(K^0-\bar{K}^0\) mixing in the minimal flavor-violating two-Higgs-doublet models

The two-Higgs-doublet model (2HDM), as one of the simplest extensions of the Standard Model (SM), is obtained by adding another scalar doublet to the SM, and is featured by a pair of charged scalars, which could affect many low-energy processes. In the "Higgs basis" for a generic 2HDM, only one scalar doublet gets a nonzero vacuum expectation value and, under the criterion of minimal flavor violation, the other one is fixed to be either color-singlet or color-octet, which are named as the type-III and the type-C 2HDM, respectively. In this paper, we study the charged-scalar effects of these two models on the \(K^0-\bar{K}^0\) mixing, an ideal process to probe New Physics (NP) beyond the SM. Firstly, we perform a complete one-loop computation of the box diagrams relevant to the \(K^0-\bar{K}^0\) mixing, keeping the mass and momentum of the external strange quark up to the second order. Together with the up-to-date theoretical inputs, we then give a detailed phenomenological analysis, in the cases of both real and complex Yukawa couplings of the charged scalars to quarks. The parameter spaces allowed by the current experimental data on the mass difference \(\Delta m_K\) and the CP-violating parameter \(\epsilon_K\) are obtained and the differences between these two 2HDMs are investigated, which are helpful to distinguish them from each other from a phenomenological point of view.