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

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

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.

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

Comparison of three processes 6 additional operators Various llqq operators

Tau LFV processes Various flavor structures and their CP conjugates Current bounds for tau LFV processes: 10-7- 10-8 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)

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.

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

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

(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

(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

(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

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

“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

(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

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