Probe a family non-universal Z' boson effects in B(s)-> phi mu(+) mu(-)decay

Motivated by the recent measurement on ${\cal B}(\bar{B}_s\to \phi \mu^+\mu^-)$ by CDF collaboration, we study the effects of a family non-universal $Z^{\prime}$ boson on rare semileptonic $\bar{B}_s \to \phi\mu^+\mu^-$ decay. In our evaluations, we analyze the dependences of the dimuon invariant mass spectrum and normalized forward-backward asymmetry on $Z^{\prime}$ couplings and show that these observables are highly sensitive to new $Z^{\prime}$ contributions. Three limiting scenarios are presented in the detailed analyses. Numerically, within the allowed ranges of $Z^{\prime}$ couplings under the constraints from $\bar{B}_s-B_s$ mixing, $B\to\pi K$, $\bar{B}_d\to(X_s,K,K^{\ast})\mu^+\mu^-$ decays and so on, ${\cal B}(\bar{B}_s\to \phi \mu^+\mu^-)$ and $A_{FB}^{(L)}(\bar{B}_s\to \phi \mu^+\mu^-)$ could be enhanced by about 96% and $17%\,(133%)$ respectively at most by $Z^{\prime}$ contributions. However, ${\cal B}(\bar{B}_s\to \phi \mu^+\mu^-)$ is hardly to be reduced. Furthermore, the zero crossing in $A_{FB}(\bar{B}_s\to \phi \mu^+\mu^-)$ spectrum at low dimuon mass always exists.