${ϵ}_K^{\mathrm{\prime }}\mathrm{/}{ϵ}_K$ and $K\to \pi \nu \bar{\nu }$ in a two-Higgs doublet model

The Kaon direct CP violation $Re({ϵ}_K^{\mathrm{\prime }}\mathrm{/}{ϵ}_K)$ below the experimental data of a $2\sigma$ in the standard model, which is calculated using the RBC-UKQCD lattice and a large $N_c$ dual QCD, indicates the necessity of a new physics effect. In order to resolve the insufficient $Re({ϵ}_K^{\mathrm{\prime }}\mathrm{/}{ϵ}_K)$, we study the charged-Higgs contributions in a generic two-Higgs-doublet model. If we assume that the origin of the CP-violation phase is uniquely from the Kobayashi-Maskawa (KM) phase when the constraints from the $B$- and $K$-meson mixings, $B\to X_s\gamma$, and Kaon indirect CP violating parameter ${ϵ}_K$ are simultaneously taken into account, it is found that the Kaon direct CP violation through the charged-Higgs effects can reach $Re(\epsilon’K/\epsilon_K){H^\pm}\sim 8 \times 10^{-4}$. Moreover, with the constrained values of the parameters, the branching ratios of the rare $K\to \pi \nu \bar{\nu }$ decays can be $BR(K^+\to \pi^+ \nu \bar\nu)\sim 14 \times 10^{-11}$and$BR(K_L\to \pi^0 \nu \bar\nu)\sim 3.6 \times 10^{-11}$, where the results can be tested through the NA62 experiment at CERN and the KOTO experiment at J-PARC, respectively.