Flavor induced EDMs with tanbeta enhanced corrections

1. Flavor induced EDMs with tanbeta enhanced corrections Minoru Nagai (ICRR, Univ. of Tokyo) In collaborated with: J.Hisano (ICRR), P.Paradisi (Valencia) Phys.Lett.B642,510 (2006) Aug. 4, 2007 Summer Institute 2007

2. 1. Introduction • Blessings • Hierarchy problem • Gauge coupling unification • Dark matter candidate • Light Higgs • ・・・ • Supersymmetric standard models is the most well-motivated model beyond the Standard Model. Hints for the SUSY SMs • Difficulty : SUSY CP & flavor problem CP phases and flavor structures must be highly constrained. Off diagonal components of sfermion mass matrixes must be tiny. Ex.) by ΔmK

3. F term SUSY breaking terms : complex in general These phases may be suppressed by some SUSY breaking & mediation mechanisms. strongly constrained by EDM experiments What can we probe by EDMs in supersymmetric SMs? • D term SUSY breaking terms : complex hermit matrix off-diagonal components can have CP phases Even if these is no phases at the tree level, it can be generated by radiative corrections. Null results of EDMs severely constrained these off diagonal element. EDM measurements are sensitive to not only CP phases but alsoflavor structures.

4. 2. Flavor induced EDM CP violating Dim-5 operators Quark EDM Quark CEDM CP violating effects can be estimated by basis-independent measure of CP violation, Jarlskog invariants. The Standard Model The Standard Model There is only one CP violating phase in the CKM matrix and the corresponding Jarlskog invariant is highly suppressed by the ninth orders of Yukawa couplings. at 3 loop level Supersymmetric standard models There are Jarlskog invariants originated from new CP phases of squarkmass 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)

5. 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

6. 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

7. 3. New Higgs-mediated two loop contribution Effective Higgs coupling induced by radiative corrections to down-quark mass matrix Non-decoupling at the large SUSY particle mass limit Tree level 1-loop level Charged Higgs contribution to EDMs

8. 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 decoupledfor heavy charged Higgs mass. • It maydominate over 1-loop gluino contributionfor mSUSY> 1-2 TeV.

9. Hadronic EDMs in SUSY GUT models SUSY GUT models Unification of gauge couplings + Unification of (s)quarks and (s)leptons SUSY breaking mass terms of squarks and sleptons are correlated We can investigate SUSY GUT models by considering the correlation between flavor physics in the quark sector and those in the lepton sector. SU(5) GUT with right-handed neutrinos Matter multiplet : LFV、leptonic EDM Left-handed sleptonmixing Neutrino Yukawa coupling Right-handed sdownmixing SΦKs、hadronic EDM

10. Hadronic EDMs vs. LFV processes Non Universal Higgs mass scenario SuperB MEG Deuteron Deuteron Strange quark CEDM (cm) Down quark CEDM (cm) Here, we plot the gluino contribution and the total contribution (gluino + charged Higgs) for quark CEDMs changing MH+ between 200 GeV and 2000 GeV Charged Higgs contributions modify quark (C)EDMs significantly

11. Large tan β Corrections for EDMs Why the Higgs-mediated contribution can become large? • Non-decoupling in the limit of • Slow decoupling in by the logarithm term of the loop function • The effective coupling are induced by tanbeta enhanced corrections How about other contributions? Systematic calculations are needed! Gluino (Leading) Chargino Total Gluino Charged Higgs Chargino Charged Higgs Gluino Total

12. 4. Summary We discussed the flavor induced EDMswith tanbeta enhanced corrections for Yukawa couplings. • We found a charged-Higgs mediated 2-loop contribution to down quark (C)EDMs can become large and it already constrains some parameter spaces in SUSY SMs. • As long as the charged Higgs mass is light, this contribution is not decoupled even if SUSY particles is heavy and can become dominant for mSUSY> 1-2 TeV. • Even if charged Higgs is heavy, (C)EDMs originated from this contribution may be detected in future experiments due to the slow decoupling feature. • For very large tanbeta, various diagrams can become important. We calculated tanbeta enhanced corrections systematically and estimated these contributions.

13. Back Up Slide

14. 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) ]

15. 199Hg EDM ＣＰ violating hadronic interactions Quark CEDM Deuteron EDM Quark EDM Quark EDM Neutron EDM Hadronic EDMs 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

16. Systematic calculation of tan beta enhanced corrections • Write the SU(2)xU(1) invariant lagrangian and relate non-holomorphic Yukawa couplings to the corresponding quark mass corrections. • Diagonalize the quark masses and change to the CKM basis. Then relate the tree-level Yukawa couplings to the quark masses and the CKM matrix. • Putting them back to the original lagrangian then effective couplings are obtained. Calculate as a function of loop factors and mixing parameters can be expressed by and Derive Tree level Yukawa couplings are determined Loop factors