Triangle relation of dark matter, electric dipole moment, andCPviolation inB0mixing in a supersymmetricQ6model

Abstract

We consider a recently proposed supersymmetric model based on the discrete ${Q}_{6}$ family group. Because of the family symmetry and spontaneous $CP$ violation, the electric dipole moment, the $CP$ violation in the mixing of the neutral mesons, and the dark matter mass ${m}_{\mathrm{DM}}$ are closely related. This triangle relation is controlled by the size of the $\ensuremath{\mu}$ parameters. Loop effects can give rise to large contributions to the soft mass insertions, and we find that the model allows a large $CP$ violation in the ${B}^{0}$ system. Its size is comparable with the recent experimental observations by D0 and CDF, and it could be observed at the LHCb in the first years. If the parameter space is constrained by the neutron electric dipole moment, flavor changing neutral currents, and $CP$ violations in ${K}^{0}$ as well as ${B}^{0}$ mixing, the triangle relation yields the following bound on the dark matter candidate: $0.12\text{ }\text{ }\mathrm{TeV}<{m}_{\mathrm{DM}}<0.33\text{ }\text{ }\mathrm{TeV}$, which is directly observable at the LHC. We also compute ${a}_{sl}^{s}\ensuremath{-}{a}_{sl}^{d}$, which is observable at the LHCb, where ${a}_{sl}^{s(d)}$ is the semileptonic $CP$ asymmetry for the ${B}_{s(d)}$ system.