Family Non-universal Z^\prime effects on \bar{B}_q-B_q$ mixing, B\to X_s μ^+μ^- and B_s\to μ^+μ^- Decays

Abstract

Motivated by the large discrepancy of CP-violating phase in $\bar{B}_s-B_s$ mixing between the experimental data and the Standard Model prediction, we pursue possible solutions within a family non-universal $Z^{\prime}$ model. Within such a specific model, we find that both the $\bar{B}_s-B_s$ mixing anomaly and the well-known "$πK$ puzzle" could be moderated simultaneously with a nontrivial new weak phase, $ϕ^L_s\sim-72^{\circ}$ (S1) or $-82^{\circ}$ (S2). With the stringently constrained $Z^{\prime}$ coupling $B_{sb}^{L}$, we then study the $Z^{\prime}$ effects on the rare $B\to X_s μ^+μ^-$ and $B_s\to μ^+μ^-$ decays, which are also induced by the same $b\to s$ transition. The observables of $B\to X_s μ^+μ^-$, at both high and low $q^2$ regions, are found to be able to put strong constraints on the $μ-μ-Z^{\prime}$ coupling, $B_{μμ}^{L,R}\sim10^{-2}$. It is also shown that the combined constraints from $\bar{B}_s-B_s$ mixing, $B\to πK$ and $B\to X_s μ^+μ^-$ do not allow a large $Z^{\prime}$ contribution to the pure leptonic $B_s\toμ^+μ^-$ decay.

29 pages, 10 figs and 6 tables. References and discussions added. To appear in JHEP