Flavored Electric Dipole Moments in Supersymmetric Standard Models

1. Flavored Electric Dipole Moments in Supersymmetric Standard Models Minoru Nagai　（KEK） Ref: Phys.Lett.B642,510 (2006) [hep-ph/0606322] arXiv:0712.1285 [hep-ph] (arXiv:080X.XXXX in preparation) Collaborated with: J. Hisano (ICRR), P. Paradisi (Munich Tech. U.) SUSY08 @ Seoul, Korea June 19, 2008

2. Plan of my talk Introduction Flavored EDM at the LO (1-loop) Flavored EDM at the BLO Numerical Calculation in a SUSY GUT model Summary

3. （　　　　　　　） Electric Dipole Moment Electric Dipole Moment (EDM) T & Pviolating In the field theory, where CPT symmetry is conserved, the EDM for spin 1/2 fermion is given by the following effective operator. CP & Pviolating In the Standard Model (SM) Only source of CP violation is the CP phase of the CKM matrix.* Current bounds （ long range effect ） （no contribution up to 3 loop ） ⇒ Sensitive to the Beyond SM physics *) We assume a PQ symmetry to suppress the dangerous QCD term

4. Many CP sources What can we probe by EDMs in supersymmetric SMs? • Flavor-conserving terms : complex in general These phases should be suppressed by some SUSY breaking & mediation mechanisms. strongly constrained by EDM experiments • Flavor-violating terms : complex hermit matrix off-diagonal components can have CP phases Radiatively generated between the EW scale and SUSY mediation scale “Flavored” EDM GUT structure Right-handed neutrino sector FCNC, LFV…

5. 2. Flavored EDM at the LO (1 loop) CP violating Dim-5 operators Quark EDM Quark CEDM Flavor-dependent 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 squarkmass matrix. In this talk, we consider the down quark (C)EDM, which becomes important in many models. Case 1) Case 2) Case 3)

6. Heavy quark mass enhancement 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 for cf. Constraint from :

7. 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

8. 3. Flavored EDM at the BLO Importance of the BLO calculation • Contributions from are generated only 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 corrections are generated? Non-holomorphic Yukwa couplings Diagonalization

9. 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)]

10. 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] 100 10-25 (δRR) 31= (0.22)3 tanβ= 10 10 10-26 1 MH+ = 300 GeV (δLL) 13 = (0.22)3 10-27 10-1 3000 200 500 1000 1500 2000 2000 4000 5000 1000 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.

11. Gluino (1-loop) Chargino Total Gluino Charged Higgs Chargino Charged Higgs Gluino Total Large tanβ Corrections for EDMs down quark EDM 31 2 Charged Higgs contribution Chargino contribution

12. 4. Numerical Calculation in a SUSY GUT model SU(5) GUT with Right-handed neutrinos Matter multiplet : Superpotential : See-saw : for Neutrino Yukawa couplings induce flavor-violating soft masses both for quarks and leptons. LFV、leptonic EDM Left-handed sleptonmixing Neutrino Yukawa coupling Right-handed sdownmixing SΦKs、hadronic EDM

13. Down Quark EDM in SU(5) GUT with RNs (1) 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.

14. Down quark EDM in SU(5) GUT with RNs (2) down quark EDM 1000 900 800 Gluino 700 Charged Higgs 600 Chargino 500 400 300 200 100 100 200 300 400 500 600 700 800 900 1000 • For , contributions of chargino and charged Higgs is important. • As the SUSY scale becomes large, charged Higgs mediated one becomes dominant due tothe logarithm term (slow decoupling feature).

15. 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. • It turns out that the charged-Higgs and chargino contributions become dominant in many parameter regions. • We should include all of these contributions to discuss the prediction of EDMs in concrete models, such as SUSY GUTs.

16. Back Up Slide

17. Two-loop Chargino Contribution [Hisano, MN, Paradisi (2007)] Pure Higgsino contribution • large top quark mass • Light stop mass • charge Gluino contribution Chargino contribution may also become dominant over the gluino one.

18. Constraints on neutrino sector by Hadronic EDMs [Hisano, Kakizaki, MN, Shimizu (2004)] CMSSM (only gluino contribution) Strange quark CEDM (e cm) Down quark CEDM (e cm) Hg EDM Neutron EDM Right-handed tau neutrino mass　（GeV) Current experimental bound・・・ Future Neutron & Deuteron EDM・・・ dn~10-28, dD~10-(29~30) (e cm)

19. Observed EDMs and CP-odd Sources Topic in this talk Electron EDM Thallium EDM ＣＰ violating hadronic interactions 199Hg EDM CP-odd Sources in New Physics Quark CEDM Deuteron EDM Quark EDM Neutron EDM CP violating Dim-5 operator quark CEDM fermion EDM Although there could be uncertainties in the hadronic and atomic calculations, it can be estimated as Present experimental bounds Future experiments aim to improve sensitivities 2–3 orders of magnitudes

20. Sources of CP violation in SUSY SMs • Flavor-conserving CP violating terms (SUSY CP Problem) : complex in general O(1) CP phases of these parameters induce too large EDMs. ex) Constrained MSSM From neutron EDM experiments, These phases might be suppressed by some SUSY breaking & mediation mechanisms. In other word, the SUSY CP problem seems to require other mechanisms to suppress EDMs such as A=0, heavy particles, … or as a model set-up.