+eeffective angle. M ee plot of the reconstruction . I 480 / plot of the reconstruction .. 1 ** - ,. . . ,::-.:. .. - . I:*. . . .a.* mass vs. I vs. the I the square 550 I square of of the the ti m Fig. 7. 240 y A IOF ‘0 i-i w 320 confidence level of e+eeffective 360 limits mass. M ee (MeV) 280 Ninety percent as a function I on KQL -+ r'e+e- 400 .,’ ,I ::..: ,I: ‘:, -E9E- :. :. : I’,.. .:. : i 01 02 OC (9) : 0!7 1 Events 8 (m-adz) :, . . . . . . : . . ” . * .:...’ .. *, : -S9E- . . ..- -I. ‘01 ‘6 ‘6 .L -9 ‘S ‘P ‘E ..: ::, ‘._ I ... ‘Z .L 1...‘,. -99E- . ._, ..‘: alnl!lsul JwJJJ% 3vls -L9C- 8861 aql ,o ax~a~a~uo~ lez!dol aql le ua@ qlet palw( NM33 IV lN3bYM3dX3 If-VN 3Hl NI lN3W3M-lSV3Y1-+o -@)a 3HlJO snlvls (INV NOIlVlOlh d3 133t110JO NOllVhkl3S80 .-. -89E- ,I ..I _. ,. ^. : .: .- : .;. . .,c . -69E- ‘SOO’O F 900.0 + 086’0 )o anleA e o!beJ alqnop aql~o, -..: .:, I & : I’0 2‘0 1’0 1’0’ 1’0 1’0 ) 1’0 I.0 ) E’O 2’0 I’0 (- ?I OOO’OFj ‘-X+X (- = tl pau!e)qo ati sXe3ap -x+x ‘M OOO’OOE ‘& t----h <-.-‘x ooO’oof< pue 000’011 3”‘=V WJ l’-eH kmgjjau! Ja66!Jl sfewap!zme Iq sasso( pm syeg awe)dasse ol~e3 aiuw Xyj!qelsu! Jawul!Jo,q) ama6JaAlp u~eaq *n ,J’H u! amaJajj!a ha!3!jjau! Jaiunor)!ye sn ureaq sn at(l U! 6u!~aw~5 uwaq 7u u! alms WJaua u! awaiajjfp ~u+YG-‘~ “1 uo!,sa,,qns o~z~-‘n u! uo!,zw~qns uo!leJaua6au -x+x 1 o~z puno~6y3eg puno~6y3eg :sa!~lm!jj!p levmuwdxa alqe~ap!swm W!M paaewsse s! wasmd auo uey) Jawq jo uo!s!xadd aq) 03 all!wad e 40 Japx, aql jo soge~ 6uymeJq qym shap Bu!~elo!~ ,j3 jo ~ua~amseau~ au I SOm \ proton beam dump sweeping magnets k collimator \ collimators 2J- I I L. Sp cm IJ-nnA n ) calorimeter veto counters alorimctcr \ wire chamber 2 anticounter-rings I wire chamber 1 K, beam train displacement 7 anticounter-rings n \ plastic window T P w .’ .(.’ _, ., 0 01 a m 01 EVENTS s / 5 GW OldZ 1X ZOldW ‘Sh’ LOldVY 11.0 21’0 Cl.0 t1.0 51’0 91’0 I t I+ t t t I .’ ,,’ : 1 j. .:. >. :, EVENTS PER BIN OF 3 IN x’ Flg. 8 Ka doto - Closest Distance of Approach for K --) CDA KS is scaled to the K, geometry. Kl data . n’x- ways. ,‘, ‘_ .-. ‘. :’ “, ,‘. .> ‘. ‘., K VI c” Fig. 10 Comparison of R+ k* mass distributions of KL and KS. The second Fig. shows the ratio of the distributions. Flg.11 - to3 --.-.- . - -.--.- Ksdatc KI data -- lltMutkmofthmhstancaoftheDecayplanefmmtheT;rrgst. F YY- IO’ Y : 1 : 0 105 Y; F 1 DTARGET .. : : ;. ue pue 3~ Xq Buyajj!p paheq3 sa!6~aua le pamseaw Pue (o~z~-*n)~/(o~z’-ln)~ aq\ pue ,eJvlaU al(3 uaam\aq 1jys saldues ac~a,a,a~ -LLE- JO uo!wnj e se pallold s! suowd jo JaqLunu au (q UI ‘yrre,, uo!d ,sa,eau aql 01 awels!p ~!a’.0 PUP XBSUJ J!aql JO ~o!lsunje se pallold ale suoloqd ewa (e UI ale (_u+u~-~~)J/(_Y+u<-‘~)~ SoJleJ aq1 ‘SqeJs a$imJa ‘UO)~d A6xIua aq1 “1 a3”aJa,j!p aql wo y*p spl8.q ox~x+Y 4-- >I 40 wlP8JWS 2L ‘BU aq1 q6!q ,e elep aql ,o asoql q),m ,,a~ IJW ,,e JO ums aql jo uo!lnqyls!p adie &aua s! eiep ac(l ql!m wauaa~6e aql pue uo!lnq!Jls!p au punoJ6qaeq ale jo wns pau!qwoa aq) jo uo!lnq!>ls!p ‘9~ am&j u! m3~alp a4* , -uo!lnq!JluoD wnw!xeu~ SI! sly!1 s!ql .k Gu!kelJaAo ql!rn V~L--)( lelol BujKepey) 3vm.Ja~s~s e S! a,aq1 ,! ‘JaAamoj+ ‘o!*eJ a,qnop ay1 “! s,a3ue3 SW pue ‘y ,o ewads ‘( L\ ‘6!j) sa”,eAla6-‘=‘p ‘lua(ia3xa z ac(~ asp amu~aq~mj umoqs SJ saldues -.--.-.-.--.--.- -.- -.--:-1 ,o auo aq, ueq, daa)s ssa, kju!e)m s! ,nq Xlqe+u partdun aq louuec~ punoJ68xeq ‘06Jw1p aql ,A Gu!r(eldaAo ou ql!m ,,u-Y+UL+ alq!ssod SJql )O “o!l”q!Jls!p JO lunoue ~letus e JOI ulco~ sa~eq saleuylsa asaul u! 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Dlarq gt 5 d Sum of reference samples 5 z ‘0 loo with Large dtupt Energy t CeV samples Dlorqqt5 Sum of reference KI dota. -’ I -1I- Rg. 17 comparison 60 CI- 50, - too 150 200 250 5 E 300 z' G ,D +Jo % 2 5L 350 .‘. ; ,,. ‘, ‘ :: ‘: ‘I,,... : ;:.: ~ 2 tmrtsx~m :, ,, ,,: ,’ ,,.. “,, ., ‘_ position. of Decays Near the AMcounter. is a fit to the anticounter Dlstrlbutlon The solid cuwz flg. 18 Vertex R OS ot I -28C- 1’0 (I’Z-+8’L t JO m:3e, Kq su!q z-3 40 t4 ahew (IS01 SluaAa PO06 JO x OS) S‘L 01 5’2 UOJ, pa6uev In3 5 E’l Y3 uJ3 11 01 f 40 P-lsu! 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Introduction The Collider tracking Detector and proton-antiproton derived overview run at of the density and the CDF Detector CDF apparatus here coordinates only ) as the the polar the and beam. over and the great detail during After I will inclusive .. .. ,I : j:.. the a brief present results charged particle of the coil, calorimeters are a set R-s reconstruction tracking are divided and segmentation plates, region into the and into a larger uses plastic region, outer between and regions time be CTC projection particles is complemented based 17 I <l.O, part, to the quality. tower by geometry. on very the natural plug with as sampling is part, with steel absorbers. medium, ,:. region In all cases there electromagnetic hadronic scintillator wires is of order of charged 2.2< Iv I <4.0. an inner sense is measured of 8 vertex region, solenoid wire on a projective three for of per measurement central the forward layers position based angle is a cylindrical Lying pipe the l.O< lvl<2.2, I~l<l. vertex polar substitute 7 II 4.0 for 8=2’. resolution and provide calorimetry constraints: 86 I q=-ln(tan(B/2)). volume resolution momentum event to by 2, and use spherical superconducting magnetic with Ref. B as the , and a 1.5 Tesla (CTC), of the 4s sampling axis, 7, given the in 1. We is convenient of 1.2 m. The beam which on Fig. r) N 1 for b’=40° transverse a measurement central set, ..1:;:- of on resuIts collected and polar It around Within a mechanical The as the for ~~22.0 GeV/c beryllium absorbing line chamber (VTPC) geometric based a radius 5 0.002~~ Outside The the tracking almost in overview comparisons: with the magnetic products here Collider. data “pseudo-rapidity” is built modules 1987 physics, the I report of 30 nb-’ coordinate. detector distributed and 1.8 TeV. is described the beam angle 200 pm, the purpose study Tevatron jet azimuthal Some convenient bp,/p, and a brief with and central = to spectra. The coaxial 6 luminosity production, 2. The The is a general designed Fermilab detector boson present at an integrated data on vector Fermilab device collisions from 1987 at calorimetric lead and is -416- :’ : .- segmented into electromagnetic resolution uE/E absorption = regions and Muon system size the deep use A#=150 and has a depth and central has hadronic o,.E gas proportional Av~0.1. of 20 radiation = central and a data is 5 written compartment 70%/a. sampling The with thresholds The lengths plug a tower size in the behind the is essentially regions scintillation 100% on magnetized central hadron region consists calorimeters efficient for both sides are toroids with drift of 4 layers in the muons muon region over 3 GeV/c. spectrometers chamber of and 4. of sets forward counters are mounted calorimeters electromagnetic “beam-beam” counters (BBC) in the are used for on the region front TeV. 3.2<lt71<5.9. luminosity neutlinos3 The Data Fermilab These based measurement in the on instantaneous logged luminosities several kinds The “Level energies. Collider momentum physics supplied from of order of data 10” by to cm-‘s.r depending sets, 1 Buffet” selected colliding February data the set beams May were on contains following high calorimetric the beam to >20-45 GeV Electron: 1 tower in EM CMU: Central muon FMU: Track in towers calorimeter stub candidate matched with 1.0 GeV with Et in forward muon Level combination counters 1 triggers with during the consisted of the presence a 15 nsec window of hits any of on both centered sides on the beam The of a counters in events were recorded of 9,400 events was recorded decays into at CDF other Drell-Yan leptons with of isolated set of 25.3 converge detector the nb-” malfunctions. on and analyses,one associated but cross-check the identification data detector systematics, a powerful via charged in two parallel on the a common gross different Et analysis of the Et ring Et -417- passed on culled The two the same performance and these energy beam and opposite of Etmiss by of the occur with leading comparing required required as over all events to was applied to have a jet Igl less than region Etmias signal. that outside Mismeasured the Etmiss energy algorithm are in the by requiring of any jet defined 1.0.’ cuts. deposition crossing. absence 3.6 and clustering events GeV 2. We transverse less than on the quality hadronic the A jet 15.0 are suppressed + cone of 180°*300 significance array, than in Fig. of ITI 25.0 GeV. greater selected the sum in the region splashes at the is outlined vector of 1614 events by requiring in beam-beam crossing. very from free tower with the central of the beam-beam with 56,000 energy the start calorimeter the main conditions have towers We next GeV. track. road. above are missing ‘centered Valid paths that than A total or more. >(7.0-12.0) to a trigger were collected in pp collisions their transverse and Etmias greater cluster CEt set was in the sample were studied missing magnitude have tracking triggers: Jet: by \V bosom providing calorimeter transverse and data of hits are produced identified neutrino, Both The CDF and delivered efficiencies. Average achieved. triggers a constant 70 nb-’ Production then runs sample, of protons 1987. to maintain of the Approximately a smaller W bosons the approaches period coincidence crossing. addition, unreconstructed and Set Tevatron antiprotons only The electrons. 1987 bias” Boson and from S. The or “minimum beam In Vector of the triggering. and the process of scintillation bias requiring Intermediate triggering counters. Two luminosity 30 nb-’ the consisting planes with Approximately at 4% = 0.63 TeV. The In adjusted rate. low with at I.8 drift 1~1<0.7. roughly to tape. trigger of time coverage were acquisition Another and Aq=O.l. chambers forward of 14%/a; lengths forward A4=50 large towers compartment Et QCD dijets than it to the rays 3.0 of a 20 nsec greater cluster. Cosmic less than Finally, size of the were and GeV of window suppressed 5.0 GeV in the we evaluate overall the random : ..,. .,. .:’ I_._ ;;:. -,-... E Analysis -Missing -T“Good” error from bias events, width 4 Runs where 1.0 v in the x lo5 events calorimeter and of After Missing 1614 E, p such events @T- > 25GeV Cl > 15GeV typical projection of the calorimeter out of time dijet cut (E, $,/K events > 2.8 J 11 track with trk EC’ / p < 2.0 The W boson analysis on missing Et. -418- top with energy to have a : .: ,., : GeV vs. in Figs. Most kinds two at large passes events the is consistent dijet is cut; the the with the signature based on electrons, 4b, Et for we see one stiff electromagnetic in the the and the tower in electron shows the and a clear non-electron backgrounds Etmias in Fig. R-( LEG0 event. for events other the a cursor unoccupied of missing the we see that 4a and of and CTC, EtmiaS significance electron 3, where rectangle in an otherwise of momentum of the plot, loose such page, In the LEG0 samples. which the were rather track Fig. a tower (The the These the contained of to GeV. In to in is beneath. to be the tri-jet, described 4b is a mismeasured contains a narrow W + 7~ followed by hadronic hadronic decay. The W analysis selection of events central region cluster has the calorimeter based the found One of the cluster; 2 required a matched is shown is displayed test the containing l~l<l.O with ratio Ehad/Eem beam data. in a cone of radius Fig. minimum transverse remained. events between above. tau Electron Cluster Eem, Etot > 0.85 39.0 events were and were events with pointing of Etmi*’ sample jet GeV program.) distribution separation > 5 GeV, qS -+ 150”) at calorimeter 28.3 recording non-electron in to be Gaussian of the according along event is has Et em=27.2 The E, < 3GeV = 115 cuts, Twenty-two CTC display actually 115 measured sum Events clusters such of the pt interactive I& OualitY quality Etot/p<2.0. A with scalar calorimeters. of Eem/Eto’>0.85 that representation I is the electron-like signatures. track < 1.0 ;,:1, plug Etmis* for requirements EtPC is well of Etmisa is found Etmias/~>2.8. these searched This distribution where central significance i. = 25.3 nb-’ fluctuations. the “isolation” outlined an isolated cluster Et>15 1ess than in Fig. electromagnetic GeV. 0.05, An a value 5, begins cluster with the in the “electromagnetic” determined from If we let Etcone be the total transverse energy R =[Av’+A# 2] l/Z =0.4, centered on the electromagnetic is defined to be: ccJne clus I I % - Et E clus t ‘. . ‘: - . m td. d c _.i Electron Analya “Good” x IO5 events 4 Runs We required cuts. In momentum second were 452 I Cluster Of the cluster remaining described the above. electron show events We take The 2M EM Cluster in in these electron 22 Fig. in be about identified result G = electrons. -420- with 9a; And have a ..: : :. .,_., -- these in Fig. Etmiaa the smooth in Figs. 7a,b,c of and apparently happily, Et as distributions ALL of these analysis. analysis as our anticipated of transverse [zE”,E”,(~ loose cut distributions most pt has the = relatively anti-dijet The the missing the distribution for the beam-beam cracks, were 30%. for the this and and final Jacobian W form, msss - COSA~~J~~* curve is the ISAJET cross the the first result for with The from various effect of the were studied data. The net from jets were estimated sequential background decay via the measured corrections Monte rapidity Carlo; efficiency all other is estimated from jet data W + 7 * Y was estimated contribution is less than for cuts, 1 event. to and from We section: error is displayed 1.8 TeV.516 and the from total is derived counters backgrounds. Backgrounds The process thresholds derived from Carlo; agreement on isolated from the the are presented via of electron section the background where based of Eclua/p is depicted demanded characteristics, events acceptance, efficiencies < 0.5 events requirements. 8. The cross calorimeter > 3GeV we then found. o.B analysis pair; the event that GeV/c’.’ efficiency, Ehod/Eem < 0.05 W boson cluster for were the is shown find The mass candidates distribution as seen in Fig. Monte 5 to Twenty-one in the sample sample. The Fig. found One such both track 6 were and clean were M,=83.0 I(R=0.4) and a large Z” study. pass and GeV by the selection luminosity @T > 25GeV dijet cut events, which a charged cluster, Et misa>25.0 Mt ET events that of variables rather unbiased Ec’/ptrk < 2.0 ET 4521 electromagnetic 169 events signature > 1 CTC track with Missing found demanded 175 passing to a separate Et events / to the the electromagnetic In < 0.10 175 2.0. and 6. events Ehod/Eem< 0.05 Track Match 0.10 we further p extrapolate removed missing I(R=0.4) than events, be less than 2 = 25.3 nd’ EM I less these is statistical along the = 2.6 f 0.6 f 0.4 nb with theoretically and previous _. the second is systematic. results in Fig. Sb, and calculated increase of W Our shows good production for ” (P.0 > a) UorlQlosI -. 01lQtl ,s., ,‘. W3/PQH ‘. ,, >. :-:, -_ .,. : ,: r W Electron z Et ISAJET 5.36 (63 GeV) _ 6- 40 Fig. 9a 60 80 Transverse Mass (GeVh?) Transverse mass distribution for 100 W sample. 40 Et (GeV) :_ :: Fig. 8 Electron p, in the LO 210 E,,(TeV) W sample. Fig. 9b W production cross section. ..-‘. ., 5. Jet Production At 6 = triggers to parton 1.8 TeV, scatterings event is shown a. Jet The array we expect be dominated and by associated in Fig. kinematics the jet direction is measured by the total cluster The pions by of the jet central and associates electrons. has anticipated absolute various unavoidable effects energy. The measured using tracking and cracks. from After resolution the cross A typical two-jet which of energy tracks net energy jets due of about are balance distribution u=9.0 Jet effect the The measured energies CTC. was Charged of fragmentation effect varies from error and studied of leakage from 40 on 33% GeV this to to the correction interval. we in of opposite measure two-jet jet the intrinsic events.8 For momenta jet a jet Et Et=50 has a Gaussian GeV. Cross differential measured luminosities section was derived cross section, GeV. same applied, momentum the goes through in the study great of 50 lasers, have low the effects energy 250 the to and We at in to these as that forward errors reconstructed correction with beams to response used pursued 2%. contribute of calorimeter corrections apparent clusters: in test about used to study Inclusive the jet of flashers also the calorimeter and is tracked was with the into been a variety were we find apparent and accuracy 12% to 4% over distribution has calibration sources isolated cluster all scale Carlo the The LEt parton- to has been calibrated Carlo via b. high hard energy centroid, Monte measured varies applying deposited Monte The of the GeV, Cs13’ nonlinearity fluctuations; by cluster energy The internal highest our from bremsstrahlung. locally the calorimeter movable 20% from energy.7 validation industry. and gluon are reconstructed which an states resulting 10. an algorithm GeV final jets Reconstruction jet The the hadronic Section cross section, and the number by deconvoluting a procedure whose du/dEt, of jets the jet uncertainty can be computed at each Et Et. resolution is estimated from The from true the Fig. to vary -423- 10 A generic two-jet event. from 25% to 5% over 11 we show fiducial this central have a good have good insure Et vertex timing greater the luminosity error ranges 250 GeV Also QCD EE, the 70% in Fig. with CDF 12.” cross missing in the Et above. The section over ,_ :.: :_ .. ) To jet with include the uncertainties in full :I. . . . ,- :. -:: and analysis. bin from analysis center, a central each the section as the jet best current limit that progress this will the c. Jet 400 this In this advantage Angular Normdication EHLQlQ’=2E: systematic the ,lO Cc\’ the graphs, of curves as momentum all lowest to D+02Q2=2~ transfer EHLQ2Q*=fEf order evolved arises from CDF Prei. the scale.g The show good calculations well to large this Et, known contact Et experiments the experiments, on about confirmed limit out case, the by to about advantage of a factor of increased Ts of possible constituent an enhancement compositeness UA in of quark predicts based energies is a probe parameterization the other as a result distribution interaction approaches GeV, Et at scale which find that In Fig. 600 nb-‘.‘O in A*.ii The A* is 13 we the CDF data; analysis in 700 GeV, based only 30 of higher energy of 20 in integrated on of the jet two and t,hnx-jet subprocesses with center events. of quark-quark the characteristic of mass is seen to far Et (GeV) luminosity. scattering In lhc live-jet and has been Fig. cabs, the l)rcdomin~mt. gluon-gluon Rutherford angle scattering Uncerta;ntJ D+O2Q’=f@ Distributions distribution to occur from 2 + 2 tree family errors with jet is obviously n~ei~surctl in both the sensitivity is from move of data.” outweigh and highest The about uses as. The Within as a 4-fermion than of predictions calculation is compared cross expected discussed Fig. over data. increased At substructure. t-channel detector required errors . In used in this contributions of the running function the The scattering The 34% absolute. result is apparent. nb-’ The 11 is a range This and is agreement show threshold. to in the GeV averaged of the we also corrections of structure greater described acceptance, and from normalization quark 60 cm as systematic functions The within sense to 250 section 171 < 0.7. Events as well calculation. structure Fig. the 40 GeV cross interval. shown choice located in the than interval 0.1 < understood error Et differential eta interval a well statistical the jet corrected are form: -424- 11 The inclusive jet cross section. 1 : - A UAl-- T/F= 630&V + UA2 - - fi t 10’ = 630GeV MS--&=63GeV ----- 10' QCD (Duke-Owens z p D 100 5 c zlo-' w 4 D 10-a lo- 9’1 I Et 0 100 200 300 200 100 0 (GaV) 300 Et (GeV) Fig. Fig. 12 Jet spectra in colliding hadron experiments. 13 compositeness -425- Inclusive jet cross section at scale A* = 400 GeV. with modification for quark ..:::, .‘I. :. , _- : : :.1 ... . -. . .I E* is the where momentum result of gluon have the Rutherford cuts jet opposite the the jets angular Et leading t jet interval and beam axis. effect of limited 0.51~~ - y,I, To study the effect of this cut, 0.7, 1.2. acceptance Carlo, and jet jet subprocess is usually is expected The are small for the the events 6* to the again y, into to be the the angle of by cutting jet rapidities. the three were and 180°i300 acceptance corrections cut of of ys are the we examined first the boosted taken and satisfied requirement interval were was detector where which additional azimuthal passing frame, = 1.0, t is the a sample and in the The to the the y* using analysis 10 GeV jet. respect We controlled the distributions center-of-mass with and B* of the leading inclusive with longitudinal angle case, since the third form. jet of the a second scattering In the three-jet bremsstrahlung, We studied quality center-of-mass transfer. requirements determined of order I y* I < via 20% for on Fig. Monte the cut. Three The angle distribut,ion 8* dN/dcos@* Fig. 14a, along that the the discussion the There of the most three-jet, supplemented and good care the initial data sets our good for QCD di-jets. Jet Angular Distrtbution et in Note Et trigger of 114, agreement 140, with acceptances. events. regarding the theory as the state with show calculation between calculation. thresholds dN/dcos6* The sets is displayed QCD mass 14b we show or final data acceptance required QCD agreement cos0*=tanh(y*). order invariant of different events can be described with a first has been done for lhrcc-jet case. In Fig. jet, relation angular three additional in this is, again, All in spite analysis leading finite the in the two-jet from two-jet respectively. of the acceptance for the three effective prediction, A similar from the curve produces 164 GeV QCD for with combination thresholds and is obtained 14a third gluon 13 for detector distribution from and result See Ref. uniform the data, a dN/dcos6* previous plot. indicating that of a 2 + 2 subprocess bremsstrahlung. Fig. -426- 14b dN/dco&* for QCD tri-jets. 6 = 1 .3 l’ev d. Jet The CDF Fragmentation excellent central track finding tracking fragmentation in hadronically for are this study inclusive measurements estimated the pt dense jet those in overlayed tracking inferred jets. Sec. with efficiency the from events, rapidity the y of the jet calorimeter cluster that with “rapidity plateau” number of tracks core to the pt cutoff Fig. Hadronically 15b, multiplicity e+e‘ results jet along produced core in the The jets which at much on track and an 85% in tracking respect jet Note jet energy. (400 results MeV/c) high from energies with binned and other used , Y L,’ 3 2 = 4 s particles in 6 5-Ln(E+PL/‘E-PL) the Fig. a small 158 measured the effect of of di-jet mass is with dN/dy for respect to the jet charged jets. Rapidity y is axis. experiments.r5 are seen to have a smooth .t,...I.‘..l,. 0 of as a measure eliminates as a function jet the suggestion We axis cut the sample, the to the jet to 15a shows a mean extrapolation from energies. Bias Physics One of the most familiar plateau in defined a large rapidity multiplicity at very Minimum rapidity real provided Figure masses. respect is consistent lower f or The with with increasing y 1 2 with multiplicity. event. tracks centroid. dN/dy broadens having charged underlying the section which events invariant 6. the in jet distribution in in the particle requirements in Carlo sets of dijet shown quality briefly Monte corrected due Track by charged of 90% to three the afforded the Studies 6. according bias of discussed efficiency of the jet resolution study core.‘” We measured axis to spectra were average and allows produced similar charged efficiency chamber results charged from high particle energy production. hadron The collisions is rapidity is as :. _ For which light particles we define this as the is approximately a function of polar angle : ..~-.. alone, “pseudo-rapidity”: Fig. y 2 7 = -In(tan(6/2)). 15b to the jet -427- Jet axis. total charged “multiplicity” with y 2 2 with respect -. -._ :. .. ., At CDF, the charged VTPC particles uncorrected sample chambers with good distribution is shown data shows The effects of in Fig. a plateau measure the efficiencies dN/dq vs. 16, along with out to the polar between 7 for the results limits angle distribution rapidities UA5.‘s acceptance of t3.0. minimum from of our of The bias data The CDF at 7 = 2.8. 7- of reconstruction interactions are under correction will understood dN/dy study; be less in terms is flat. efficiency, The 630 GeV result 1800 GeV result 10%. conversions, results The difference central the preliminary than of the The decays, slight dip between densities indicate at y and are measured that the . CDF 1.8 TeV total 7 can 6. be 7; the distribution l CDF 0.63 TeV of to be: = dN/dq)t=O = 3.98 t 0.4 at 1800 GeV lies secondary small dN/d~),,=c is in good and 2.95 e 0.3 at 630 GeV agreement above the with best results In(s) fit from to the UA5, lower but energy data.17 The inclusive minimum Tracks with certain quality (ITI samples down requirements, and l.O), in R-l sample transverse was momenta less than vertex this charged bias and was momentum measured in to 400 MeV/c including an to within estimated the were the extrapolation to several included within track methods in tracking traversal 5 cm in s. The via distribution central if they passed of all CTC layers 5.0~ of the event finding to the system. be efficiency 00. 0.4 0.6 1.2 1.6 2. 2.4 2.6 r) in approximately 99%.=’ The observed decays, and uncertainty due momentum section particles Our 0.63 pt spectrum conversions, to from are assumed result TeV were the 1.8 pt found to spectrum for decay in flight, correction larger and distortion the be negligible. and the The measured than neutral 5%. due to invariant The Fig. finite cross luminosities. in Fig. TeV. The 17 for the smooth two center-of-mass curves are a All energies fit to 18 experiments. to be pions. is shown and corrected no misreconstruction resolution follows was with the parameterization: -428- dN/dq for the CDF minimum bias samples and other d3, E----c---“. AP ” d3p Our lo-24y results, and a comparison A18 0 I CDF 1800 GeV CDF 630 GeV We find above. off. to 0.63 are as follows: TeV 0.55 TeV (UAl) 1.3 GeV/c 1.3 GeV/c 1.3 GeV/c n 8.28t.02 8.89t.06 9.14*.02 A 0.45i.01 0.33*.01 0.46k.01 that p0 and fit our flatten n are highly result result result;lg TeV to UAl PO The Our (Pt+Po) was found at 0.63 TeV correlated, and to be independent is in reasonable result at 1.8 TeV shows that with increasing c.m. energy simply fix of the lower agreement the p, with value pt cut- the UAl pt distribution continues as observed in other experiments.” 7. Conclusion Analysis 1 o-3o results of a small on W boson, establishing 1 O-3’ the at fi=1.8 run 1 o-32 0 2 4 6 8 in luminosity 10 P, (GeV/c) for the 17 the minimum The bias inclusive charged transverse momentum spectrum for work and hard the staffs of construction samples. Nazionale and -429- work our of one not of the Nucleare and has for produced significant production, for the 1988/1989 picobarn, as well reconstructing next Tevatron foresee and an CDF as physics Collider integrated stands poised to the Top. been possible Accelerator detector. of Japan, detector inverse have of the Energy, di Fisica Education than set particle expectations Winter institutions of the Department CDF to go right would data inclusive of the and of more skill, and Realistic Fall opportunity This Fig. power TeV. the preliminary jet, Division for their many This work was National of Italy, the Alfred without dedication, We contributions supported Science the the of Fermilab. Ministry P. Sloan by Foundation, of Science, Foundation. thank to the the U.S. Istituto Culture ‘: 1:::-: : c. .‘: “- :: : References 1. Argonne National Laboratory; Brandeis University; University of Chicago; Fermi National Accelerator Laboratory; INFN, Laboratori Nasionali di Frascati, Italy; Harvard University; University of Illinois; KEK, Japan; Lawrence Berkeley Laboratory; University of Pennsylvania; INFN, University and Scuola Normale Superiore of Pisa, Italy; Purdue University; Rockefeller University; Rutgers University; Texas A&M University; University of Tsukuba, Japan; University of Wisconsin. 2. F. Abe et al., Nucl. 3. S. D. Drell, 4. The and 5. C. Albajar al., Phys. Lett. m, 6. G. Altarelli, 7. The cluster algorithm is described in a talk Physics in Collision 7, Tsukuba (1987). 8. We have used the technique described Phys. Lett. m, 283 (1984). 9. E. Eichten et al., Rev. Mod. Phys. 56, 579 (1984); and J. Owens, Phys. Rev. E, 49 p84). T-M. Instrum. Yan, Phys. Methods Rev. u, Lett. 387 (1988). K. 271 (1987); G. Arnison Banner et al., Phys. 3. Appel et al., Phys. al., Phys. Lett. B, 11. E. Eichten, (1983). 12. 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Lett. 198B, Lett. 122B, 103 (198rM. 476 (1983). 15. 5& et 811 : I. Topical Workshop on Proton-Antiproton National Accelerator Laboratory (1988). -._ -1.. on ProtonAccelerator -430- :. : I 1988 SLAC SUMMER INSTITUTE LIST OF PARTICIPANTS Iris Abt SLAC Mail Bin 96 P.O. Box 4349 Stanford, CA 94309 Bimet: ABTQSLACVM Gerard D. Agnew Brunel University Rm. F67, GEC Mirst Research East Lane, Wernbley Middx., HA9 7PP, England Bitnet: GAGNEW@VZ.RL.AC.UK :AanCgim Ahn MailBin P.O. Box 4349 Stanford, CA 94309 Bimet: AHNQSLACVM Roy Aleksan SLAC MaiI Bin 78 P.O. Box 4349 Stanford, CA 94309 Bimet: ROYQSLACVM JamesAlexander SLAC Mail Bin 61 P.O. Box 4349 Stanford, CA 94309 Bimet: JIMAGSLACVM Max J. Allen University of Victoria Dept. of Physics P.O. 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D-5900 Siegen, West Germany Tianchi Zhao University of Washington Dept. of Physics Seattle, WA 98 195 Bitnet: TCZ@FNAL ._. -443- -446 THE SLAC SUMMER INSTITUTES ON PARTICLE PHYSICS 1973 - 1967 1973 DEEP INELASTIC “Hadton Production in Deep Inelastic Processes” “Hadron Production in the Collision of Virtual Photons with Nucleons - an Experimental Review” “Phenomenological Analysis” “Asymptotic Behavior and Short Distance Singularities” WEAK 1976 ELECTROPRODUCTION CURRENTS AND J. D. Bjorken M. Per1 “Weak Interaction Theory and Neutral “Weak Interactions at High Energy” “$ Spectroscopy” “A New Lepton?” “Lectures on the New Particles” “New Particle Production” F. J. Gilman Y. Frishman 1977 Notes of Lectures on Current and PCAC” “Experimental Phenomenology” Algebra “Gauge-Theories of Weak and Electromagnetic Interaction” “How to Transform Current Quarks to Constituent Quarks and Try to Predict Hadron Decays” THE STRONG S. Drell DEEP HADRONIC STRUCTURE THE NEW PARTICLES J. Primack M. Kugler 1978 D.W.G.S. Leith M. Davier J. S. G. G. J. D. D. Bjorken G. Wojcicki J. Feldman J. Feldman D. Jackson Hitlin H. S. F. M. Harari D. Drell J. Gilman L. Per1 AND WEAK INTERACTIONS AND FUTURE R.J. Cashmore F. J. Gilman 1979 D. Sivers R. Blankenbecler H.D.I. Abarbanel QUANTUM J. D. Bjorken M. Davier H. Harari G. H. Trilling -445- D. J. H. S. H. Perkins Ellis Quinn Wojcicki CHROMODYNAMICS “Lepton Nucleon Scattering” “Massive Lepton Pair Production” “QCD Phenomenology of the Large Pr Processes” “Perturbative Quantum Chromodynamics” “Elements of Quantum Chromodynamics” F. J. Gilman E. D. Bloom K. C. Myffeit - PRESENT “Accelerator Neutrino Experiments” “Weak Interactions at High Energies” “Gauge Theories of the Weak Interactions” “Weak Decays” AND “Leptons as a Probe of Hadronic Structure” “Lepton Scattering as a Probe of Hadron Structure” “High pl Dynamics” “Hadronic Collision and Hadronic Structure (An Experimental Review)” “The New Spectroscopy” “The New Spectroscopy (An Experimental Review)” QUARK SPECTROSCOPY HADRON DYNAMICS “Quarks and Leptons” “Quark Confinement” “Hadron Spectroscopy” “Lectures on the Quark Model, Ordinary Mesons, Charmed Mesons, and Heavy Leptons” “Quarks and Particle Production” M. Schwartz S. Wojcicki T. Appelquist INTERACTIONS “Diffractive Processes” “Amplitude Structure in Two- and Quasi-Two-Body Processes” “Resonances: Experimental Review” “Resonances: A Quark View of Hadron Spectroscopy and Transitions” “Lectures on Inclusive Hadronic Processes” “Large Momentum Transfer Processes” “Hadron Dynamics” 1975 Currents” AND INTERACTIONS “Raw 1974 WEAK INTERACTIONS AT HIGH ENERGY THE PRODUCTION OF NEW PARTICLES W. G. Atwood R. Stroynowski R. Stroynowski S. J. Brodsky J. D. Bjorken 1980 THE WEAK 19S3 INTERACTIONS “Gauge Theories of Weak Interactions” “Neutrinos and Neutrino Interactions” “Weak Decays of Strange and Heavy Quarks” “From the Standard Model to Composite Quarks and Leptons” “Physics of Particle Detectors” 1981 THE STRONG M. F. D. H. J. Veltman J. Sciulli Hitlin Harari AT S. Ellis R. Hollebeek R. F. Schwitters M. E. Peskin M. G. D. Gilchriese J. Ellis A. H. Walenta “Jets in QCD: A Theorist’s Perspective” “Jets in e+e- Annihilation” “Jet Production in High Energy Hadron Collisions” “Aspects of the Dynamics of Heavy-Quark Systems” “Heavy Particle Spectroscopy and Dynamics B’s to Z’s” “ And for Our Next Spectroscopy?” “Review of the Physics and Technology of Charged Particle Detectors” “A Review of the Physics and Technology of High-Energy Calorimeter Devices” D. M. Ritson J. Jaros J. Marx H. A. Gordon R. S. Gilmore W. B. Atwood 1954 PHYSICS SPECTROSCOPY :..:.:::::.:,..i:,.;- P. M. Mockett INTERACTIONS “Quark-Antiquark Bound State Spectroscopy and &CD” “Meson Spectroscopy: Quark States and Glueballs” “Quantum Chromodynamics and Hadronic Interactions at Short Distances” “Untangling Jets from Hadronic Final States” “Heavy Flavor Production from Photons and Hadrons” “Design Constraints and Limitations in e+e- Storage Rings” “Linear Colliders: A Preview” 1982 DYNAMICS AND HIGH ENERGY AT VERY HIGH E. D. Bloom M. S. Chanowitz S. J. Brodsky G. C. J. H. THE SIXTH QUARK “The Last Hurrah for Quarkonium Physics: The Top System” “Developments in Solid State Vertex Detectors” “Experimental Methods of Heavy Quark Detection” “Production and Uses of Heavy Quarks” “Weak Interactions of Quarks and Leptons: Experimental Status” “The Experimental Method of Rine-Imaging Cherenkov (RICH) Counters” “Weak Interactions of Quarks and Leptons (Theory)” Fox A. Heusch LeDuff Wiedemann E. Eichten C. T. G. S. J. S. Damerell Himel L. Kane Wojcicki T. Ekelaf II. Harari ENERGIES PIEF-FEST LLExpectations for Old and New Physics at High Energy Colliders” “Beyond the Standard Model in Lepton Scattering and Beta Decay” “Grand Unification, Proton Decay, and Neutrino Oscillations” “e+e- Interactions at Very High Energy: Searchine Beyond the Standard Model” “The Gauge Hierachy Problem, Technicolor, Supersymmetry, and All That” “Composite Models for Quarks and Leptons” “Electron-Proton Colliding Beams: The Physics Programme and the Machine” R. N. Cahn “Pief’ “Accelerator Physics” “High Energy Theory” “Science and Technology Policies for the 1980s” “Inclusive Lepton-Hadron Experiments” “Forty-Five Years of e+e- Annihilation Physics: 1956 to 2001” “We Need More Piefs” M. Strovink H. H. Williams J. Dorfan L. Susskind S. R. T. F. J. B. Drell R. Wilson D. Lee Press Steinberger Richter J. Wiesner ::: H. Harari B. H. Wiik -446- “_ I 1985 SUPERSYMMETRY “Introduction to Supersymmetry” “Signatures of Supersymmetry in e+e- Collisions” “Properties of Supersymmetric Particles & Processes” “Supersymmetry: Experimental Signatures at Hadron Colliders” “Superworld/Hyperworlds” “Very High Energy Colliders” “Some Issues Involved in DesiRning a 1 TeV (cm.) e* Linear Collider Using ?on;entional T&h&logy” “Wake Field Accelerators” “Plasma Accelerators” “Collider Scaling and Cost Estimation” 1986 PROBING THE STANDARD LOOKING BEYOND Polchinski Burke M. Barnett Darriulat M. E. Peskin B. Richter G. A. Loew P. B. Wilson R. D. Ruth & P. Chen R. B. Palmer MODEL “Electroweak Interactions -Standard and Beyond” “CP and Other Experimental Probes of Electroweak Phenomena” “Pertubative QCD: K-Factors” “Experimental Tests of Quantum Chromodynamics” “Phenomenology of Heavy Quark Systems” “Heavy Quark Spectroscopy and Decay” “Some Aspects of Computing in High Energy Physics” “Data Acquisition for High Energy Physics Experiments” 1987 J. D. R. P. H. Harari B. Winstein R. Field J. Dorfan F. Gilman R. Schindler P. Kunz M. Breidenbach THE Z “Theory of e+e- Collisions at Very High Energy” “Prospects for Physics at, e+e- Linear Colliders” “Physics with Polarized Electron Beams” “Electron-Proton Physics at HERA” “Hadron Colliders Beyond the Z”” “Physics at Hadron Colliders (Experimental View)” “The Dialogue Between Particle Physics and Cosmology” M. E. Peskin G. J. Feldman M. L. Swartz G. Wolf C. Quigg J. L. Siegrist B. Sadoulet -447- ‘, : :./ ‘. ““‘I ,.’ .,’ ,,,. .’ :.,., ,’ _: ; ,A,’ ,. ,/ ,:, /’ ., ‘:* “’ :: ,,, :‘. ;:g ,:/:’ ,,,, ,,,. 1’