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$B_s^0-\bar B_s^0$ mixing in a family non-universal $Z^{\prime}$ model revisited

Motivated by the very recent measurements performed at the LHCb and the Tevatron of the $B_s^0-\bar B_s^0$ mixing, in this paper we revisit it in a family non-universal $Z^{\prime}$ model, to check if a simultaneous explanation for all the mixing observables, especially for the like-sign dimuon charge asymmetry observed by the D0 collaboration, could be made in such a specific model. In the first scenario where the $Z^\prime$ boson contributes only to the off-diagonal element $M_{12}^s$, it is found that, once the combined constraints from $ΔM_s$, $ϕ_s$ and $ΔΓ_s$ are imposed, the model could not explain the measured flavour-specific CP asymmetry $a_{fs}^s$, at least within its $1σ$ ranges. In the second scenario where the NP contributes also to the absorptive part $Γ_{12}^s$ via tree-level $Z^\prime$-induced $b\to c\bar{c}s$ operators, we find that, with the constraints from $ΔM_s$, $ϕ_s$ and the indirect CP asymmetry in $\bar{B}_d\to J/ψK_S$ taken into account, the present measured $1σ$ experimental ranges for $a_{fs}^s$ could not be reproduced too. Thus, such a specific $Z^\prime$ model with our specific assumptions could not simultaneously reconcile all the present data on $B_s^0-\bar B_s^0$ mixing. Future improved measurements from the LHCb and the proposed superB experiments, especially of the flavour-specific CP asymmetries, are expected to shed light on the issue.