Sensitivity of the squark flavor mixing to the CP violation of K, B0 and Bs mesons

Abstract

We study the sensitivity of the squark flavor mixing to the CP violating phenomena of $K$, $B^0$ and $B_s$ mesons in the framework of the split-family scenario, where the first and second family squarks are very heavy, ${\cal O}(10)$TeV, on the other hand, the third family squark masses are at ${\cal O}(1)$TeV. In order to constrain the gluino-sbottom-quark mixing parameters, we input the experimental data of the CP violations of $K$, $B^0$, and $B_s$ mesons, that is $\epsilon_K$, $\phi_d$, and $\phi_s$. The experimental upper bound of the chromo-EDM of the strange quark is also input. In addition, we take account of the observed values $\Delta M_{B^0}$, $\Delta M_{B_s}$, the CKM mixing $|V_{ub}|$, and the branching ratio of $b\to s\gamma$. The allowed region of the mixing parameters are obtained as $|\delta_{13}^{dL(dR)}|=0\sim 0.01$ and $|\delta_{23}^{dL(dR)}|=0\sim 0.04$. By using these values, the deviations from the SM are estimated in the CP violations of the $B^0$ and $B_s$ decays. The deviation from the SM one is tiny in the CP asymmetries of $B^0\to \phi K_S$ and $B^0\to \eta 'K^0$ due to the chromo-EDM of the strange quark. On the other hand, the CP asymmetries $B_s \to \phi \phi$ and $B_s \to \phi \eta '$ could be largely deviated from the SM predictions. We also predict the time dependent CP asymmetry of $B^0\to K^0\bar K^0$ and the semi-leptonic CP asymmetries of $B^0 \to \mu ^-X$ and $B_s \to \mu ^-X$. We expect those precise measurements at Belle II, which will provide us interesting tests for the squark flavor mixing.