Searching for New Physics in muon lepton flavor violating processes Yasuhiro Okada (KEK) November 14-21 ISS Physics working group meeting Imperial College London

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 m-e conversion search at 0(10^{-18}) will be possible in a future experiment at J-PARC (PRIME)

Tau LFV processes Many processes. Most of bounds are 10^{-7} Relation between mu and tau LFV processes depends on new physics Model. Y.Miyazaki ESP 2005

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)

SUSY and LFV 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 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

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.

Muon polarization m-> eg If the muon is polarized, we can define a P-odd asymmetry for mu -> e gamma and T-odd and P-odd asymmetries for mu ->3e. These asymmetries are useful to distinguish different models. For example, the parity asymmetry in mu ->e gamma reflects whether left-handed or right-handed sleptons have flavor mixing. m-> eg

Two P-odd and one T-odd asymmetries

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

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

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.

Examples of new physics models Several examples with specific features in ratios of branching ratios in three processes, asymmetries in polarized muon decay, Z-dependence of the mu-e conversion. SUSY seesaw model with large tan beta Triplet Higgs model Left-right symmetric model R-parity violating SUSY model

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 Higss VEV. N.Kakizaki,Y.Ogura, F.Shima, 2003 Neutrino mass is generated by a triplet Higss VEV. Connection between LFV and neutrino mixing matrix. Mu to 3e processes are enhanced because of the tree-level charged Higgs excahnge.

Three branching ratios depends on neutrino mass pattern.

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) V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004

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) > 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 and tau LFV processes. Different neutrino mass generation mechanism predicts different characteristic signals in LFV processes.