Light gauge boson in rare K decay

We study the production of a light gauge boson in K−→π−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→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−→π−X in the W-boson annihilation is suppressed by mX2ϵX⋅pK; however, no such suppression is found via the loop-induced s→dX. The constraints on the relevant couplings are studied.