Strange processes in general two Higgs doublet model

In the general two Higgs doublet model (g2HDM) that has extra Yukawa couplings, we analyze their New Physics (NP) contributions to kaon mixing parameter $\varepsilon_K$, direct CP violation parameter $\varepsilon^\prime/\varepsilon$, and rare $K^+ \to \pi^+\nu\bar\nu$, $K_L \to \pi^0\nu\bar\nu$, and $K_{L, S} \to \mu^+ \mu^-$ decays. We study correlations between these observables, and call special attention to a unique complementarity of kaon mixing and rare $K\to \pi \nu\bar\nu$ decays in probing the exotic Higgs mass spectrum of g2HDM. The importance of kaon physics in probing NP vis-\`a-vis B physics is stressed. One unexpected feature we uncover is the special sensitivity of $K^+ \to \pi^+\nu\bar\nu$ to TeV scale charged Higgs boson.