Impact of Family Non-universal $Z^{\prime }$ Boson on Pure Annihilation $B_s\to {\pi }^{+}{\pi }^{-}$ and $B_d\to K^{+}{K}^{-}$ Decays

Abstract

We study the $B_s\to {\pi }^{+}{\pi }^{-}$ and $B_d\to K^{+}{K}^{-}$ decays in the standard model and the family non-universal $Z^{\prime }$ model. Since none of the quarks in final states is the same as the initial quark, these decay modes can occur only via power-suppressed annihilation diagrams. Despite the consistence of the standard model prediction with the available data, there is a surviving room for a light $Z^{\prime }$ boson. Taking into account the $Z^{\prime }$ contribution, we find theoretical results for branching fractions can better accommodate the data. With the relevant data, we also derive a constraint on the parameter space for the $Z^{\prime }$. Moreover, for the $B_d\to K^{+}{K}^{-}$, both the direct and the mixing-induced $CP$ asymmetry are sensitive to the couplings between $Z^{\prime }$ and fermions in the parameter spaces constrained by data. The measurements at future experimental facilities, including the LHC-b, Belle-II and the proposed high energy $e^{+}{e}^{-}$ collider, will provide us useful hints for direct searching for the light $Z^{\prime }$ boson.

10 pages, 7 figures