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

TL;DR

This paper investigates how a family non-universal $Z'$ boson could influence rare $B$ meson decays, showing it can improve data agreement and constrain new physics parameters, with implications for future experiments.

Contribution

It introduces the effects of a light $Z'$ boson on rare $B$ decay modes, providing improved theoretical predictions and constraints based on current data.

Findings

$Z'$ contribution improves fit to decay data.

Constraints on $Z'$ couplings derived from decay measurements.

Future experiments can test $Z'$ effects through CP asymmetries.

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.