1. Lepton Flavor Violation
Yasuhiro Okada (KEK)
March 20, 2005
MEG meeting, University of Tokyo

2. Lepton Flavor Violation in charged lepton processes
Charged lepton LFV is a clear evidence of physics beyond the Standard Model.
Neutrino mixing suggests existence of lepton flavor mixing. Large LFV in charged lepton processes is possible, if there is new physics at the TeV scale.
There are various processes and observable quantities in muon and tau LFV processes. These are keys to choose a correct model among various candidates.

3. Contents of this talk Phenomenology of muon and tau LFV processes.
SUSY and LFV
Neutrino mass and LFV

4. Lepton Flavor Violation
No lepton flavor violation (LFV) in the Standard Model.
LFV in charged lepton
processes is negligibly small for a simple seesaw　neutrino model.

5. Three muon LFV processes
Back to back emission of a positron
and a photon with an energy of a half
of the muon mass.
Nucleus
A monochromatic energy electron emission for
the coherent mu-e transition.
Muon in 1s state

6. Experimental bounds Process Current Future
(Ti)
Mu-e conversion search at the level of 10^{-18} is proposed
in the future muon facility at J-PARC (PRIME).

7. Muon polarization and LFV processes
If the muon is polarized, we can define a P-odd asymmetry for m -> e g
and T-odd and P-odd asymmetries for m->3e. These asymmetries are useful
to distinguish different models.
m-> 3e
Two P-odd and
one T-odd asymmetries
Example :
A= -1 for the SUSY seesaw model

8. Background suppression for m->eg search
Polarized muon is also useful to reduce physics and accidental background for the m -> eg search.
Y. Kuno, Y.Okada,1996
Physics background n
Energy resolution

9. Accidental background: Both ~52.8 MeV e+ from m->e+ nn
Y. Kuno, A.Maki, Y.Okada,1997
Accidental background: Both
~52.8 MeV e+ from m->e+ nn
~52.8 MeV g from m->e+nng
follow the 1+Pm cosq distribution.
Suppression factor of the accidental
background by restricting the detector
Angle.
Pm=97%
Pm=100% qD

10. Z dependence of mu-e conversion branching ratio
R.Kitano, M.Koike and Y.Okada. 2002
We have calculated the coherent mu-e conversion branching ratios in various nuclei for general LFV interactions to see:
(1) which nucleus is the most sensitive to mu-e conversion searches,
(2) whether we can distinguish various theoretical models by the Z dependence.
Relevant quark level interactions
Dipole
Scalar
Vector

11. mu-e conversion rate normalized at Al.
The branching ratio is largest
for the atomic number of Z=30 – 60.
For light nuclei, Z dependences
are similar for different operator forms.
Sizable difference of Z dependences for dipole, scalar and vector interactions. This is due to a relativistic effect of the muon wave function.
Another way to discriminate different models
vector
dipole
scalar

12. Comparison of three processes
If the photon penguin process is dominated, there are simple relations among
these branching ratios.
In many case of SUSY modes, this is true, but there is an important case
In which these relations do not hold.

13. Tau LFV processes
Various flavor structures
and their CP conjugates

14. Experimental upper bound
Y.Miyazaki ESP 2005
Most of processes are bounded by 0(10^-7)

15. Future experimental prospects for tau LFV search
Super KEKB LoI
e+e- B factory

16. Supersymmetry and LFV quark squark lepton slepton gluon gluino W,Z,g,
Supersymmetry is a new type of symmetry connecting bosons and fermions.
Gauge coupling unification is realized with SUSY particles.
The LHC experiment can find squarks and gluon up to 2-3 TeV.
Coupling unification
In SUSY GUT
W,Z,g, H
gluon
lepton
quark
neutralino,
chargino
gluino
slepton
squark
SM particles
Super partners
Spin 1/2
Spin 0
Spin 1

17. Slepton flavor mixing g-2: the diagonal term EDM: complex phases
In SUSY models, LFV processes are
induced by the off-diagonal terms
in the slepton mass matrixes
g-2: the diagonal term
EDM: complex phases
LFV: the off-diagonal term
Off-diagonal terms depend on how SUSY breaking is generated and
what kinds of LFV interactions exist at the GUT scale.

18. SUSY GUT and SUSY Seesaw model
L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986
The flavor off-diagonal terms in the slepton mass matrix are induced by renormalization effects
due to GUT and/or neutrino interactions.
@ M_planck
GUT Yukawa
interaction
Neutrino Yukawa
CKM matrix
Neutrino oscillation
LFV

19. m -> e g branching ratio (typical example)
SUSY seesaw model
J.Hisano and D.Nomura,2000
SU(5) and SO(10) SUSY GUT
K.Okumura
SO(10)
SU(5)
Right-handed selectron mass
The branching ratio can be large
in particular for SO(10) SUSY GUT model.
Right-handed neutrino mass

20. SU(5) SUSY GUT + right-handed neutrinos
B(m->eg) can be close to the experimental bound even if
SUSY particles’ masses are in a few TeV range.
sneutrino mass (GeV)
500
1000
1500
T.Goto, Y.Okada,Y.Shimizu,T.Shindou,M.Tanaka, 2004

21. m->e g and m->3e asymmetries in SUSY models
P and T-odd asymmetries in minimal SUSY GUT models
The T-odd asymmetry
can be 10 % level for
some parameter space
of the SU(5) SUSY GUT
and the SUSY seesaw
model.
Information on lepton
sector CP violation
Y.Okada,K.Okumura,and Y.Shimizu, 2000
T-odd asymmetry in the SUSY seesaw model
J.Ellis,J.Hisano,S.Lola, and M.Raidal, 2001

22. Neutrino and LFV
Although the simple seesaw or Dirac neutrino model predicts too small generate branching ratios for the charged lepton LFV, other models of neutrino mass generation can induce observable effects.
SUSY seesaw model (F.Borzumati and A.Masiero 1986)
Triplet Higgs model (E.J.Chun, K.Y.Lee,S.C.Park; N.Kakizaki,Y.Ogura, F.Shima, 2003)
Left-right symmetric model (V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004)
R-parity violating SUSY model (A.de Gouvea,S.Lola,K.Tobe,2001)
Generalized Zee model (K.Hasagawa, C.S.Lim, K.Ogure, 2003)
Neutrino mass from the warped extra dimension (R.Kitano,2000)

23. SUSY seesaw with a large tan b
R.Kitano,M.Koike,S.Komine, and Y.Okada, 2003
SUSY loop diagrams can generate
a LFV Higgs-boson coupling
for large tan b cases. (K.Babu, C.Kolda,2002) s m e
The heavy Higgs-boson exchange provides
a new contribution of a scalar type.
Higgs-exchange contribution
Photon-exchange contribution

24. Ratio of the branching ratios and Z-dependence of mu-e conversion rates
mu-e conversion is enhanced.
Z-dependence indicates the scalar exchange contribution.

25. Triplet Higgs model Neutrino mass is generated by a triplet Higgs VEV.
N.Kakizaki,Y.Ogura, F.Shima, 2003
Neutrino mass is generated by a triplet Higgs VEV.
Connection between LFV and neutrino mixing matrix.
m -> 3e processes are enhanced because of
the tree-level charged Higgs excahnge.
m ->eg
m->3e
m-e conv

26. Three branching ratios
depends on neutrino
mass pattern.
B(m->eg)~B(mA-eA)
Absolute scale can be changed.

27. LFV in LR symmetric model
V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004
(Non-SUSY) left-right symmetric model
L<->R parity
Higgs fields, (bi-doublet, two triplets)
Low energy (TeV region ) seesaw mechanism for neutrino masses

28. Four lepton interactions are dominant among various LFV processes.
In general,
(kf~a 0(1) number)
A.Akeroyd, M.Aoki, Y.Okada,2006

29. A1 asymmetry in polarized mu ->3e
Asymmetry in mu->3e and tau->3mu
Since the flavor mixing in
left and right handed doubly charged
Higgs interaction is the same in this
Model, the parity-odd asymmetry in
mu to 3e and tau to 3mu processes
are only a function of two Higgs boson
masses.
A.Akeroyd, M.Aoki and Y.Okada, 2005

30. SUSY with R parity violation
A.de Gouvea,S.Lola,K.Tobe,2001
Depending on assumption of coupling combination, various pattern
can arise for ratios of the three branching ratios and asymmetry.

31. Comparison of three muon processes in various new physics models
SUSY GUT/Seesaw
B( m->e g ) >> B(m->3e) ~B(mA-eA)
Various asymmetries in polarized m decays.
SUSY with large tan b
m-e conv. can be enhanced. Z-dependence in m-e conv. branching ratio.
Triplet Higgs for neutrino
B(m->3e) > or ~ B(m->eg) ~B(mA-eA)
RL model
B(m->3e) >> B(m->eg) ~B(mA-eA)
Asymmetry in m->3e
RPV SUSY
Various patterns of branching ratios and asymmetries

32. Summary
Muon LFV experiments provide various opportunities to search for new physics effects.
Large effects are expected in well-motivated models of SUSY for LFV processes.
If there are new particles at the TeV region related to the lepton flavor mixing, the neutrino oscillation may have some connection to the charged lepton LFV processes.
There are various observable quantities in muon LFV processes. Different neutrino mass generation mechanism predicts different characteristic signals in LFV processes.