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

Abstract

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 $\Delta M_s$, ${\varphi }_s$ and $\Delta {\Gamma }_s$ are imposed, the model could not explain the measured flavour-specific CP asymmetry $a_{fs}^s$, at least within its $1\sigma$ ranges. In the second scenario where the NP contributes also to the absorptive part ${\Gamma }_{12}^s$ via tree-level $Z^{\prime }$-induced $b\to c\bar{c}s$ operators, we find that, with the constraints from $\Delta M_s$, ${\varphi }_s$ and the indirect CP asymmetry in ${\bar{B}}_d\to J/\psi K_S$ taken into account, the present measured $1\sigma$ 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.

Comments: 30 pages, 6 figures, 1 table, pdflatex; accepted by JHEP