Kaon processes in general 2HDM

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