# 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

## TL;DR

This paper investigates how a family non-universal Z' model can simultaneously address anomalies in B_s mixing and B to pi K puzzles, while constraining Z' effects on rare B decays with experimental data.

## Contribution

It demonstrates that a specific Z' model with a nontrivial weak phase can resolve multiple B physics anomalies and provides constraints on Z'-mediated processes from various decay measurements.

## Key findings

- Z' model can moderate B_s mixing and pi K puzzle anomalies.
- Strong constraints on Z'-muon couplings from B to X_s mu+ mu- decays.
- Large Z' contributions to B_s to mu+ mu- decay are not supported by combined data.

## 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, $\phi^L_s\sim-72^{\circ}$ (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 $B\to X_s \mu^+\mu^-$ 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, $B_{\mu\mu}^{L,R}\sim10^{-2}$. 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.