Constraints on Hidden Sectors Using Rare Kaon Decays

The charged Kaon meson ($K^+$) features several hadronic decay modes, but the most relevant contribution to its decay width stems from the leptonic decay $K^+ \rightarrow \mu^+ \nu_\mu$. Given the precision acquired on the rare decay mode $K^+ \rightarrow \mu^+ \nu_\mu + X$, one can use the data to set constraints on sub-GeV hidden sectors featuring light species that could contribute to it. Light gauge bosons that couple to muons could give rise to sizeable contributions. In this work, we will use data from the $K^+ \rightarrow \mu^+\nu_{\mu} l^+l^-$, and $K^+ \rightarrow \mu^+ \nu_{\mu} \nu \bar{\nu}$ decays to place limits on light vector bosons present in Two Higgs Doublet Models (2HDM) augmented by an Abelian gauge symmetry, 2HDM-$U(1)_X$. We put our findings into perpective with collider bounds, atomic parity violation, neutrino-electron scattering, and polarized electron scattering probes to show that rare Kaon decays provide competitive bounds in the sub-GeV mass range for different values of $\tan\beta$.