1. Theoretical Status of LFV and Rare Tau decays
Yasuhiro Okada(KEK/Sokendai)
September 8, 2009
BEAUTY 2009, Haidelberg University

2. Contents Brief introduction to muon and tau LFV processes
Some new physics examples
Use of muon polarization and decay angular distributions.

3. 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.

4. Three muon LFV processes
m-e conversion search at 0(10-16) is planned at
PRIME (KEK) and Mu2e (Fermilab) experiments

5. Comparison of three processes
6 additional operators
Various llqq operators

6. Tau LFV processes Various flavor structures and their CP conjugates
Current bounds for tau LFV processes: from Belle and BaBar.
O(10-9) at e+e- Super B factories.
CMS study: B(t->3m) < 3.8x10 -8 at 30 fb-1 (R. Satinelli and M. Biasini 2002)

7. Relationship of various LFV branching ratios
(1) If the photon penguin process is dominant, there are simple relations
among these branching ratios.
In many case of SUSY modes, this is true.
Other cases:
Additional Higgs exchange diagram (SUSY with large tan b)
Dominance of tree exchange diagrams (LR symmetric models)
Loop-induced but Z-penguin dominance (Little Higgs with T-parity)
(2) No particular scaling relations exists among tau and muon LFV
branching ratios.
=> Depends on flavor structure of LFV couplings.

8. Flavor univesrality of
New physics examples
(1) SUSY GUT/Seesaw models
LFV is a probe to interactions at very high energy scales
Quark and neutrino Yukawa coupling constants at the GUT/ Seesaw scale
can induce large flavor off-diagonal terms in sqaurk/slepton mass matrices.
Flavor univesrality of
SUSY breaking terms
at the cutoff scale
Quark FCNC
LFV
Quark Yukawa coupling
Neutrino Yukawa coupling Yq Yn
Neutrino seesaw model
mSUGRA
GUT
L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986

9. SU(5) SUSY GUT with seesaw neutrinos
correlation between
t->m(e) g and m->eg
t->mg
t->eg
m->eg
T.Goto, Y.Okada, T.Shindou, and M.Tanaka, 2008

10. (2) SUSY seesaw model with large tanb
For large values of the two Higgs vacuum expectation values (tanb), a heavy Higgs exchange diagram can be large. Processes like mu-e conversion, t->3m, t->mh, t->mfo, etc become important. m t s m e
K.Babu, C.Kolda,2002; M.Sher, 2002;
R.Kitano,M.Koike,S.Komine, and Y.Okada, 2003
V. Cirigliano, R.Kitano, Y.Okada, and P.Tuson, 2009
M.J.Herrero, J.Portoles and A.M.Rodriguez-Sanchez, 2009

11. (3) Little Higgs Model with T-parity
A composite Higgs model based on a new strong interaction
at ~10 TeV. New gauge bosons and fermions are introduced
at ~1 TeV.
Heavy partners (T-odd partners) of quarks and leptons
introduce new flavor mixing matrices.
All LFV processes are generated at one loop level.
m-e conv vs. m ->eg
t->mp vs. t->mg
M.Blanke, A.J.Buras, B.Duling, S.Recksiegel and C.Tarantino, 2009

12. (4) Left-Right symmetric model
Neutrino mass generation at the TeV scale.
Doubly charged Higgs bosons induce LFV processes at the tree level.
A.G.Akeroyd, M.Aoki, and Y.Okada, 2007

13. 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

14. “Polarized” tau decay
(1)Using angular correlation of tau decay products in signal and opposite sides,
asymmetries of “polarized” tau decay are obtained at e+e- colliders.
Example:
R.Kitano and Y.Okada 2001
Correlation between A(t->3m) and A(m->eg) in RL symmetric model
A.G.Akeroyd, M.Aoki, and Y.Okada, 2007

15. (2) At LHC, ts from W decays are polarized. We can use asymmetry
observables to distinguish different models in t->3m decays.
t-> 3m
M.Giffels, J.Kallarackal, M.Kramer, B.O'Leary and A.Stahl, 2008

16. Summary
Muon and tau LFV processes are a promising probe to physics beyond the SM. These are likely to be related to neutrino mass generation mechanism.
Three muon processes need dedicated experiments. There are many tau LFV processes, which can be explored at future flavor factory as well as LHC experiments.
Moun and tau polarization information is important to distinguish different new physics models