Searching for the squark flavor mixing in CP violations of B_s → K⁺K⁻ and K⁰ K-bar⁰ decays

We study CP violations in the B_s→K⁺K⁻ and B_s→K⁰K-bar⁰ decays in order to find the contribution of the supersymmetry, which comes from the gluino–squark-mediated flavor-changing current. We obtain the allowed region of the squark flavor mixing parameters by putting the experimental data, the mass difference ΔM_Bs, and the CP-violating phase ϕ_s in B_s→J/ψϕ decay and the b→sγ branching ratio. In addition to these data, we take into account the constraint from the asymmetry of B⁰→K⁺π⁻ because the B_s→K⁺K⁻ decay is related to the B⁰→K⁺π⁻ decay by replacing the spectator s with d. Under these constraints, we predict the magnitudes of the CP violation in the B_s→K⁺K⁻ and B_s→K⁰K-bar⁰ decays. The predicted region of the CP violation C_K⁺K⁻ is strongly constrained from the direct CP violation of B-bar⁰→K⁻π⁺; therefore, the deviation from the SM prediction of C_K⁺K⁻ is not found. On the other hand, the CP violation S_K⁺K⁻ may possibly deviate considerably from the SM prediction in the region of 0.1–0.5. Since the standard model predictions of C_K⁰K-bar⁰ and S_K⁰K-bar⁰ are very small, the squark contribution can be detectable in C_K⁰K-bar⁰ and S_K⁰K-bar⁰. These magnitudes are expected in the region C_K⁰K-bar⁰=−0.06–0.06 and S_K⁰K-bar⁰=−0.5–0.3. More precise data of these CP violations provide us with a crucial test for the gluino–squark-mediated flavor-changing current