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

TL;DR

This paper investigates potential direct CP violation in certain charmed meson decays within an extended gauge model, linking it to new physics effects and correlations with kaon decay parameters.

Contribution

It provides a quantitative analysis of direct CP violation in charmed meson decays in an $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ model, highlighting the role of right-handed currents and QCD effects.

Findings

Maximal direct CP violation can be achieved in the studied decays.

A correlation between CP violation in meson decays and $\epsilon'$ in kaon decays is established.

The model predicts observable effects if right-handed gauge bosons are within accessible mass ranges.

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 $D^0\to K^-\pi^+$, $D_s^+\to \eta\pi^+$ and $D_s^+\to \eta'\pi^+$ 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 $\sim(\alpha_s(M_{W_L}^2)/4\pi)\log(M_{W_R}^2/M_{W_L}^2)$. 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 $K\to\pi\pi$ decay parametrized by $\epsilon'$, since $W_R^+$ gauge boson has a sizable impact on the latter.