Slides

André de Gouvêa
Northwestern
Phenomenological Perspective on
(Charged-)LFV Processes
André de Gouvêa
Northwestern University
NuFlavor 2009
June 8–10, 2009, Cosener’s House, UK
[session: interplay between neutrino masses and other phenomenological signatures]
June 9, 2009
NuFlavor
André de Gouvêa
Northwestern
Outline
1. Brief Introduction;
2. Old and ν Standard Model Expectations;
3. A Model Independent Approach;
4. Interplay with ν Masses, Leptogenesis and the LHC via Examples;
5. Conclusions.
June 9, 2009
NuFlavor
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Northwestern
Ever since it was established that µ → eν ν̄, people have searched for
µ → eγ, which naively could arise at one-loop:
ν
µ
γ
e
The fact that µ → eγ did not happen, led one to postulate that the
two neutrino states produced in muon decay were distinct, and that
µ → eγ, and other similar processes, were forbidden due to symmetries.
To this date, these so-called individual lepton-flavor numbers seem to be
conserved in the case of charged lepton processes, in spite of many
decades of (so far) fruitless searching. . .
June 9, 2009
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UL Branching Ratio (Conversion Probability)
Searches for Lepton Number Violation (µ and e)
10
10
10
10
10
10
10
10
10
10
-1
-3
-5
-7
-9
-11
-13
-15
-17
µ →eγ
µ- N→ e- N
µ+e-→ µ-e+
µ →eee
KL → π+ µ e
KL → µ e
KL → π0 µ e
-19
1950
1960
1970
1980
1990
2000
2010
Year
[hep-ph/0109217]
June 9, 2009
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Northwestern
SM Expectations
In the old SM, the rate for charged lepton flavor violating processes is trivial to
predict. It vanishes because individual lepton flavor number is conserved:
• Nα (in) = Nα (out), for α = e, µ, τ .
————————
However, the old SM is wrong: NEUTRINOS change flavor after propagating a
finite distance.
• νµ → ντ and ν̄µ → ν̄τ — atmospheric experiments
[“indisputable”];
• νe → νµ,τ — solar experiments
[“indisputable”];
• ν̄e → ν̄other — reactor neutrinos
[“indisputable”];
• νµ → νother from accelerator experiments
[“indisputable”].
Lepton Flavor Number NOT a good quantum number.
June 9, 2009
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Hence, in the “New Standard Model” (νSM, equal to the old Standard Model
plus operators that lead to neutrino masses) µ → eγ is allowed (along with all
other charged lepton flavor violating processes).
These are Flavor Changing Neutral Current processes, observed in the quark
sector (b → sγ, K 0 ↔ K̄ 0 , etc).
Unfortunately, we do not know the νSM expectation for charged lepton flavor
violating processes → we don’t know the νSM Lagrangian !
June 9, 2009
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Northwestern
One contribution known to be there: active neutrino loops (same as quark sector).
In the case of charged leptons, the GIM suppression is very efficient. . .
e.g.: Br(µ → eγ) =
3α
32π
P
2
2
∆m
∗
Uei M 21i < 10−54
i=2,3 Uµi
W
[Uαi are the elements of the leptonic mixing matrix,
∆m21i ≡ m2i − m21 , i = 2, 3 are the neutrino mass-squared differences]
June 9, 2009
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MAX B(CLFV)
e.g.: SeeSaw Mechanism [minus “Theoretical Prejudice”]
10
τ→ µγ
-9
-10
10
τ→ µµµ
-11
10
10
µ→e conv in
-12
48
Ti
µ→ eγ
-13
10
-14
10
10
µ→ eee
-15
-16
10
June 9, 2009
20
40
60
80
100
120
140
160
180 200
m4 (GeV)
arXiv:0706.1732 [hep-ph]
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Northwestern
Independent from neutrino masses, there are strong theoretical reasons to
believe that the expected rate for flavor changing violating processes is
much, much larger than naive νSM predictions and that discovery is just
around the corner.
Due to the lack of SM “backgrounds,” searches for rare muon processes,
including µ → eγ, µ → e+ e− e and µ + N → e + N (µ-e–conversion in
nuclei) are considered ideal laboratories to probe effects of new physics at
or even above the electroweak scale.
Indeed, if there is new physics at the electroweak scale (as many theorists
will have you believe) and if mixing in the lepton sector is large
“everywhere” the question we need to address is quite different:
Why haven’t we seen charged lepton flavor violation yet?
June 9, 2009
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Model Independent Approach
As far as charged lepton flavor violating processes are concern, new physics
effects can be parameterized via a handful of higher dimensional operators. For
example, say that the following effective Lagrangian dominates CLFV
phenomena:
LCLFV
κ
mµ
µ
µν
µ
¯
µ̄R σµν eL F +
µ̄L γµ eL ūL γ uL + dL γ dL
=
(κ + 1)Λ2
(1 + κ)Λ2
First term: mediates µ → eγ and, at order α, µ → eee and µ + Z → e + Z
Second term: mediates µ + Z → e + Z and, at one-loop, µ → eγ and µ → eee
Λ is the “scale of new physics”. κ interpolates between transition dipole
moment and four-fermion operators.
Which term wins? → Model Dependent
June 9, 2009
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• µ → e-conv at 10−17 “guaranteed” deeper
probe than µ → eγ at 10−14 .
Λ (TeV)
André de Gouvêa
B(µ→ e conv in 48Ti)>10-18
• We don’t think we can do µ → eγ better than
10−14 . µ → e–conv “only” way forward after MEG.
10
4
B(µ→ e conv in 48Ti)>10-16
• If the LHC does not discover new states
µ → e-conv among very few process that can
B(µ→ eγ)>10-14
access 10,000+ TeV new physics scale:
tree-level new physics: κ 1,
1
Λ2
∼
g 2 θeµ
.
2
Mnew
B(µ→ eγ)>10-13
10
3
EXCLUDED
10
June 9, 2009
-2
10
-1
1
10
10
κ
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2
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Other Example: µ → ee+ e−
LCLFV =
mµ
µ̄ σ e F µν +
(κ+1)Λ2 R µν L
Λ (TeV)
André de Gouvêa
4000
-16
B(µ→ eee)>10
3000
κ
µ
+ (1+κ)Λ
2 µ̄L γµ eL ēγ e
B(µ→ eγ)>10-13
B(µ→ eee)>10-15
2000
• µ → eee-conv at 10−16 “guaranteed” deeper
B(µ→ eee)>10-14
probe than µ → eγ at 10−14 .
• µ → eee another way forward after MEG?
• If the LHC does not discover new states
1000
900
800
700
600
500
µ → eee among very few process that can
400
access 1,000+ TeV new physics scale:
tree-level new physics: κ 1,
1
Λ2
∼
g 2 θeµ
.
2
Mnew
10
June 9, 2009
EXCLUDED
300
-2
10
-1
1
10
10
κ
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2
André de Gouvêa
Northwestern
What is This Good For?
While specific models (discussed in several earlier talks) provide estimates
for the rates for CLFV processes, the observation of one specific CLFV
process cannot determine the underlying physics mechanism (this is
always true when all you measure is the coefficient of an effective
operator).
Real strength lies in combinations of different measurements, including:
• kinematical observables (e.g. angular distributions in µ → eee);
• other CLFV channels;
• neutrino oscillations;
• measurements of g − 2 and EDMs;
• collider searches for new, heavy states;
• etc.
June 9, 2009
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Vector 4-Fermion Interaction (Z)
∝ (µ̄γα e)(q̄γ α q)
Vector 4-Fermion Interaction (γ)
Dipole (∝ µ̄σαβ eF αβ )
Scalar 4-Fermion Interaction
∝ (µ̄e)(q̄q)
June 9, 2009
[Cirigliano, Kitano, Okada, Tuzon, 0904.0957]
NuFlavor
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Northwestern
Example: Anomalous Magnetic Moment of the Muon, (g − 2)/2 ≡ aµ
June 9, 2009
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Model Independent Comparison Between g − 2 and CLFV:
The dipole effective operators that mediate µ → eγ and contribute to aµ
are virtually the same:
mµ µν
mµ µν
µ̄σ µFµν
×
θeµ 2 µ̄σ eFµν
Λ2
Λ
θeµ measures how much flavor is violated. θeµ = 1 in a flavor indifferent
theory, θeµ = 0 in a theory where individual lepton flavor number is
exactly conserved.
If θeµ ∼ 1, µ → eγ is a much more stringent probe of Λ.
On the other hand, if the current discrepancy in aµ is due to new physics,
θeµ 1 (θeµ < 10−4 ). This is hard to satisfy in, say, high energy SUSY
breaking models. . .
[Hisano, Tobe, hep-ph/0102315]
Comparison restricted to dipole operator. If four-fermion operators are
relevant, they will “only” enhance rate for CLFV with respect to
expectations from g − 2.
June 9, 2009
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Northwestern
[Hisano, Tobe, hep-ph/0102315]
June 9, 2009
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Northwestern
Example: Input From/To Leptogenesis
(⇒ talk by Asmaa Abada, plus Discussion)
In the case of the seesaw mechanism, the matter-antimatter asymmetry
generated via leptogenesis is (yet another) function of the neutrino Yukawa
couplings:
If one is to hope to ever reconstruct the seesaw Lagrangian and test
leptogenesis, LFV needs to be measured.
Note that this is VERY ambitious, and we need to get lucky a few times:
• Weak scale SUSY has to exist;
• “Precision” measurement of µ → e, τ → µ, τ → e;
• “Precision” measurement of SUSY masses;
• Very good understanding of mechanism of SUSY breaking;
• There are no other relevant degrees of freedom between the weak scale and
> 109 GeV;
• etc
Other ways to do this would be much appreciated!
June 9, 2009
NuFlavor
André de Gouvêa
Northwestern
Randall-Sundrum Model
(fermions in the bulk)
- dependency on UV-completion(?)
- dependency on Yukawa couplings
- “complementarity” between µ → eγ,
µ → e conv
[Agashe, Blechman, Petriello, hep-ph/0606021]
June 9, 2009
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Little Higgs Models: M. Blanke, et al, JHEP 0705, 013 (2007).
R!ΜTi$eTi"
1. ! 10"11
1. ! 10"13
1. ! 10"15
Br!Μ$eΓ"
1. ! 10"151. ! 10"141. ! 10"131. ! 10"121. ! 10"11
June 9, 2009
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Northwestern
SUSY with R-parity Violation
The MSSM Lagrangian contains several marginal operators which are allowed
by all gauge interactions but violate baryon and lepton number.
A subset of these (set λ00 to zero to prevent proton decay, and ignore bi-linear
terms, which do not contribute as much to CLFV) is:
L
+
c
λijk (ν̄Li
eLj ẽ∗Rk + ēRk νLi ẽLj + ēRk eLj ν̃Li )
0
jα
c
∗
˜
¯
˜
¯
λijk V
ν̄Li dLα dRk + dRk νLi dLα + dRk dLα ν̃Li
−
λ00ijk
=
KM
ūcj eLi d˜∗Rk
+ d¯Rk eLi ũLj + d¯Rk uLj ẽLi + h.c.,
The presence of different combinations of these terms leads to very distinct
patterns for CLFV. Proves to be an excellent laboratory for probing all different
possibilities.
[AdG, Lola, Tobe, hep-ph/0008085]
Bottom Line: This is simple a scenario where:
κ 1,
June 9, 2009
λ2
1
∼ 2
Λ2
m̃
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Northwestern
4×10−4
Br(µ+ →e+ γ)
Br(µ+ →e+ e− e+ )
−
−
=
R(µ →e in Ti (Al))
Br(µ+ →e+ e− e+ )
m2
1− ν̃2τ
2m
ẽR
2
' 1 × 10−4
β
=
−5
2 (1)×10
β
5
6
+
m2ν̃τ
12m2ẽ
R
µ+ → e+ e− e+ most promising channel!
June 9, 2009
+ log
(β ∼ 1)
m2e
m2ν̃
τ
2
+δ
' 2 (1) × 10−3 ,
[AdG, Lola, Tobe, hep-ph/0008085]
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André de Gouvêa
Br(µ+ →e+ γ)
Br(µ+ →e+ e− e+ )
Northwestern
= 1.1
(md˜ = mc̃L = 300 GeV)
R
R(µ− →e− in Ti (Al))
Br(µ+ →e+ e− e+ )
= 2 (1) × 105
µ → e-conversion “only hope”!
June 9, 2009
[AdG, Lola, Tobe, hep-ph/0008085]
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On CLFV Processes Involving τ Leptons (Brief Comment)
Current Bound On Selected τ CLFV Processes (All from the B-Factories):
• B(τ → eγ) < 1.1 × 10−7 ; B(τ → µγ) < 6.8 × 10−8 .
(µ → eγ)
• B(τ → eπ) < 8.0 × 10−8 ; B(τ → µπ) < 1.1 × 10−7 .
(µ → e–conversion)
• B(τ → eee) < 3.6 × 10−8 ; B(τ → eeµ) < 2.0 × 10−8 ,
(µ → eee)
• B(τ → eµµ) < 2.3 × 10−8 ; B(τ → µµµ) < 3.2 × 10−8 .
(µ → eee)
Relation to µ → e violating processes is model dependent. Typical
enhancements, at the amplitude-level, include:
• Chirality flipping: mτ mµ ;
• Lepton mixing effects: Uτ 3 Ue3 ;
• Mass-Squared Difference effects: ∆m213 ∆m212 ;
• etc
June 9, 2009
NuFlavor
André de Gouvêa
-4
-3
Rate
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-5
10
Northwestern
10
-2
10
–
ε=0.003, Λ=1 TeV, (λ=0.54)
-4
10
-3
ε=0.003, Λ=10 TeV, (λ=5.4)
P(νµ→νe)
τ→µγ
τ→µγ
eγ
µ→
µ-e conv
µ→eγ
-15
µ-e conv
µ→eee
10
10
-11
-13
10
P(νµ→ντ)
P(νµ→νe)
-9
10
-1
–
P(νµ→ντ)
-7
10
-2
10
10
µ→eee
10
-17
-5
e.g.: Large Extra-Dimensions
-7
-9
-11
-no ambiguity in y (neutrinos Dirac)
-dependency on UV-completion
-13
-15
-17
Rate
10 -5
10 -5
–
–
ε=0.0003,
Λ=1
TeV,
(λ
=0.17)
ε=0.0003,
Λ=10
TeV,
(λ
=1.7)
10
10
10
10
10
10
10
10
-7
P(νµ→ντ)
P(νµ→ντ)
10
P(νµ→νe)
10
-9
P(νµ→νe)
-11
τ→µγ
τ→µγ
10
-13
-15
10
µ→eγ
µ-e conv
µ→eee
-17
10
-4
June 9, 2009
10
-3
10
-2
10
|Ue3|
µ-e conv
µ→eγ
µ→eee
-4
10
10
-3
10
-2
10
10
|Ue3|
-1
-7
-9
Other example: neutrino masses from
Higgs triplets
-11
-13
-15
-17
[AdG, Giudice, Strumia, Tobe, hep-ph/0107156]
NuFlavor
André de Gouvêa
Northwestern
UL Branching Ratio (Conversion Probability)
Searches for Lepton Number Violation
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10
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10
10
10
10
10
10
10
-1
⇓
-3
-5
-7
-9
-11
-13
-15
-17
µ →eγ
µ- N→ e- N
µ+e-→ µ-e+
µ →eee
KL → π+ µ e
KL → µ e
KL → π0 µ e
⇑
-19
1950
1960
1970
1980
1990
2000
2010
Year
[hep-ph/0109217]
June 9, 2009
NuFlavor
André de Gouvêa
Northwestern
Brief: where is CLFV going (experiments)?
• MEG will aim at B(µ → eγ) > several×10−14 . Can anyone do better?
Looks very challenging!
• Different new initiatives in Fermilab (Mu2e) and in Japan (COMET) will
aim at B(µZ → eZ) > 10−16 . No showstopper for doing (much?) better.
Concrete discussions at Fermilab (with Project X) and Japan (PRISM). See
also NuFact study at CERN, hep-ph/0109217
• Recent discussions of new µ → eee effort at PSI. Perhaps
B(µ → eee) > 10−14 or 10−15 . Is it possible to do better? How much?
• Sensitivity to CLFV involving taus can improve past the 10−8 level with
Super-B factories. B(τ → `X) > 10−9 seems feasible. Naively unlikely that
LHC can contribute (in spite of huge τ event sample). LHCb?
June 9, 2009
NuFlavor
André de Gouvêa
Northwestern
Summary and Conclusions
• We know that charged lepton flavor violation must occur. Naive
expectations are really tiny in the νSM (neutrino masses too small).
• If there is new physics at the electroweak scale, we “must” see CLFV very
soon (MEG the best bet – stay tuned!). ‘Why haven’t we seen it yet?’
• It is fundamental to probe all CLFV channels. While in many scenarios
µ → eγ is the “largest” channel, there is no theorem that guarantees this
(and many exceptions).
• CLFV may be intimately related to new physics unveiled with the discovery
of non-zero neutrino masses. It may play a fundamental role in our
understanding of the seesaw mechanism, GUTs, the baryon-antibaryon
asymmetry of the Universe. We won’t know for sure until we see it!
⇒
June 9, 2009
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• Complementary to LHC and other searches for new physics. Guaranteed to
learn something regardless of scenario:
– New d.o.f. at LHC and positive signal for next-generation CLFV: best case
scenario. Differentiate new scenarios for the new physics. Connections to
neutrino masses?
– New d.o.f. at LHC and negative signal for next-generation CLFV: New
physics flavor blind. Why? Neutrino masses are very high energies?
Leptogenesis disfavored? Neutrino Mass Physics Weakly Coupled?
– No new d.o.f. at LHC and positive signal for next-generation CLFV: New
physics beyond the reach of LHC. Can we learn more? How?
– No new d.o.f. at LHC and negative signal for next-generation CLFV:
Next-next generation CLFV (possibly µ → e-conversion) among very few
probes of new physics scales (along with neutrino oscillation experiments,
astrophysics, cosmology, etc). How do we learn more?
June 9, 2009
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Northwestern
Backup Slides . . .
June 9, 2009
NuFlavor
André de Gouvêa
Northwestern
“Bread and Butter” SUSY plus High Energy Seesaw
→ θeµ ∼
κ 1 while
1
Λ2
∼
∆m2ẽµ̃
m̃2
g2 e
16π 2 m̃2 θeµ ,
where m̃2 is a typical supersymmetric mass.
θeµ measures the “amount” of flavor violation.
For m̃ around 1 TeV, θẽµ̃ is severely constrained. Very big problem.
“Natural” solution: θeµ = 0
June 9, 2009
→ modified by quantum corrections.
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André de Gouvêa
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The Seesaw Mechanism
αβ
MN
2
Nα Nβ + H.c., ⇒ N α gauge singlet fermions,
L ⊃ −yiα L HN −
αβ
yiα dimensionless Yukawa couplings, MN
(very large) mass parameters.
i
α
At low energies, integrate out the “right-handed neutrinos” Nα :
L⊃
−1 t
yMN
y ij
Li HLj H + O
1
2
MN
+ H.c.
y are not diagonal → right-handed neutrino loops generate non-zero ∆m2ẽµ̃
∆m2`˜L
αβ
MU V
3m20 + A20 X
∗
(y)
(y)
ln
,
'−
kα
kβ
8π 2
M Nk
MU V = MPlanck , MGU T , . . .
k
If this is indeed the case, CLFV would serve as another channel to probe
neutrino Yukawa couplings, which are not directly accessible experimentally.
Fundamentally important for “testing” the seesaw, leptogenesis, GUTs, etc.
June 9, 2009
NuFlavor
André de Gouvêa
Northwestern
What are the neutrino Yukawa couplings → ansatz needed!
B(µ → eγ) × 1011
tan β = 10
title10
1000
CKM
007
000
100
SO(10) inspired model.
10
Now
1
remember B scales with y 2 .
y
0.1
0.01
MEG
2 [ln(M /M )]2
B(µ → eγ) ∝ MR
R
Pl
0.001
0.0001
1e-05
1e-06
1e-07
0
200
400
600
800
x
1000
1200
1400
1600
M1/2 (GeV)
[Calibbi, Faccia, Masiero, Vempati, hep-ph/0605139]
June 9, 2009
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µ → e conversion is at least as sensitive as µ → eγ
B(µTi → eTi) × 1012
tan β = 10
title10
1000
CKM
MNS
SO(10) inspired model.
100
10
Now
1
remember B scales with y 2 .
y
0.1
2 [ln(M /M )]2
B(µ → eγ) ∝ MR
R
Pl
0.01
0.001
1e-04
1e-05
PRIME
1e-06
1e-07
0
200
400
600
800
x
1000
1200
1400
1600
M1/2 (GeV)
[Calibbi, Faccia, Masiero, Vempati, hep-ph/0605139]
June 9, 2009
NuFlavor