New rare meson decay constraints on a light vector in $U(1)_{B-L}, U(1)_R$ and the dark photon

TL;DR

This work constrains a light vector boson $X$ arising from anomaly-free $U(1)$ extensions by computing one-loop induced flavor-changing couplings that mediate $B^- o K^- X$ and $K^- o \pi^- X$, followed by on-shell $X$ decays to SM fermions. The analysis covers three benchmark models—dark photon, minimal $U(1)_{B-L}$, and minimal $U(1)_R$—and uses precise form-factor descriptions and CKM-structured loop amplitudes to derive bounds from existing $B$ and $K$ decay data, including a prompt-decay requirement for $X$. A key feature is the longitudinal enhancement of the $X$ width for light $m_X$, which strengthens the bounds in the resonant region (notably around $m_X\sim 2\,\text{GeV}$ for the dark photon) and makes $K^+\to\pi^+ X$ particularly constraining in the $U(1)_{B-L}$ scenario. Overall, the rare meson decays probe parameter regions beyond direct searches, and future experiments such as FASER2 can further test these light-vector scenarios.

Abstract

We evaluate constraints from flavor changing rare meson decays to a light vector boson $X$, followed by the decay of the on-shell $X$ into the SM fermions. The flavor changing meson decay emitting the light $X$ is induced by loop processes where the up-type quarks, the $W$ boson, or charged scalar bosons are running inside loops. We calculate all one-loop diagrams with neglecting all masses of light quarks except for the top quark in a general anomaly free extra $U(1)$ model. Our theoretical evaluation of the branching ratio of charged $B$ meson decay and charged kaon decay is compared to experimental results, and we derive new constraints for dark photon, $U(1)_{B-L}$ and $U(1)_R$ models.

Figures (6)

• Figure 1: $\mathrm{Br}(X \rightarrow \ell^-\ell^+)$ (purple curve) and $\mathrm{Br}(X \rightarrow \nu\bar{\nu})$ (brown curve) for $x_H=0$ as a function of $m_X$.
• Figure 4: The constrained region by $B\rightarrow KX$ followed by $X\rightarrow \ell^+\ell^-$ is indicated by shading with blue. The other shaded regions are excluded by various beam dump, fixed target and collider experiments, and SN1987A. The future prospect for the FASER2 experiment is indicated by the red dashed curve.
• Figure 5: Constraints for the minimal $U(1)_{B-L}$ with $\epsilon =0$. The color code is the same as in Fig. \ref{['Fig:DarkPhoton']}.
• Figure 6: Constraints for the minimal $U(1)_R$ with $\epsilon =0$. The color code is the same as in Fig. \ref{['Fig:DarkPhoton']}.
• Figure : Vertex correction diagrams induce $d_i \rightarrow d_j X$.