CP violations in Kaons: precision tests of $\varepsilon_K$

We review recent progress in determining $\varepsilon_K$ in lattice QCD. We find that the SM evaluation of $\varepsilon_K$ with lattice QCD inputs is 3.4 sigma away from the experiment. In order to clarify this issue, we need to reduce the error in $V_{cb}$. We explain our efforts to calculate $V_{cb}$ using the OK action formulation of heavy quarks. In order to explain the gap of 3.4 sigma, we also calculate the BSM B-parameters. We present the results and compare them with those of RBC-UKQCD and ETM.