CP violation in seesaw mechanism Junji Hisano (ICRR, Univ. of Tokyo) International Conference on the Seesaw Mechanism (SEESAW25) June 2004, Institut Henri Poincare, Paris.

Neutrino oscillation: Finite, but small neutrino mass Baryon in Universe: Leptogenesis (B-L violation by Majorana mass ) Unification of Matter in SO(10) GUT: Seesaw model (Introduction of right-handed neutrinos ) Superheavy : We need Supersymmetry (SUSY) 1, Introduction

Charged Lepton-Flavor Violation in SUSY seesaw model Non-vanishing LFV slepton masses by radiative correction And then, (Borzumati&Masiero) The charged LFV,, may be observed in near future experiments.

SUSY GUT with right-handed neutrinos Matter unification: GUT relation in flavor physics ( :generic CP phase in GUT) Flavor-violating right-handed current might predict deviation of and so on. (moroi) Colored Higgs Flavor Higgs

Contents of my talk Introduction CP violation in SUSY seesaw model CP violation in SUSY SU(5) GUT with right-handed neutrinos Summary

2, CP violation in SUSY seesaw model Radiative decay processes: Non-vanishing LFV slepton masses by radiative correction Sizable effect and where

Degrees of freedom of physical observables In (Hermitian) Real: 6,Phase:3 In light mass matrix M:3, :3, CP:1(mixing)+ 2(Majorana) In Seesaw model, M:3+3, :6,CP:4(mixing)+2(Majorana) We can take and for parameterization of seesaw model, and neutrino and charged lepton experiments give independent information of seesaw model. Bottom-up approach to seesaw model

CP violating observables in leptonic sector: T-odd asymmetry in LFV decay, It depends on a a Jarlskog invariant, Electric dipole moments of electron and muon. When right-handed neutrino masses are degenerates, EDMs are suppressed so much, similarly to neutron EDM originated from CKM phase. However, if they are not degenerate, EDMs are proportional to

T-odd asymmetry in LFV decay, T-odd asymmetry in polarized muon decay. This is smaller than 24%. Various contribution to and asymmetry comes from the interference. (photon and Z penguin, and box diagrams) However, photon penguin tends to dominate due to phase space. Thus, when and photon penguin is suppressed accidentally, T-odd asymmetry is sizable. Jarlskog inv. polarization vector (Gouvea, Lola, Tobe)

Branching ratios and T-odd asymmetry Accidental cancellation enhances T-odd asymmetry. (Ellis, JH, Lola, Raidal)

Leptonic EDMs Threshold correction to slepton mass due to the non-degeneracy of right-handed neutrinos enhances the leptonic EDMs. One-loop correction to and. (Farzan and Peskin) Thus, (Ellis, JH, Raidal, Shimizu)

CP violation in SUSY SU(5) GUT with right-handed neutrinos the neutrino Yukawa induces the flavor violating right-handed currents, ex, (2.7 sigma deviation observed in Belle experiments.) (1,2) mixing and (2,3) and (1,3) mixings are constrained by and hadronic EDMs, respectively. Here, is the CP phase in colored Higgs interaction. CP and flavor violation in the RH currents give rich hadron physics

Hadronic EDMs Current bounds on Mercury and neutron EDMs constrain the SUSY models. Choromoelectric dipole moments (CEDM) generate CP violating hadron interaction, which generates EDMs of Mercury and neutron. Strange quark component in necleon is not negligible. From baryon mass and sigma term in chiral perturbation theory, Thus, hadronic EDMs depend on the strange quark CEDM via K or eta meson interaction.

Hg atom EDM Hg is a diamagnetic atom, and the EDM is sensitive to CP- violating nuclear force induced by pion and eta exchange, which generates T-odd EM potential (Shiff momentum). Recent evaluation of Shiff momentum reveals that contribution to EDM from isoscalar channel for meson exchange is suppressed by 0.01 compared with previous estimate. From it, it is found that the strange quark CEDM contribution comes from pi-eta mixing. 199 (JH, Shimizu)

Neutron EDM This evaluation is a difficult task. The QCD sum rule is useful for evaluation of only contribution valence quarks. Here, we present our result by a traditional calculation of the loop diagrams. Strange quark contribution to neutron EDM is not suppressed. Here, Peccei-Quinn symmetry is assumed. Axion suppresses strange quark CEDM contribution for valence quarks, while above formula is not changed so much even if no PQ symmetry. (JH, Shimizu)

Hadronic EDM constraint on in SUSY GUT If the off-diagonal term in has a CP phase, it contributes to CEDM in the cooperation with the left-handed squark. The off-diagonal terms in are induced by the top quark Yukawa coupling with CKM. Here, Enhanced by heavier fermion mass In typical model, the left-handed squark mixing induced by top quark are

Constraints on the flavor violation in squark mass term From neutron (Hg atom) EDM Constraints on (1-3) and (2-3) mixing for the right-handed squark Mixings are stringent. (1-2) mixing is constrained by and (JH, Shimizu)

CEDMs in SUSY SU(5) GUT with right-handed neutrinos For Here, diagonal right-handed neutrino mass matrix is assumed, and then parameters in neutrino sector are given by oscillation data. New technique for deuteron EDM may reach to This corresponds to and (JH, Kakizaki, Nagai, Shimizu)

in SUSY GUT Non-negligible may lead to the deviation of CP asymmetry since is a radiative processes. The dominant contribution comes from the gluon penguin diagram in the broad parameter space. The effective operator for induced by :

CP asymmetry in v.s. Strange quark CEDM CP asymmetry in and strange quark CEDM are strongly correlated.

Assuming The neutron EDM bound is one or two orders of magnitude stronger for a sizable deviation in (JH, Shimizu)

Summary Seesaw mechanism is the most fascinating model for neutrino mass. However, it is difficult to reconstruct it from the neutrino oscillation data. In the supersymmetric extensions, the flavor and CP violating processes are important for the purpose. In this talk, we show the aspect of the CP violation. In the SUSY seesaw mechanism, CP violating observables are T-odd asymmetry in lepton decay and leptonic EDM. However, they tends to be suppressed except for accidental cases. In the extension of SUSY GUT, right-handed squark mixings are generated by the neutrino Yukawa interaction. The hadronic EDMs are good probes for (1-3) and (2-3) mixing of the right-handed squark mixing. New deuteron EDM measurement may give more stringent constraints on them or find the signal.