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The charged Kaon meson ($K^+$) features several hadronic decay modes, but themost relevant contribution to its decay width stems from the leptonic decay$K^+ \rightarrow \mu^+ \nu_\mu $. Given the precision acquired on the raredecay mode $K^+ \rightarrow \mu^+ \nu_\mu + X$, one can use the data to setconstraints on sub-GeV hidden sectors featuring light species that couldcontribute to it. Light gauge bosons that couple to muons could give rise tosizeable 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 HiggsDoublet Models (2HDM) augmented by an Abelian gauge symmetry, 2HDM-$U(1)_X$. Weput our findings into perpective with collider bounds, atomic parity violation,neutrino-electron scattering, and polarized electron scattering probes to showthat rare Kaon decays provide competitive bounds in the sub-GeV mass range fordifferent values of $\tan\beta$.

Constraints on Hidden Sectors Using Rare Kaon Decays