1. Lepton Flavor Violation in muon and tau decays
Yasuhiro Okada (KEK)
December 6, 2005
Nagoya University

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 LFV processes
Phenomenoloy of tau LFV processes.
Two examples
(1) Muon LFV processes in SUSY models including Higgs exchange contributions.
(R.Kitano　and Y.O)
(2) Muon and tau LFV processes in the Left-Right symmetric model.
(A.Akeroyd, M.Aoki, and Y.O)

4. (1) Muon 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. 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.

8. Muon polarization m-> eg m-> 3e
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.
Polarized muon is also useful to reduce
physics and accidental background for the
m -> eg search (Y. Kuno, A.Maki, Y.Okada,1997)
m-> 3e
Two P-odd and one T-odd asymmetries

9. P and T-odd asymmetries in 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

10. Z dependence of mu-e conversion processes.
:dipole
:scalar
:vector
Z-dependence can
distinguish different LFV
Interactions.
R.Kitano, M.Koike and Y.O. 2002

11. 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

12. 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

13. Uncertainty of the calculation
The mu-e conversion amplitude is given
by overlapping integral among three quantiites
Main uncertainty in the evaluation came from the input proton and neutron
density distribution in nuclei.
The proton density is precisely determined by electron scattering experiments.
The neutron density is main source of uncertainty.
Error of the branching ratio from ambiguity of
the neutron distribution is a few % for light nuclei.
Even for a heavy nuclei such as Pb, the uncertainty
Is reduced by new proton scattering experiments.

15. (2) Tau LFV processes Various flavor structures
and their CP conjugates

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

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

18. “Polarized” tau decay
R.Kitano and Y.O. 2001
Using angular correlation of tau decay products in signal and opposite sides,
asymmetries of “polarized” tau decay are obtained.
A=-1 case
Example:
Similarly, two P-odd and one T-odd asymmetries can be defined for
tau -> lll decays.

19. (3) LFV and new physics
Many models beyond the Standard Model contain sources of 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.
Generalized Zee model (K.Hasagawa, C.S.Lim, K.Ogure, 2003)
Neutrino mass from the warped extra dimension (R.Kitano,2000)
R-parity violating SUSY model (A.de Gouvea,S.Lola,K.Tobe,2001)
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)
SUSY seesaw model (F.Borzumati and A.Masiero 1986)

20. Muon LFV in SUSY models In SUSY models, LFV processes are
induced by the off-diagonal terms
in the slepton mass matrixes
In many cases, LFV processes are dominated by the m->e g amplitude.

21. 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

22. 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

23. Enhancement due to Higgs exchange contribution at large tan b case
Higgs exchange diagram have a ( tan b )^6 contribution. We have
shown impact of this contribution in the SUSY seesaw model
(LL case).
R.Kitano, M. Koike and S. Komine and Y.O. 2003
Higgs-exchange contribution s m e
Photon-exchange contribution
Dominance of the Higgs exchange affects the Z dependence
dipole, scalar, vector

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. Higgs exchange contribution in general case.
R.Kitano and Y.O.
LL:　 Flavor mixing in the left-handed slepton sector (ex. SUSY seesaw model)
RR: Flavor mixing in the right-handed slepton sector
LR, RL: Flavor mixing in the A term RR LL

26. LR RL
Higgs exchange effect is evident for the LL case.
Situation is more complicated in the RR case due to possible cancellation in both m -> eg and m-e conversion amplitudes.
Higgs exchange effects are seen in LR/RL cases.

27. LFV in LR symmetric model
A.Akeroyd, M.Aoki, Y.O.
(Non-SUSY) left-right symmetric model
V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004
O.M.Boyarkin, G.G.Boyarkina, T.I.Bakanova, 2004
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,
We consider following questions:
Which is important, m->3e or t ->lll ?
What are sizes of various tau decay modes?
What is the asymmetry of the tau LFV decay?
Heavy particles at the TeV region

29. Relationship between tau and mu decays depends on heavy neutrino
Masses.
Hierarchical heavy neutrino masses -> large tau decay processes
Blue
MR3 can be much
Heavier than MR1 and
MR2.
Pink:
nearly degenerate
Heavy neutrinos

30. Case 2
Case 1
Dominant modes depend on flavor mixings in the heavy neutrino sector.

31. Independent of LFV decay modes
including m-> 3e.
Summary
Tau vs. mu :
heavy neutrino mass hierarchy
(2) Various tau modes:
flavor mixing in heavy neutrino sector
(3) t ->3l (or m -> 3e) asymmetry:
ratio of the left and right doubly charged Higgs boson masses.

32. Summary
Experimental Improvement is expected in coming years for m -> eg (MEG) and various tau LFV processes (B factory, LHC).
If there are new particles at the TeV region related to the lepton flavor mixing, the neutrino oscillation can have connection to the charged lepton LFV processes.
There are various observable quantities in muon and tau LFV processes. Different neutrino mass generation mechanism predicts different characteristic signals in LFV processes.