Kaon processes in general 2HDM

We discuss new physics (NP) contributions to kaon mixing parameter ${\epsilon }_K$, direct CP violation parameter ${\epsilon }^{\mathrm{\prime }}\mathrm{/}\epsilon$ of $K\to \pi \pi$, and rare decays $K^{+}\to {\pi }^{+}\nu \bar{\nu }$, $K_L\to {\pi }^0\nu \bar{\nu }$ and $K_{L,S}\to {\mu }^{+}{\mu }^{-}$ in the context of general two Higgs doublet model. We focus on contributions of top quark related exotic couplings, and show that simultaneous presence of flavor conserving and flavor violating interactions can lead to large NP effects in kaon sector, while being consistent with the stringent constraints from B physics observables such as $B_{s(d)}$-${\bar{B}}_{s(d)}$ mixing, $B_s\to {\mu }^{+}{\mu }^{-}$, and $b\to s\gamma$. We stress on the importance of correlations between ${\epsilon }_K$, $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ and $B_s\to {\mu }^{+}{\mu }^{-}$ that can be exploited to distinguish the parameter space corresponding to a light (sub-TeV) or heavy (TeV) scale charged Higgs boson.