Effects of supersymmetric CP violating phases on B → X s l + l − and ǫ

We consider effects of CP violating phases in μ and At parameters in the effective supersymmetric standard model on B → Xsll and ǫK . Scanning over the MSSM parameter space with experimental constraints including edm constraints from Chang-Keung-Pilaftsis (CKP) mechanism, we find that the Br(B → Xsll) can be enhanced by upto ∼ 85% compared to the standard model (SM) prediction, and its correlation with Br(B → Xsγ) is distinctly different from the minimal supergravity scenario. Also we find 1 ∼ ǫK/ǫ K ∼ 1.4, and fully supersymmetric CP violation in KL → ππ is not possible. Namely, |ǫSUSY K | ∼ O(10−5) if the phases of μ and At are the sole origin of CP violation. [email protected] [email protected] 1 1. In the minimal supersymmetric standard model (MSSM), there can be many new CP violating (CPV) phases beyond the KM phase in the standard model (SM) both in the flavor conserving and flavor violating sectors. The flavor conserving CPV phases in the MSSM are strongly constrained by electron/neutron electric dipole moment (edm) and believed to be very small (δ < ∼ 10 for MSUSY ∼ O(100) GeV ) [1]. Or, one can imagine that the 1st/2nd generation scalar fermions are very heavy so that edm constraints are evaded via decoupling even for CPV phases of order O(1) [2]. Also it is possible that various contributions to electron/neutron EDM cancel with each other in substantial parts of the MSSM parameter space even if SUSY CPV phases are ∼ O(1) and SUSY particles are relatively light [3] [4]. In the last two cases where SUSY CPV phases are of ∼ O(1), these phases may affect B and K physics in various manners. In the previous letter [5], we presented effects of these SUSY CPV phases on B physics : the B − B0 mixing and the direct asymmetry in B → Xsγ, assuming that EDM constraints and SUSY FCNC problems are evaded by heavy 1st/2nd generation scalar fermions. In this letter, we extend our previous work to B → Xsll and ǫK (see also Ref. [6].) within the same assumptions. An important ingredient for large tanβ in our model is the constraint on the μ and At phases coming from electron/neutron edm’s through Chang-Keung-Pilaftsis (CKP) mechanism [7]. Two loop diagrams with CP-odd higgs and photon (gluon) exchanges between the fermion line and the sfermion loop (mainly stops and sbottoms) can contribute significantly to electron/neutron edm’s in the large tanβ region. The authors of Ref. [7] find that ( df e )CKP = Qf 3αem 64π2 Rf mf M A ∑