Minoru Nagai (ICRR, Univ. of Tokyo) ‘Flavored’ Electric Dipole Moments in Supersymmetric Theories 　 Minoru Nagai　 (ICRR, Univ. of Tokyo) ( KEK ) Ref: Phys.Lett.B642,510 (2006) arXiv:0712.1285 [hep-ph] Collaborated with: J.Hisano (ICRR), P.Paradisi (Munich, Tech. U.) Feb. 22, 2008 特定領域「フレーバー物理の新展開」研究会

Sensitive to the Beyond SM physics 1. Introduction Electric Dipole Moment (EDM) The EDM for spin 1/2 fermion is given by the following effective operator. CP & P violating Hadronic EDMs (dn, dHg) are generated by the CP violating operators, such as quark EDMs and CEDMs (ChromoElectric Dipole Moments). Quark EDM Quark CEDM Current experimental bound …… Future : The Standard Model (SM) Only source of CP violation is the CP phase of the CKM matrix. （　　　　　　　） ⇒ Sensitive to the Beyond SM physics

Many sources of CP violation The Minimal Supersymmetric Standard Model (MSSM) Many sources of CP violation Phases of gaugino masses, A term and B term. Phases of off diagonal components in the sfermion mass matrices strongly constrained by EDM experiments They might be suppressed by some SUSY breaking & mediation mechanisms : complex hermit matrix Off-diagonal components can have CP phases. Null results of EDMs severely constrained these off diagonal element. We systematically discussed the flavor induced EDMs originated from the squark flavor mixing. Especially we included tanbeta enhanced threshold corrections, which appear to be very important to discuss them.

2. Flavored EDM at the LO (1-loop) CP violating Dim-5 operators Quark EDM Quark CEDM CP violating effects can be estimated by basis-independent measure of CP violation, Jarlskog invariants. SM There is only one CP violating phase in the CKM matrix. at 3 loop level MSSM There are Jarlskog invariants originated from new CP phases of squark mass matrix. In this talk, we consider the down quark (C)EDM, which tend to dominate the up quark one. Case 1) Case 2) Case 3)

gluino contribution to EDMs Case 1) [S.Dimopoulos & L.J.Hall (1995)] Jarlskog invariant An odd number of Yukawa coupling appear to have a chirality-flip gluino contribution to EDMs Heavy quark mass enhancement cf. Constraint from :

There is no contribution at 1-loop Case 2) [M.Endo et al. (2004)] Higgsino contribution to EDMs Case 3) Need couplings with both charged and neutral particles There is no contribution at 1-loop

4. Flavored EDM at the BLO Importance of the BLO calculation Contributions from are generated only at above two-loop levels. At the BLO, tanbeta enhanced interactions are generated through the radiative corrections to the quark mass terms. They give corrections to the EDMs at least. How such tanbeta enhanced interactions are generated? Non-holomorphic Yukwa couplings Diagonalization

Higgs-mediated Two-loop Contribution Effective Higgs coupling induced by radiative corrections to down-quark mass matrix Down quark mass : Tree level 1-loop level Non-decoupling at the large SUSY particle mass limit Charged Higgs contribution to EDMs [Hisano, MN, Paradisi (2006)]

Features of the Higgs-mediated Two-loop Contribution Ratio of 1 and 2-loop contribution: dd (Higgs) / dd (gluino) down quark (C)EDM: dd/e (dcd) [cm] 10 -25 100 (δRR) 31 = (0.22)3 tanβ= 10 10 10 -26 1 MH+ = 300 GeV (δLL) 13 = (0.22)3 10 -27 10 -1 200 500 1000 1500 2000 1000 2000 3000 4000 5000 Charged Higgs mass: MH+ [GeV] SUSY particle mass: mSUSY [GeV] It is slowly decoupled for heavy charged Higgs mass. It may dominate over 1-loop gluino contribution for mSUSY> 1-2 TeV.

Tanβ Enhanced Corrections for EDMs down quark EDM Charged Higgs Chargino Gluino Total Gluino (1-loop) 2 31 Charged Higgs contribution Chargino contribution

Prediction in SU(5) SUSY GUT with RNs down quark EDM -26 10 Chargino -27 10 Gluino Charged Higgs -28 10 Total -29 10 5 10 60 In the concrete SUSY GUT models, not only gluino but also chargino and charged-Higgs may contribute to the EDMs at the same order of magnitude.

4. Summary We discussed the flavored EDMs, which are sensitive to the non-minimal flavor structure of squark masses and already constrain some parameter spaces in the MSSM. Especially we classified the relevant CP-odd phases in terms of Jarlskog invariants, and performed systematical calculation at the BLO. Tanbeta enhanced corrections play important role to discuss the prediction of EDMs in the MSSM. In the case of and/or , charged-Higgs contributions tend to become important. Chargino contributions also become dominant for large tanbeta. We should include all of these contributions to discuss the prediction of EDMs in concrete models, such as SUSY GUTs.

Back Up Slide

CP phase constraints From the neutron EDM experiment, CP phases in the MSSM are constrained by Here, we use the following formula. [M.Pospelov and A.Ritz (1999) ]

Present experimental bounds Hadronic EDMs 199Hg EDM Neutron EDM Deuteron EDM ＣＰ violating hadronic interactions Quark CEDM Quark EDM CP violating Dim-5 operator quark EDM quark CEDM Although there can be large hadronic uncertainty, it can be estimated as [Hisano & Shimizu (2004) ] Present experimental bounds