Direct CP Violation in Cabibbo-Favored Charmed Meson Decays and ${ϵ}^{\mathrm{\prime }}\mathrm{/}ϵ$ in $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ Model

Since the standard model contribution is virtually absent, any observation of direct CP violation in the Cabibbo-favored charmed meson decays would be evidence of new physics. In this paper, we conduct a quantitative study on direct CP violation in $D^0\to K^{-}{\pi }^{+}$, $D_s^{+}\to \eta {\pi }^{+}$ and $D_s^+\to \eta’\pi^+$decaysinthe$SU(2)_L\times SU(2)R\times U(1){B-L}$ gauge extension of the standard model. In the model, direct CP violation arises mainly from the interference between the decay amplitude coming from the SM left-left current operators and that from the right-right current operators induced by $W_R^{+}$ gauge boson exchange. Interestingly, the strong phase between the two amplitudes is evaluable, since it stems from difference in QCD corrections to the left-left and right-right current operators, which is a short-distance QCD effect given by $\sim ({\alpha }_s(M_{W_L}^2)\mathrm{/}4\pi )\log (M_{W_R}^2\mathrm{/}{M}_{W_L}^2)$. We assess the maximal direct CP violation in the above decays in the $SU(2)_L\times SU(2)R\times U(1){B-L}$ model. Additionally, we present a correlation between direct CP violation in these modes and one in $K\to \pi \pi$ decay parametrized by ${ϵ}^{\mathrm{\prime }}$, since $W_R^{+}$ gauge boson has a sizable impact on the latter.