Strange processes in general two Higgs doublet model

Abstract: 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.