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

Abstract

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 $D^0\to K^-π^+$, $D_s^+\to ηπ^+$ and $D_s^+\to η'π^+$ decays in the $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ 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 $\sim(α_s(M_{W_L}^2)/4π)\log(M_{W_R}^2/M_{W_L}^2)$. 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 $K\toππ$ decay parametrized by $ε'$, since $W_R^+$ gauge boson has a sizable impact on the latter.

18 pages, 2 tables and 3 figures; v3: Discussion on the effect of $SU(3)$ flavor symmetry breaking is added