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

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

3.  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 also flavor structures. What can we probe by EDMs in supersymmetric SMs?  F term SUSY breaking terms : complex in general These phases may be suppressed by some SUSY breaking & mediation mechanisms. strongly constrained by EDM experiments

4. at 3 loop level 2. Flavor induced EDM CP violating Dim-5 operators Quark EDMQuark CEDM CP violating effects can be estimated by basis-independent measure of CP violation, Jarlskog invariants. 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. The Standard Model Supersymmetric standard models 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) The Standard Model

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

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

7. 3. New Higgs-mediated two loop contribution Charged Higgs contribution to EDMs Effective Higgs coupling induced by radiative corrections to down-quark mass matrix Non-decoupling at the large SUSY particle mass limit Tree level1-loop level

8. Features of the higgs-mediated two loop contribution down quark (C)EDM: d d /e ( d c d ) [cm] 20010002000 Charged Higgs mass: M H + [GeV] 10 -1 1 10 100 10 -26 10 -27 10 -25 5001500 1000 2000 3000 40005000 Ratio of 1 and 2-loop contribution: d d (Higgs) / d d (gluino) SUSY particle mass: m SUSY [GeV] tanβ= 10 M H + = 300 GeV (δ LL ) 13 = (0.22) 3 (δ RR ) 31 = (0.22) 3  It is slowly decoupled for heavy charged Higgs mass.  It may dominate over 1-loop gluino contribution for m SUSY > 1-2 TeV.

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

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

11.  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 Why the Higgs-mediated contribution can become large? Large tan β Corrections for EDMs How about other contributions? Systematic calculations are needed! Charged Higgs Chargino Gluino Total Gluino Charged Higgs Chargino Gluino (Leading)

12. We discussed the flavor induced EDMs with tanbeta enhanced corrections for Yukawa couplings. 4. Summary  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 m SUSY > 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. Hadronic EDMs CP violating Dim-5 operator quark EDMquark CEDM Although there can be large hadronic uncertainty, it can be estimated as [Hisano & Shimizu (2004) ] Present experimental bounds 199 Hg EDM Neutron EDM Deuteron EDM ＣＰ violating hadronic interactions Quark CEDM Quark EDM

16. 1.Write the SU(2)xU(1) invariant lagrangian and relate non-holomorphic Yukawa couplings to the corresponding quark mass corrections. 2.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. 3.Putting them back to the original lagrangian then effective couplings are obtained. Systematic calculation of tan beta enhanced corrections Calculate as a function of loop factors and mixing parameters Derive Tree level Yukawa couplings are determined can be expressed by and Loop factors