Light gauge boson in rare $K$ decay

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 $m_X^2{ϵ}_X\cdot p_K$; however, no such suppression is found via the loop-induced $s\to dX$. The constraints on the relevant couplings are studied.

Comments: 10 pages, 4 figures, version accepted for publication in Physics Letters B