Constraints on Dark Photon and Dark $Z$ Model Parameters in the $B$ and $K$ Meson Decays

Abstract

The study investigates flavor-changing neutral current (FCNC) decays of $B$ and $K$ mesons in the context of a dark $U(1{)}_D$ model with a dark photon/dark $Z$ mass between 10 MeV and 2 GeV. While the model improves the fit to certain decay distributions, such as $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B_s\to \varphi {\mu }^{+}{\mu }^{-}$, it is ruled out by stringent experimental constraints, including atomic parity violation, $K^{+}\to {\mu }^{+}+\text{invisible}$, and $B_s-{\overline{B}}_s$ mixing. To address these constraints, the model is extended with three modifications; allowing additional invisible decays of $Z_D$, introducing a direct vector coupling of $Z_D$ to muons, and including a direct coupling of $Z_D$ to both muons and electrons, with fine-tuning to cancel the mixing-induced coupling to electrons. Among these extensions, only the third scenario, involving fine-tuned electron coupling, remains consistent with all experimental constraints.

Comments: 17 pages, 1 table, 14 figures