Re(ϵ′ K/ϵK) and $$ K\to \pi \nu \overline{\nu} $$ in a two-Higgs doublet model

Abstract

Abstract The Kaon direct CP violation Re(ϵ K ′ /ϵ K ) below the experimental data of a 2σ 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 ′ /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 → X s γ, 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(ϵ K ′ /ϵ K ) H  ± ∼ 8 × 10− 4. Moreover, with the constrained values of the parameters, the branching ratios of the rare $$ K\to \pi \nu \overline{\nu} $$ K → π ν ν ¯ decays can be $$ BR\left({K}^{+}\to\ {\pi}^{+}\nu \overline{\nu}\right)\sim 13 \times 1{0}^{-11} $$ B R K + → π + ν ν ¯ ∼ 13 × 1 0 − 11 and $$ BR\left({K}_L\to {\pi}^0\nu \overline{\nu}\right)\sim 3.6\times 1{0}^{-11} $$ B R K L → π 0 ν ν ¯ ∼ 3.6 × 1 0 − 11 , where the results can be tested through the NA62 experiment at CERN and the KOTO experiment at J-PARC, respectively.