Rare Kaon Decay to Missing Energy: Implications of the NA62 Result for a $Z^{\prime }$ Model

Abstract

Meson decays offer a good opportunity to probe new physics. The rare kaon decay $K^{+}\to \ddot{I}{€}^{+}\hat{I}½\bar{\hat{I}}½$ is one of the cleanest of them and, for this reason, is rather sensitive to new physics, in particular, vector mediators. NA62 collaboration, running a fixed-target experiment at CERN, recently reported an unprecedented sensitivity to this decay, namely a branching fraction of $BR(K^{+}\to \ddot{I}{€}^{+}\hat{I}½\bar{\hat{I}}½)=(11_{-3.5}^{+4.0})\times 10^{-11}$ at 68\% C.L. Vector mediators that couple to neutrinos may yield a sizeable contribution to this decay. Motivated by the new measurement, we interpret this result in the context of a concrete $Z^{\prime }$ model, and put our findings into perspective with the correlated $K_L\to \ddot{I}{€}^0\hat{I}½\bar{\hat{I}}½$ decay measured by KOTO collaboration, current, and future colliders, namely the High-Luminosity and High-Energy LHC.