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

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.

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

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.

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

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).

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

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

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

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

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

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.

Tau LFV processes Various flavor structures and their CP conjugates

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

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

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

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.

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

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

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

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

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)

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

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.

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

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

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

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

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

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.

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

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.