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 $Z^{\mathrm{\prime }}$ 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 $Z^{\mathrm{\prime }}$ couplings and show that these observables are highly sensitive to new $Z^{\mathrm{\prime }}$ contributions. Three limiting scenarios are presented in the detailed analyses. Numerically, within the allowed ranges of $Z^{\mathrm{\prime }}$ 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$A{FB}^{(L)}(\bar{B}_s\to \phi \mu^+\mu^-)$couldbeenhancedbyabout96$17%,(133%)$ respectively at most by $Z^{\mathrm{\prime }}$ contributions. However, ${\cal B}(\bar{B}s\to \phi \mu^+\mu^-)$ishardlytobereduced\mathrm{.}Furthermore,thezerocrossingin$A{FB}(\bar{B}_s\to \phi \mu^+\mu^-)$ spectrum at low dimuon mass always exists.