Family Non-universal Z^\prime effects on \bar{B}_q-B_q$ mixing, B\to X_s \mu^+\mu^- and B_s\to \mu^+\mu^- 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 "$\pi K$ puzzle" could be moderated simultaneously with a nontrivial new weak phase, ${\varphi }_s^L\sim -72^{\circ }$ (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 $B\to X_s{\mu }^{+}{\mu }^{-}$ and $B_s\to {\mu }^{+}{\mu }^{-}$ decays, which are also induced by the same $b\to s$ transition. The observables of $B\to X_s{\mu }^{+}{\mu }^{-}$, at both high and low $q^2$ regions, are found to be able to put strong constraints on the $\mu -\mu -Z^{\prime }$ coupling, $B_{\mu \mu }^{L,R}\sim 10^{-2}$. It is also shown that the combined constraints from ${\bar{B}}_s-B_s$ mixing, $B\to \pi K$ and $B\to X_s{\mu }^{+}{\mu }^{-}$ do not allow a large $Z^{\prime }$ contribution to the pure leptonic $B_s\to {\mu }^{+}{\mu }^{-}$ decay.

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