Fits de la matrice CKM avant l`été 2009 et sensibilité à la Nouvelle

Fits de la matrice CKM avant l’été 2009 et sensibilité à la Nouvelle
Physique au travers de la violation de CP et des saveurs lourdes
V. Tisserand*, LAPP-Annecy (CNRS-IN2P3 et Université de Savoie),
pour le groupe CKMfitter,
Séminaire LAPP, 12 juin 2009.
http://ckmfitter.in2p3.fr/plots_Moriond09/
p
p
p _
J. Charles, Theory, CPT Marseille
O. Deschamps, LHCb, LPC Clermont-Ferrand
S Descotes-Genon,
S.
Descotes-Genon Theory
Theory, LPT Orsay
R. Itoh,
Belle, KEK Tsukuba
A. Jantsch, ATLAS, MPI Munich
H. Lacker, ATLAS & BABAR, Humboldt U. Berlin
A. Menzel, ATLAS, Humboldt U. Berlin
S. Monteil, LHCb, LPC Clermont-Ferrand
V. Niess ,
LHCb, LPC Clermont-Ferrand
J. Ocariz, BABAR, LPNHE Paris
S. T’Jampens, LHCb, LAPP, Annecy-le-Vieux
K. Trabelsi, Belle, KEK Tsukuba
* V.T also BABAR.
The UNITARY CKM Matrix: mixing the 3 quark generations and CP violation
• Strong
St
hi
hierarchy
h in
i EW coupling
li off the
th 3 families:
f ili
diagonal ≈1 & between 1 ↔ 2: ∝λ≈0.22,
2 ↔ 3: ∝λ2, and 1 ↔ 3: ∝λ3.
• KM mechanism: 3 generations Î 1 phase
as only source of CP violation in SM.
• Consider the Wolfenstein parameterization,
1‐λ2/2
λ
Aλ3(ρ‐iη)
‐λ
1‐λ2/2
Aλ2
Aλ3(1
(1‐ρ‐iη)
ρ iη) ‐Aλ
Aλ2
1
defined to hold to all orders in λ and re-phasing invariant (EPJ C41, 1-131, 2005) :
Î4 parameters: A, λ, É, and ¿ to describe the CKM matrix, to extract from data the
Unitary Triangle.
Ru=
V. Tisserand, LAPP
=Rt
2
The unitary CKM Matrix: mixing the 3 quark generations and CP violation
’08
“for the discovery of the origin of the broken g f
symmetry which predicts the existence of at least three families of quarks in nature”
3rd generation: See Prog. Theor.
Phys. 49, 652 (1973)
Î
Î4 parameters: A,
A λ, É,
É and ¿ to describe the CKM matrix,
matrix to extract from data the
Unitary Triangle: nucleons, K, D, B(s),
and top quark physics.
|Vtb| > 0.89 @ 95% C.L
0 89 @ 95% C L
(D∅: PRL 100, 192003 (08)
=Rt
Ru=
Not in CKM fit)
V. Tisserand, LAPP
3
Global SM CKM fit: the inputs
Details:
http://ckmfitter.in2p3.fr/plots_Moriond09/
CP
P violating
CP con
nserving
CKM matrix within a frequentist
q
framework (≅χ
χ² minimum ) + uses all constraints on which we think we
have a good theoretical control + Rfit treat. for theory errors with flat likelihoods (EPJ C41, 1-131, 2005)
Î data=weak ⊗ QCD ⇒need for hadronic inputs (often LQCD: Our Own Average (OOA) of latest results)
Phys param
Phys.param.
Experim observable
Experim. observable
Theory method/ingredients
|Vud|
Superallowed β decays
Towner & Hardy, PRC 77, 025501 (2008)
|Vus|
Kl3 (WA Flavianet: KLOE)
f+Kπ (0)
(0)=0
0.964(5)
964(5) (most precise: RBC
RBC-UKQCD)
UKQCD)
|Vcb|
HFAG incl.+excl. B→Xclν
40.59(38)(58) ×10‐3
|Vub|
HFAG incl.+excl.
incl +excl B→Xulν
OOA (specif. uncer. budget): 3.87(9)(46) ×10
3.87(9)(46) ×10‐3
Δmd
last HFAG WA Bd-Bd mixing
^ ^
OOA: BBs/BBd= 1.05(2)(5) + fBs + fBd
Δms
CDF Bs-B
Bs mixing
^
OOA: BBs= 1.23(3)(5) + f
1 23(3)(5) + fBs + fBd
B+→τ+ν
last 08 WA: BaBar/Belle
OOA: fBs/fBd= 1.196(8)(23) & fBs= 228(3)(17)
| K|
|ε
K°-K°
K
-K (PDG08: KLOE,
KLOE
NA48,KTeV)
PDG param.
param (Buchalla et al
al. ‘96) +
^
OOA: BK= 0.721(5)(40)
β/φ1
latest WA HFAG charmonium
-
α/φ2
last WA ππ/ρπ/ρρ
isospin SU(2) (GL )
γ/φ3
latest WA HFAG B-→D(*)K(*)-
NEW
GLW/ADS/GGSZ
4
Global CKM fit: a little of
Statistics
V. Tisserand, LAPP
5
Global
Gl
b l
CKM fit:
the Big
g
(É,¿)
Picture
V. Tisserand, LAPP
6
Global CKM fit: the Big (É,¿) Picture
• overall consistency
Inputs:
at 95% CL.
• KM mechanism is
at work for CPV and
dominant in B’s.
• Some
S
tension in
B+→τ+ν Î the fit χ²min
drops by 2.4 σ when
removing this input.
• and NP ? (see later)
É= 0.139 +−00..025
027
¿= 0.341+−00..016
¿
015
details :
V. Tisserand, LAPP
http://ckmfitter.in2p3.fr/plots_Moriond09/
7
Global CKM fit: the Bd mesons (É,¿) plane
O single
One
i l minimum
i i
Î Some tension in B+→τ+ν Î the fit χ²min drops by
2.4 σ when removing this input.
V. Tisserand, LAPP
8
Global CKM fit: testing the paradigm
Inputs:
CP-conserving observables
Inputs:
|Vub |
εK
B → τν
sin2β
Δmd
α
Δms
Inputs:
sin2β
α
γ
CP-violating observables
γ
Angles (small theor. uncertainties)
NEW
Inputs:
No angles (large theo. Uncertainties: LQCD…)
εK
|Vub |
B → τν
Δmd
Δms
V. Tisserand, LAPP
9
Global CKM fit: other numerical results, a selection
Physics param./Observable
param /Observable
Central ± 1 σ
A
0.8116 [+0.0096 ‐0.0241]
λ
0.22521 [+0.00082 ‐0.00082]
0.22521 [+0.00082 0.00082]
J [10-5]
2.92 [+0.15 ‐0.15]
α (deg) (meas. not in the fit)
95 6 [+3 8 ‐8
95.6 [+3.8 8.8]
8]
β (deg) (meas. not in the fit)
21.66 [+0.95 ‐0.87]
γ (deg) (meas.
(meas not in the fit)
67 8 [+4 2 ‐3
67.8 [+4.2 3.9]
9]
βs(deg) (meas. not in the fit)
1.035 [+0.049 ‐0.046]
∆ms [ps-11] (meas.
(meas not in the fit)
17 6 [+1 7 1 8]
17.6 [+1.7 ‐1.8]
|Vub| [10-3] (meas. not in the fit)
3.50 [+0.15 ‐0.14]
BR(B->τν)
BR(B
>τν) [10-44] (meas.
(meas not in
the fit)
BR(B->μ+μ-) [10-11]
0.796 [+0.154 ‐0.093]
10.8 [+0.4 ‐0.9]
Results and plots at: http://ckmfitter.in2p3.fr/plots_Moriond09/
V. Tisserand, LAPP
10
Why need for LQCD
own average ? :
the hadronic inputs
V. Tisserand, LAPP
11
Why need for LQCD own average ? :
the hadronic inputs
p
The Situation:
• Several hadronic inputs required as inputs for CKMfitter: εK, Δms, Δmd, |Vub|τν
Need fB, fBs, BB, BBs, BK …
• Lattice QCD the almost only tool able to estimate them with uncertainties that
can be checked and improved (other: quark models, sum rules …)
• But many collaborations with different methods of simulations, results, and
estimations
ti ti
off errors. Î Nothing
N thi lik
like HFAG (Heavy
(H
Flavor
Fl
A
Averaging
i G
Group)) or
FlaviaNet
Need to perform our own average (OOA):
• Up to now : we used reviews from the lattice community (e.g., Tantalo CKM 06)
• Problem : averages often performed in a rather personal manner
• Recently,
Recently we attempted to perform our own averages
Z. Ligeti at USLQCD Dec’07 on lack of LQCD averages: “If experts cannot agree,
it’ unlikely
it’s
lik l the
th restt off the
th community
it would
ld believe
b li
a claim
l i off new physics”.
h i ”
V. Tisserand, LAPP
12
Sources of uncertainties for LQCD
V. Tisserand, LAPP
13
LQCD: Our Own Average (OOA)
•
• use only
l unquenched
h d results
lt with
ith 2 or 22+11
d
dynamical
i l ffermions
i
((sea quarks),
k)
also include staggered fermions (even if : still QCD?) , where error estimated
splited into stat. and syst. parts.
Îpapers & proceedings
Î
d
: RBC, UKQCD, HPQCD, JLQCD, CP-PACS, FNAL Lattice, MILC, ETMC, NPLQCD…
Î need to update for new papers (unpublished proceedings).
ÎCorrelations among observables rarely given.
• Our Own Average this time “educated Rfit” :
1) standard χ² fit with only the statistical errors (parabolic)
2) theoretical uncertainty of the combination Rfit flat likelihoodÎ the one of the most precise method
Î conservative approach :
• the present state of art cannot allow us to reach a better theoretical accuracy than the best of all estimates
• this best estimate should not be penalized by less precise methods (opposed to comb. syst
syst=dispersion
dispersion of central values).
V. Tisserand, LAPP
Details: http://ckmfitter.in2p3.fr/plots_Moriond09/
14
LQCD: Our Own Average (OOA): an example
Decay constants and bag factors,
factors example of
the fBs decay constant (MeV):
1-CL
V. Tisserand, LAPP
15
Global CKM fit, the Bd mesons (É,¿) plane
from LP’07 to Winter ’09: impact of LQCD errors
2007
Î
V. Tisserand, LAPP
2009
same B and K mixing inputs !
16
Any tension
wrt Standard
Model ?
V. Tisserand, LAPP
17
Global CKM fit: testing the paradigm
Inputs
Inputs:
Observables w/ “Tree” processes
Inputs:
|Vub |SL
εK
B → τν
γ
sin2β
π−α−β
Δmd
Observables involving Loops
(
(theo.
uncertainties, except ffor β))
Δms
Assuming there is no NP in ΔI=3/2 b→d EW penguin amp.
Use α with β (charmonium) to produce a new
Tension in between sin(2β) (Ι) &
BR(B+→τ+ν) (ΙΙ) (through |Vub|):
γ
either removing Ι/ΙΙ in the CKM global fit
the χ²min drops by 2.3/2.4 σ. reasons why:
- Experim. fluctuations,
- LQCD,
- New Physics … ? in Mixing ?
V. Tisserand, LAPP
‘Tree’.
meas.
fit prediction
(non triv.
triv Correl.)
Correl )
18
|V(u,c)b|
|Vcb| (→ A) is important in the
kaon system (εK, BR(K→πνν ), …)
|Vub| (→ É2 +¿2) is crucial for the
SM prediction of sin(2β )
* |Vcbb|: already precision measurement: 1.7% !
|Vcb|incl.[×10‐3]= 41.67(44)(58)
HAFG
summer 08
|Vcb| [×10-3]= 40.59(38)(58)
Note: |Vcb|excl. [×10‐33]= 38.20(78)(83)
(dominated by Form Factor F(1) =0.921(13)(20))
|Vub|:| room for questions !
*
Very difficult as phase space cuts applied to suppress
g ((~x 50)) complicate
p
b →clv bgd
the theoryy for
inclus. Meas.: lower scales (non perturb. function),
renorm. shape functions, structure of sub-leading
terms complicated.
B beam techniq
se eral kinematic variables:
ariables
Use the B-beam
techniquee & several
El, mX, q², …
V. Tisserand, LAPP
SF params. from b→clν , OPE from BLNP
BR precision ~8%, |Vub| excl. ~ 14%: FF theory dom.
(B Æ πlυ important also for ππ, Κπ decays …)
Î adapted from HFAG summer 08:
|Vub|incl.[×10‐3]= 4.38(16)(57) our syst. estimate
|Vub|excl. [×10‐3]=3.46(11)(46)
19
|Vub| and |εK| vs. global fit (i.e.: sin2β): tension ?
V. Tisserand, LAPP
20
|Vub| vs. global fit (i.e.: sin2β): tension ?
ÎIt is actually more a |Vub|incl vs |Vub|excl tension.
We are living with a significant difference between exclusive and
incl si e meas
inclusive
measurements:
rements a longstanding issue.
iss e The sin2β
measurement prefers the exclusive value.
V. Tisserand, LAPP
21
|εK| from neutral Kaons mixing
Only input from indirect CP violation in mixing and in K°-K°
K interference w. and w.o. mixing:
• dominated by badly controlled long distances contributions but accountable
corresponding systematic.
• Note : ε’ direct CPV has much larger hadronic uncertainties (gluonic penguins): excluded.
=
Where S0 is an Inami-Lim loop function, xq=m2q/m2W, and ηij are perturbative QCD corrections.
• The constraint from in the (É,¿ ) plane is bounded by approximate hyperbolas.
• The dominant uncertainties are due to the bag parameter, for which we use
^
BK =0.721(5)(40) from LQCD (@5‐6%),
and the parametric uncertainty approximately proportional to σ(|Vcb|4)~8%,
comparable in size.
‐3
|εK|PDG08,exp= 2.229(10) ×10‐3 and |εK|CKMfit= (2.06 +−00..47
53 ) ×10
V. Tisserand, LAPP
22
|εK| vs. global fit (i.e.: sin2β): tension ?
^
BK=0.721(5)(40)
=0 721(5)(40) from LQCD (@5-6%)
(@5 6%)
Î entering precision era need to account for CPV in K mixing
‐3 and |ε
|εK|PDG08,exp
( )
|εK|CKMfit= (2.06 +−00.47
×10‐3
PDG08 exp= 2.229(10) ×10
.53
53 )
CPV
Neglected
So far
≠45°
≠45
Î Recent work by Buras & Guadagnoli (+Soni & Lunghi) suggest an additional effective suppression
multiplicative factor κε=0.92(2), 0 not clear yet how we understand this parameter 0 in PRD 78,
033005 (2008) : “our very rough estimate at the end of the paper show that our very rough estimate at the end of the paper show that κε<0.96, with 0.94(2) being a plausible figure
<0.96, with 0.94(2) being a plausible figure”..
Î BTW when plugging sin2β WA + other relevant inputs, they quote:
|εK|SM= 1.78(25) ×10‐3 i.e.: deviation in K mixing
@2σ ⇒ NP ?!
Î Error budget/ stat. treatment:
p p
tension vanishes with proper
systematic uncertainty à la Rfit
(flat). QCD parameters ARE NOT
DOMINATED by Gaussian (stat.)
uncertainties!
t i ti !
V. Tisserand, LAPP
23
B+→τ+ν
experim.
helicity-suppressed annihilation decay sensitive to fB×|Vub|
Sensitive to tree-level charged Higgs replacing the W propagator.
b
τ+
W+
B+
ντ
u
BR[10-4]=1.80 ± 0.63
1.80±1.00 (had)
1 80±0 81 (semi-lept)
1.80±0.81
BR[10-4]=1.70 ±
0.42
1.79 0.71 (had)
1.79±0.71
1.65±0.52 (semi-lept)
Measurement are consistent & WA:
BF[ -44]=
BF[10
]
1.73 ± 0.35
Measurement from global CKMfit:
BF[10-4]= 0 . 796
V. Tisserand, LAPP
Inputs:
fBd from our own LQCD average:
fBs/fBd= 1.196(8)(23) & fBs= 228(3)(17)
|Vub |
Δmd
Δms
εK
sin2β
deviation : 2.4σ
α
γ
+ 0 . 154
− 0 . 093
new CLEO-C ’09 D+s →τ+ν (~fine)…
24
Δms = 17.77(10)(7) ps‐1 Δmd & Δms
Î a 5.4 σ measurement PRL97, 242003 (2006)
HFAG : Δmd = 0.507(5)
0 507(5) ps‐1 Î uncertainty σ(Δms)=0.7% already smaller than σ(Δmd)≈1% !
Very weak dependence on É and ¿
ξ=
fBs Bs
the SU(3) breaking corrections (largest uncertainty)
fBd Bd
Measurement of Δms reduces the uncertainties on f2Bd Bd since ξ is better known from LQCD
ÎLeads to improvement of the constraint from Δmd measurement on |VtdV*tb|2
V. Tisserand, LAPP
HFAG : Δmd = 0.507(5) ps-1
25
B+→τ+ν
theory
theory.
Powerful together with Δmd : removes fB (Lattice QCD) dependence
(left with Bd errors anyway). If error of fBd small : 2 circles that intersect at ~90°
2
m τ2 2 sin2 ( β )
BR ( B + → τ +υ ) 3π m τ τ B
1
=
(1 − 2 )
2
Δm d
4 mW S ( x t )
m B sin2 (γ ) V 2 B
ud
Bd
+
Inputs:
Theory free prediction for BBd
Δmd
B → τν
γ(=π−β−α)
sin2β
deviation : 2.7σ
2 7σ
|Vud|
1.18±0.14
+0.15
−0.11
0.52
BBd
The ttension
Th
i is
i a STANDING ISSUE and
d it’s
it’
not driven by Vub (SL) nor fBd (nor εK)
V. Tisserand, LAPP
26
Testing LQCD inputs
Let’s let fBd and BBd be
completely free and fit them
from all observables.
Wh t d
What
do we get?
t?
֜No more tension / no more
constraints
֜The global fit is
accommodated keeping
fBd2×BBd≈const to fit Δmd while
increasing fBd to fit B+ Æ τ+ν
Î Would require significantly out of range LQCD errors
V. Tisserand, LAPP
27
See CKM angle review at
Moriond EW 09
by K .Trabelsi
V. Tisserand, LAPP
The CKM
angles
28
sin(2β) angle
Time-dependant CP asymmetries in B mixing.
Largely dominated by ccs
*transitions
(and used in the global
fit): a 4% precision measurement
Sin(2β)=0.671±0.023
cos(2β) <0 solution ruled out from J/ψK*, D*D*Ks,
and D0(Ksππ)h0 color
color-suppressed
suppressed decays
Others channels: s-penguin transitions
*
(β for NP effects search)
eff
ÎNo obvious tension
•Others channels: ccd (D(*)D(*), J/ψ π°)
good aggreement with ccs
V. Tisserand, LAPP
29
α from B→ρρ, ρπ, ππ: new WA
NEW
ρ+ρ0 has changed :
PRL 102, 141802 (2009)
α= (89.0 +−44..42 )°
{ [+9.1 °‐8.3°] 95% CL}
CKM fit: ( 95.6 +−38..38 )°
+6.1
Summer’08 was:
was (88.2 −4.8 )°
α is NOW a PRECISE
measurement @5% !?
Note that β is @
@4.2%
Sin(2β)=0.671±0.023
V. Tisserand, LAPP
30
α from b→uʉd, B→ρρ, ρπ, ππ
Tree ∝λ3
A
= A+- =
VubV
V*ud T + VtbV
V*td P
(B0→h+h-)
sin2α from time dep. CP:
B0
b
dB 0
W
−
u
d
u
d
hh+
+
B0
b
W−
t , c, u
g
d
Penguin ∝λ3
d
u
u
d
hh+
Γ(B0(t)→h‐h+)∝[1+ChhcosΔmt‐ShhsinΔmt]
sin2αeff =Shh/(1‐C²hh)1/2
• Strong effective phases arise from P :
effective angle αeff measured (not α!)
Gronau London SU(2) isospin triangle:
Δα = 2(αeff ‐ α)
• So far the ρρ dominates, R=P/T:
R(π+π−) > R(ρ+π−) ~ R(ρ−π+) > R(ρ+ρ−)
smaller |Δα| isopin bound
• 8 fold ambiguities (4 Δα, 2 αeff)
• h+h0 : pure tree.
V. Tisserand, LAPP
Δα
31
α from B→ρρ
Winter’ 09 BaBar ρ+ρ0 update (0921.3522) BR(fL) Ò by ~2(1)σ.
D i t WA
Dominates
• Inputs : B+-, B0+, B00,C+-,S+-,C00,
BR (ρ+ρ0)[10-6]]= 18.2 (3.0) 18.2 (3.0) → 24.0 (1.9)
24.0 (1.9)
fL(ρ+ρ0)= 0.912(44) → 0.950(15)
S00,,fL+-,,fL0+ ,,fL00
B→ρρ amps.
& B amps has similar pictures • higher BR: Both B and B isospin triangles do not close (consistent within uncert.)
• mirror solutions are degenerated in a single peak.
32
α from b→uʉd, B→ρρ
• Inputs
p : B+-, B0+, B00,C+-,S+-,C00,
S00,fL+-,fL0+ ,fL00
• The 2 triangles do not close
→ 44-fold
fold solution for α
V. Tisserand, LAPP
33
α from B→ρρ
α = (89.9 ± 5.4)°
Δα = (1.4 ± 3.7)°
Summer’08 was :
6.7
α = (90.9 +−14
.9 )°
Δ = ( 0.5+−125.5.6 )°
Δα
Î
H lucky
How
l k are we?? toy
t study:
t d
Gaussian smearing of all inputs at best CKM
fitted α by 1σ half interval : BR+-, BR0+, BR00,
C+-,S+-,C00, S00, fL+-,fL0+,fL00
• average toy error: 7.5° (observed 5.4°)
• long asymmetrical tail (→20
→20° !) when triangle
Summer’08
closes ⇒ pseudo mirror solution above the 1σ CL(α)
threshold. Only ~34% of SU(2). triangles close:
• same behavior when 2σ half interval (less fluctuating).
34
Δα = (1.4 ± 3.7)°
Breaking isospin triangle in B→ρρ
Î Already sensitive to sources of
SU(2) breaking (J. Zupan CKM’06):
- mu≠md & Qu ≠ Qd:
(mu-md)/ΛQCD ~1%
- extend the basis of EW penguins: Q7…10
ΔαEWP
1.5
5°
EWP ~1
- mass Eigen-States (EG) ≠ isospin EG:
(ρ−ω) mixing <2%
‐ Γρ≠0⇒ I=1 contribution possible:
possible
O(Γ²ρ/m²ρ)~ 4%
- ΔI=5/2 operators no more negligible.
-…
Î Possible way out: K*ρ SU(3) constraints
Î
B k the
Break
th triangle
ti
l closure:
l
A+0 → A+0 + ΔA+0
⇒additional Amp. with ΔT’s & ΔP’s
(arbitrary phases)
• tested |ΔA+0|: 4, 10
4 10 & 15%
• small correction breaks SU(2) at 90°
but restore SU(2) in the ~0° vicinity
15% to restore SU(2) at ~90°
90
• need ~15%
• BTW small impact on ππ/ρρ/ρπ WA combo.
35
Breaking isospin triangle in B→ρρ WA + all channels
• tested |ΔA+0|: 4, 10 & 15%
• small impact on ππ/ρρ/ρπ WA combo.
combo
⇒only visible @95 % CL
⇒A NICE CONSTRAINT in ANY CASE!
36
γ from interference in charged B-→D~ *
K(*)- decays
( )0
(Cabibbo & color)-suppressed
Cabibbo-“favored”
b
(*)-
K
b
B-
z
Vcb
Acb (D(*)0K(*)-) ∝ λ3
D(*)0
z
B-
c
u
Vub
D(*))0
K(*)e i(δB‐γ)
Aub(D(*)0K(*)-) ∝ λ3
relative strong & weak phases
Î Measurement of γ using
g direct CP violation ((interference [[b→c ⇔ b→u]] )):
~
• 3 various B-→D(*)0K(*)- charged decays (no time dependence): DK, D*K, and DK*.
• Size of CPV is limited by the size of |Aub/Acb| amplitudes ratio: 3 r(*)(s)B nuisance parameters (~5‐30% ?).
~
Î 3 methods that need a lot of B mesons:
Same D0≡[D0/D
D0] final state
• GLW: D ≡CP-eigenstate: many modes, but small asymmetry.
• ADS: D ≡DCS: large asymmetry, but very few events.
• GGSZ:
GGSZ D ≡Dalitz: better
b
than
h a mixture
i
off ADS+GLW
ADS GLW ⇒ large
l
asymmetry in
i some regions,
i
b
but
~
~
~
strong phases varying other the Dalitz plane.
V. Tisserand, LAPP
37
Combining methods on γ not always leads
to what one naïvely expects ((nuisance params.))
V. Tisserand, LAPP
Î statistical treatment matters!
38
γ from interference in charged B-→D~ *
K(*)- decays
( )0
γ= ( 70 .9 +− 2729 )° { [+44 °‐41°] 95% CL}
CKM fit MEW’09: ( 67 . 8 +− 43..29 )°
Î Only recent meas. is ADS/GLW BaBar DK* at CKM’08
V. Tisserand, LAPP
39
Any Other Inputs ?
K
V. Tisserand, LAPP
M
40
B→(ρ,ω)γ & K*γ exclusive b→ Dγ [D=(d,s)]
• access to |Vtd /Vts| within SM, in ratios of excl. BRs: R(d/s)γ
• cross check of neutral Bd,s mixing: penguins vs box Δmd,s
• loop : sensitive to NP, in addition to accurate (N)NLO B →Xsγ (inclusive, Misiak et al. ’06)
• available many recent(’08), more & more accurate excl. meas. B→Vγ at B-factories.
• But hadronic effects difficult to estimate:
-1- early attempts: Ali, Lunghi, Parkhomenko (’02,’04,’06).
-2- QCD Factorization for LO in 1/mb up to O(αs) (Bosch and Buchalla (’02)).
V. Tisserand, LAPP
41
B→(ρ,ω)γ & K*γ exclusive b→ Dγ [D=(d,s)]
• access to |Vtd /Vts| within SM, in ratios of excl. BRs: R(d/s)γ
• cross check of neutral Bd,s mixing: NP penguins vs box Δmd,s ?
• But hadronic effects difficult to estimate:
-1- early attempts: Ali,
Ali Lunghi,
Lunghi Parkhomenko (’02,’04,’06).
(’02 ’04 ’06)
-2- QCD Factorisation (Bosch and Buchalla (’02)).
-3- use a more sophisticated analysis beyond QCDF : adding 1/mb-suppressed terms from
light-cones sum rules (long dist. γ emission & soft gluon): Ball,
Jones, Zwicky (’06).
Œeach exclusive decay described individually
Œisospin breaking (FF,
(FF strong phase)/CP asym.
asym + weak annihilation (tree) can be large in (ρ,ω)γ
(ρ ω)γ ...
Œu and c internal loops (long and short distance) + other operators than magnetic operator Q7 only
Œnon trivial CKM matrix elements sensitivity
D=(d,s)
U=u c t
U=u,c,t
V. Tisserand, LAPP
42
B→(ρ,ω)γ & K*γ impact on (É,¿)
• HFAG WA ’08,
’08 allll BFs
BF updated
d t d (×10
( 10-6):
)
K*-γ: 45.7±1.9
K*0γ: 44.0±1.5
ρ+γ: 0.98 +−00..2524
ρ0 γ: 0.86 +−00..1514
+0.18
0
.
44
ωγ:
− 0.16
•
’08 (×10-6):
ƒ BF(Bs→φγ
φ )=57±22 (strange counter part B→ K*γ)
ƒ ACP(B-→ K
K*-γ))=‐0.11±0.32±0.09
0.11±0.32±0.09
(γ polar: NP ? + check strong dynamic)
Î Penguins
g
constraint at 95% CL,, as g
good as box B mixing
g Δmd alone,,
and at 68% CL almost as good as Δmd&Δms
V. Tisserand, LAPP
43
CHARM sector: |Vcd| & |Vcs| status
• Charm
Ch
sector
t favorite
f
it place
l
tto test
t t
LQCD [mc~ΛQCD] for form fact. and
decay constants (access |Vc(d,s)|)
only at first non trivial order in λ.
λ
+ B physics ⇒ indirect strong
constraint
|Vcss|
• K and nucleon: Vud~Vcs (Vcd~Vus)
(from global
CKM fit).
• Unitarity constraint: |Vcd|² + |Vcs|² ≤ 1
• Direct (new) :
I. Shipsey Aspen’09
- |Vcd| from DIS νN scattering (still most precise meas. !)
|Vcd|
- |Vcs|= 1.018(10)stat(8)syst(106)theo (above 1!) from LQCD + CLEO-c D→Klν
semi-Leptonic
i L t i absolute
b l t BR
BRs ((un-)tagged 280/pb (×3 under study + future BES-III game
field!)).
V. Tisserand, LAPP
44
Measuring fDs and |Vcs|
In D+s annihilation leptonic decays
J.Hunt
Lake Louise’09
CHARM SECTOR:
Î favorite place to test LQCD [mc~ΛQCD] for form fact. & decay
constants (access |Vcs| through fDs)
Î Null test of SM (GIM mech.) + access NP large couplings 2nd family
V. Tisserand, LAPP
45
fDs Puzzle : end 2007 !
A. Kronfeld Aspen’09
Î “Accumulating
“A
l ti E
Evidence
id
ffor N
Nonstandard
t d d Leptonic
L t i Decays
D
off Ds Mesons”
M
” PRL 100,
100 241802
V. Tisserand, LAPP
46
fDs Puzzle : Jan 2009 ?
A. Kronfeld Aspen’09
CLEO-C Ds to (τ,μ)ν : PRD 79, 052001 and 052002 (2009) , the most precise and
y)
absolute BRs: <10% ((1/2 BaBar and Belle)) + τν channel ((BES III aims for 0.7 % accuracy)
fDs=(259.5±6.6±3.1) MeV
Î Experiment moves downwards back to LQCD !
V. Tisserand, LAPP
47
End 2007 trouble with |Vcs|
ONE YEAR AGO:
2σ away and unitarity
Violation !
V. Tisserand, LAPP
48
No more trouble with |Vcs| ?
• CLEO-c ’09 Ds→(τ,μ)ν & τ[eνν,πν]
annihilation: (fix |Vcs|=|Vud|): fDs=259.5(6.6)(3.1) MeV
( )( )
• Our LQD average:
fDs=246.3(1.2)(5.3) MeV
(mainly from full unquenched LQCD :
HPQCD’07 & FNAL-MILC’07)
• combined CLEO-c + LQCD:
|Vcs|=1.027±0.051
• CKM fit :
|Vcs|= 0.97347±0.00019
|Vcs|
ƒ |Vcs| situation improves : CLEO-C and LQCD have better agreement on fDs
ƒ fDs ideal for lattice (cs quarks), better but still worse than fK
V. Tisserand, LAPP
&
fK/fπ (light quarks).
49
a word on rare K+→π+νν
• Recent E949 update (arXiv:0903.0030 with 5 events (& incl. E787)):
• BR parameterization as Brod & Gorbahn ’08 (PRD 78, 034006) :
+1.15
BR [10-10]= 1.73−1.05
NLO QED-QCD & EW corr. to the charm quark contrib. (αs(m²Z)=0.1176(20) & mc(μc)=1.286(13)(40))
CKM fit: BR[10-10]=
0.730+−00..081
101
BR[10-10]
∝
Î wait for NA62: O(100 events)!
V. Tisserand, LAPP
50
New Physics in Bq=d,s mixing
V. Tisserand, LAPP
51
New Physics in Bq=d,s mixing
Assume that:
A
h
• tree-level processes are not affected by NP
(SM4FC: b→qiqjqk (i≠j≠k)) nor non-loop
d
decays,
eg: B+→τ+ν (implies
(
l 2HDM
HDM model).
d l)
• NP only affects the short distance physics in
ΔB=2 transitions.
• Model independent parameterization:
Δq = |Δq| e2iΦNPq (use Cartesian coords.)
Î SM
• Δq = r²q e2iθq = 1 + hqe2iσq
• SM ⇒ Δq =1
• MFV (Yukawa) ⇒ ΦNPq=0 and Δd = Δs
parameters are fixed by :
|Vub|SL+τν,|Vcb|,|Vud|,|Vus|,γ, γ(α)=π‐β‐α
V. Tisserand, LAPP
52
New Physics in Bq=d,s mixing
Nierste and Lenz 2007 JHEP 0706:072
Oscil.
Phases
Asym SL
Lifetime
diff.
V. Tisserand, LAPP
53
New Physics in Bd mixing
Inputs:
Warning : 68% CL
Δms
Δmd
• Dominant constraints
from β & Δmd : both
agrees with SM.
SM … but …
Î tension from BR(B→τν)
i.e.: |Vub| ⇒sin(2β)
• Cartesian coordinates
sin(2β)
α
Bd
ASL , ASL
Bs
ASL
give simple interpretation
of constraints:
ΔΓd / Γd
ΔΓs , φ s
• angles : arcs
• Δm : ellipses
+SM params:
|Vud|, |Vus|,
|Vub|, |Vcb|,
γ(α), B→τν
• |Δd| < or ~ 1 ⇒ KM
mechanism is dominant
dominant.
• sizable NP contributions
still allowed
hypothesis
hypothesis Agreement with SM :
V. Tisserand, LAPP
Δd= 1 (Re=1,Im=0)
with B
with
B+→τ+ν
with out
2.1 σ
0.6 σ
54
New Physics in Bd mixing
Inputs:
Δms
Δmd
sin(2β)
α
Bd
ASL , ASL
Bs
ASL
ΔΓd / Γd
ΔΓs , φ s
+SM params:
|Vud|, |Vus|,
|Vub|, |Vcb|,
γ(α), B→τν
hypothesis
hypothesis Agreement with SM :
V. Tisserand, LAPP
Δd= 1 (Re=1,Im=0)
with B
with
B+→τ+ν
with out
2.1 σ
0.6 σ
55
Global CKM fit: the Bs mesons (És,¿s) plane
βs = (1.035+−00..049
046 )°
(from global CKM fit MEW ’09)
EXP. CDF+D∅ HFAG’08: βs=
V. Tisserand, LAPP
.3
(22.3+−10
8.0 )°
56
New Physics in Bs mixing
• Direct constraint on NP phase in Bs mixing
- The CDF/D0 measurement of (‐2βs,ΔΓs) from the time-dependent
angular analysis of the BsÆJ/ψφ provides a direct constraint on ΦNPs
CDF ’08 update
with 2.8/fb
not yet combined
- Using the HFAG combination off CDF and D0 likelihood :
(− 2β s , ΔΓs ) / (π + 2β s ,− ΔΓs ) =
(( −44
+ 17
− 21
054
)° ,0.154 +− 00..070
ps −1
• Other constraints
)
ƒ Δms : consistent with SM expectation
ƒ ASL(Bs):
) llarge error wrtt SM prediction
di ti
ƒ τFS : weak constraint on ΔΓs
ƒ NP relation
ΔΓs ≈ ΔΓsSM cos( Φ NP
s )
ƒ ΔΓ SM = (0.090
s
+ 0 . 019
- 0.022
) ps
[Lenz,Nierste]
ƒ tends to push the NP phase ΦNPs towards SM.
Clean analysis : all theoretical uncertainties are in the ΔΓSM prediction but…
but
… it cannot tell much more on ΦNPs than the direct TeVatron measurement
V. Tisserand, LAPP
57
New Physics in Bs mixing
Inputs:
Warning : 68% CL
Δms
Δmd
Dominant constraints:
ƒ Δms agrees with SM.
sin((2β)
α
Bd
ASL , ASL
Bs
ASL
ƒ (φs=‐2βs,ΔΓs) through
time dependent angular
analysis of Bs →J/ψφ by
D∅/CDF (HFAG’08 update)
is 2.2σ away from SM.
ΔΓd / Γd
ΔΓs , φ s
+SM params:
||Vud|,
d|, ||Vus|,
s|,
|Vub|, |Vcb|,
γ(α), B→τν
hypothesis
hypothesis Agreement with SM :
V. Tisserand, LAPP
Δs= 1 (Re=1,Im=0)
with B
with
B+→τ+ν
with out
1.9 σ
1.9 σ
58
MFV in Bq=d,s mixing
additional
dditi
l constraints:
t i t
Inputs:
ΦNPq=0 and Δd = Δs= Δ
Δms
Δmd
sin(2β )
α
Bd
ASL , ASL
Bs
ASL
ΔΓd / Γd
ΔΓs , φ s
+SM params:
|Vud|, |Vus|,
|Vub|, |Vcb|,
γ(α), B→τν
SM point
Δ
In MFV scenario the impact from sin(2β) (tension from |Vub|τ+ν) &
TeVatron φs is washed out: no new NP phase !
V. Tisserand, LAPP
59
Beyond SM: 2HDM(II)
2 Higgs Doublet
Model: φ1, φ2
Î
V. Tisserand, LAPP
B+→τ+ν strikes back !
60
2HDM(II): φ1, φ2
‰ Motivation: it is a simple and predictive extension of the Standard Model. Same
structure for the quark sector but new flavor changing charged interactions mediated
by a charged Higgs, but not neutrals at tree level (Flavor Changing Neutral Currents:
FCNC). SM-like Yukawa couplings for quark sector and CKM only source of flavorchanging interactions.
‰ Charged Higgs contributions into tree or loop decays. Redefinition of the SM
expression through corrections implying only 2 additional parameters:
φ2: coupling up-quarks
φ1: coupling down-quarks
2HDM
type II
‰ 2HDM is embedded into super-symmetric models (MSSM).
‰ Charged Higgs transition is something we immediately imagine for BR(B+→τ+ν).
ν)
‰ Note: There are of course neutral higgses in 2HDM, which do not enter the processes
under consideration in this study.
V. Tisserand, LAPP
61
Observables and deviations from SM
Î We consider several observables
subjected
bjec ed to
o receive
ece e Higgs
gg contributions:
co b o :
ƒleptonic decays:
ƒsemi-leptonic (SL) decays:
ƒThe partial width of Z→ bb (used
to be a hint of NP! Rb)
ƒ b→ sγ
Î Note: we did not consider in the present
study the observables related to mixing
mixing, neither
Bs →μμ nor b →sll.
V. Tisserand, LAPP
SM pred. 2σ
z
exp. meas. 1σ
62
leptonic decays
W+
Î
For any meson M, SM leptonic decay rate [rad corr. only for M = K, π ]
Î
Charged Higgs contributions:
H+
If perfect agreement SM
SM-data
data, two distinct solutions in 2HDM(II):
• decoupling : rH = 0 (mH+ →∞, tanβ small)
• fine-tuned : rH = ‐2 (linear correlation between mH+ and large
tanβ , depends on meson mass) Îfor B+→τ+ν: BRNP >BRSM.
V. Tisserand, LAPP
63
Changing the BR of B+ Æ τ + ν
V. Tisserand, LAPP
64
leptonic decays
D→μν
K→μν/π→μν
/
V. Tisserand, LAPP
W+
H+
Ds→lν
l
B→τν
65
leptonic decays
W+
H+
ƒMost of the individual finedtuned solutions are removed
at 95% CL
ƒLarge tanβ are excluded at
small Higgs masses.
V. Tisserand, LAPP
66
semi-leptonic
decays
y
Î Semi-leptonic decays help
further to remove individual
fined-tuned
fined
tuned solutions for leptonic
decays at 95% CL.
B→Dτν
K→πlν
V. Tisserand, LAPP
67
The combined constraint
‰ χ²min≈11 obtained
for
mH+> 600 GeV/c²
‰ Rb
constrains at small tanβ (<1) ‰ We
are ending with a onedimensional constraint on the
charged Higgs mass mostly
brought by b→ sγ.
‰ Leptonic decays (mainly
BR(B+→τ+ν) ) constrains the
parameter space at large tanβ
(>30) and competes with sγ.
Î 2HDM(II) does not perform better than the SM:
• Large χ²min due to tension from large measured
that favors finedtuned low solution for mH+
• other observables agree with SM and select large mH+ (decoupling limit: charged
Higgs contributions negligible)
V. Tisserand, LAPP
68
The combined constraint
on mH+ and tanβ
β
9No constraint on tanβ at 95% CL.
V. Tisserand, LAPP
69
Conclusions, perspectives
• KM mechanism is at work and dominant for CPV and NP in
quark b sector
⇒ stillll room ffor NP both
b h in Bd and
d Bs.
• overall good agreement in the global SM CKM fit:
ƒ a step forward on α precision, but need to go beyond SU(2).
ƒ but tension sin(2β) ⇔ |Vub| with B+→τ+ν :
- wait for new measurements by B-factories,
whatever super-B factory …
- 2HDM models ?
-LQCD, … what else ?
ƒ but tension in direct TeVatron βS measurement.
measurement
⇒wait for more data & LHCb to enter the game.
• progresses on constraints from exp. vs LQCD (fDs
) b→Vγ,
b→Vγ and
D ),
rare K decays. Working NOW on b→sll.
V. Tisserand, LAPP
70
BACKUP Slides
V. Tisserand, LAPP
71
The unitary CKM Matrix: parameterization valid to all order in λ and phase
independent
(Wolfenstein valid to all orders in λ)
(Phase convention independent UT)
(Wolfenstein valid to all orders in λ + re-phasing independent)
V. Tisserand, LAPP
72
|Vud|
Vud = 0.97418 ± 0.00026
V. Tisserand, LAPP
P Gambino La Thuile‘09
73
|Vus|
V. Tisserand, LAPP
F. di Lodovico ICHEP’08
74
Improvements on |Vud| & |Vus|
S. Descotes-Genon MEW’08
V. Tisserand, LAPP
75
|Vud|2+|Vus|2
V. Tisserand, LAPP
F. di Lodovico ICHEP’08
76
New Physics in Bd & Bs mixing without B+→τ+ν
Removing B+→τ+ν impacts Δmd precision ⇒ one less constraint
f the
for
h d
decay constant fBd (only
( l LQCD
LQCD: more SM lik
like)) and
d
relaxes the sin(2β) ⇔|Vub| tension but no impact on TeVatron φs
V. Tisserand, LAPP
77
MFV in Bq=d,s mixing without B+→τ+ν
additional
dditi
l constraints:
t i t
Inputs:
ΦNPq=0 and Δd = Δs= Δ
Δms
Δmd
sin(2β )
α
Bd
ASL , ASL
Bs
ASL
ΔΓd / Γd
ΔΓs , φ s
+SM params:
|Vud|, |Vus|,
|Vub|, |Vcb|,
γ(α), B→τν
SM point
Δ
Removing B+→τ+ν impacts Δmd precision ⇒ one less constraint
for the decay constant fBd (only LQCD: more SM like)
V. Tisserand, LAPP
78
α from b→uʉd, B→ππ
V. Tisserand, LAPP
79
α from b→uʉd, B→ππ
S
Same
as for
f summer’08
’08
α= (92.4+11.2‐10.0)°
Δα = (20.0±10.3)
(20.0±10.3)°
χ²(0)~140
V. Tisserand, LAPP
80
α from b→uʉd, B→ρπ
Dominant mode ρ+π – is not a CP eigenstate
t =0
t
Aleksan et al, NP B361, 141 (1991)
ρ0π0
0
Amplitude interference in Dalitz plot
ρ+π–
ρ–π+
simultaneous fit of α and strong phases
Measure 26 (27) bilinear Form Factor coefficients
q/p
~ e−2i β
mixing
Snyder-Quinn, PRD 48, 2139 (1993)
B
0
B
CP
A+−
A−+
ρ +π −
A00
ρ 0π 0
A00
A++−
A−+
ρ −π +
correlated χ2 fit to determine physics quantities
Same as for Moriond’07
V. Tisserand, LAPP
81
α from b→uʉd, B→ρρ
fL~1 Î CP+
A.Perez Lake Louise ‘09
V. Tisserand, LAPP
82
α from b→uʉd, B→ρρ
Winter’ 09 update : B→ρ+ρ0 from BaBar (arXiv:0921.3522 wrt PRL 97, 261801 (06))
Both BR and fL increase wrt summer ’08 byy ~2σ and ~1σ, respectively
p
y
B
+0
= 16 . 8 ( 3 . 2 ) 10
−6
⇒ 23 . 7 ( 2 . 0 ) 10
−6
(BaBar)
fL+ 0 = 0 . 905 ( 47 ) ⇒ 0 . 950 ( 16 ) (BaBar)
(B B )
B
+0
= 18 . 2 ( 3 . 0 ) 10
−6
⇒ 24 . 0 ( 1 . 9 ) 10
−6
(WA)
fL+ 0 = 0 . 912 ( 44 ) ⇒ 0 . 950 ( 15 ) (WA)
V. Tisserand, LAPP
83
α from B→ρρ
α = (89.9 ± 5.4)°
Δα = (1.4 ±
(1 4 ± 3.7)
3 7)°
Summer’08 was :
α = (90.9 +−614.7.9 )°
Δα = ( 0.5+−125.5.6 )°
84
α from B→ρρ
:
α = (89.9 ± 5.4)° Summer’08+6.was
7
(
90
.
9
α
=
−14.9 )°
Δα = (1.4 ± 3.7)°
Δα = ( 0.5+−125.5.6 )°
Î
How lucky are we ? toy study:
Gaussian smear of all inputs around best
CKM fitted values: BR+-, BR0+, BR00,C
C+-,SS+-,
C00, S00,fL+-,fL0+ ,fL00
1 σ half-interval
Summer’08
~50 % of
closing
triangles
2 σ half
half-interval
interval
Moriond’09
2 σ half-interval
“Gaussian like”
85
Isospin breaking
J. Zupan CKM WS‘06
SOURCES
SIZES
V. Tisserand, LAPP
86
Isospin breaking B→ρρ
V. Tisserand, LAPP
J. Zupan CKM WS‘06
87
B→(ρ,ω)γ & B→K*γ exclusive b→ Dγ where D=(d,s)
S. Descotes-Genon MEW’08
V. Tisserand, LAPP
88
No more trouble with |Vcs|
fLatDs=241.0(1.4)(5.3) MeV
fLatDs=254.3(8)(11) MeV
|Vcs|= 1.050±0.053
|Vcs|= 0.995±0.081
|Vcs|
V. Tisserand, LAPP
|Vcs|
89
a word on rare K+→π+νν
BR parameterization as Brod & Gorbahn ’08
08
(PRD 78, 034006), NLO QED-QCD & EW corr.
to the charm quark contrib. (αs(m²Z)=0.1176(20) &
mc(μc))=1.286(13)(40)):
1.286(13)(40)):
: short distance
cham quark
0.378(15)
: long distance corr. LQCD
κ +:
higher order EW corr.
ΔEM: long dist.
dist QED corr
λi: V*isVid
X(xi): Inami Lim loop function
V. Tisserand, LAPP
∝
Pc(X)
90
J.Charles Capri ‘08
V. Tisserand, LAPP
91
rB and strong phase δB from GLW+ADS+GGSZ WA global fit
V. Tisserand, LAPP
92
γ
from direct
CKM’08
GLW ≡ D0 CP final state
CPV in charged
~0 B →D K* decays
Combination
C
bi ti may nott llead
d tto naïve
ï expectation.
t ti The
Th rB
nuisance parameter ([b→u]/[b→c] transition size), even
(
) interferes in the CKM angle γ extract:
when large(~30%) ,
• This is not a naïve GLW+ADS average (multi-dim.)
• The accuracy may degrade in combo.
⊕
ADS ≡ D0 Doub. Cabbibo Suppressed
⊕
±stat.±syst.
rD= (5.78±0.08)% CS
(5 78±0 08)% CS HFAG WA
rB ∈ [14,43]%
γ ∉ [87,94]°
@ 95 % CL
V. Tisserand, LAPP
93
γ
from direct
CPV in charged
~0 B →D K* decays
marginal sensitivity to r²B<<1
GLW
good sensitivity to r²B>r²D
ADS
=
8 fold-ambiguities
fold ambig ities on γ
rB=(31.1+7.1‐8.0)%
V. Tisserand, LAPP
γ=(34+28‐30)° or (146+30‐29)°
94
Combining methods on γ: statistical treatment matters!
So far CKMfitter
conservative
baseline method
K.Trabelsi CKM’08
V. Tisserand, LAPP
95
leptonic decays
W+
H+
ƒMost of the individual finedtuned solutions are removed
at 95% CL
ƒLarge tanβ are excluded at
small Higgs masses.
V. Tisserand, LAPP
96
semi-leptonic
decays
y
V. Tisserand, LAPP
97
b→sγ
Obviously a relevant laboratory for New Physics. Vastly investigated in the literature.
9A.J. Buras, M.Misiak, M.Munz, S. Pokorski, Nucl Phys. B424
9K. Chetyrkin, M. Misiak, M. Munz, Phys. Lett. B400.
9P Gambino
9P.
Gambino, M
M.Misiak
Misiak Nucl.,
Nucl Phys.
Phys B611
B611.
9M.Misiak, M. Steinhauser Nucl. Phys. B764.
9C. Degrassi, P. Gambino, P. Slavich, CERN/2007-265
9T. Besmer, C. Greub, T. Hurth, Nucl. Phys. B 609.
9Calculated at NNLO (Misiak et al., 2006)
9The normalized branching fraction (in notation from Gambino et al
al.)) reads as
as:
9For practical reasons, we’ve chosen to parametrize the P and N according to
9Where A and B are two functions depending on a reduced set of relevant
parameters (mb, mt, mc (btw, the most critical input)).
9Theyy are fitted to reproduce
p
the results from the open
p package
p
g SusyBSG
y
((degrassi
g
et al.)
V. Tisserand, LAPP
98