Impact of family-non-universal $$Z^\prime $$ Z ′ boson on pure annihilation $$B_s \rightarrow \pi ^+ \pi ^-$$ B s → π + π - and $$B_d \rightarrow K^+ K^-$$ B d → K + K - decays

Abstract

We study the $$B_s \rightarrow \pi ^+ \pi ^-$$ and $$B_d \rightarrow K^+ K^-$$ decays in the standard model and the family-non-universal $$Z^\prime $$ model. Since none of the quarks in the final states is the same as the initial quark, these decay modes can occur only via power-suppressed annihilation diagrams. Despite the consistency of the standard model prediction with the available data, room remains for a light $$Z^\prime $$ boson. Taking into account the $$Z^\prime $$ contribution, we find that theoretical results for the 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 $$B_d \rightarrow K^+ K^-$$ , 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 the data. The measurements at future experimental facilities, including the LHCb, Belle-II, and the proposed high energy $$e^+e^-$$ collider, will provide us useful hints for direct searching for the light $$Z^\prime $$ boson.