Light gauge boson in rare $K$ decay

TL;DR

This paper investigates the production mechanisms and constraints of a light gauge boson in rare kaon decay processes, highlighting differences between tree-level and loop-induced contributions.

Contribution

It provides a detailed analysis of how a light gauge boson can be produced in $K^- o \pi^- X$ decay, emphasizing the role of non-conserved charge currents and the dependence on gauge couplings.

Findings

Tree-level $W$-boson annihilation can produce the gauge boson.

Loop-induced $s o dX$ process is not suppressed by $m_X^2$.

Constraints on gauge couplings are derived.

Abstract

We study the production of a light gauge boson in $K^- \to \pi^- X$ decay, where the associated new charge current is not conserved. It is found that the process can be generated by the tree-level $W$-boson annihilation and loop-induced $s\to dX$. We find that it strongly depends on the $SU(3)$ limit or the unique gauge coupling to the quarks, whether the decay amplitude of $K^-\to \pi^- X$ in the $W$-boson annihilation is suppressed by $m^2_X \epsilon_X \cdot p_K$; however, no such suppression is found via the loop-induced $s\to d X$. The constraints on the relevant couplings are studied.