CPasymmetries in singly-Cabibbo-suppressedDdecays to two pseudoscalar mesons

Abstract

The LHCb Collaboration has recently reported evidence for a $CP$ asymmetry approaching the percent level in the difference between ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$. We analyze this effect as if it is due to a penguin amplitude with the weak phase of the standard model $c\ensuremath{\rightarrow}b\ensuremath{\rightarrow}u$ loop diagram, but with a $CP$-conserving enhancement as if due to the strong interactions. In such a case the magnitude and strong phase of this amplitude ${P}_{b}$ are correlated in order to fit the observed $CP$ asymmetry, and one may predict $CP$ asymmetries for a number of other singly-Cabibbo-suppressed decays of charmed mesons to a pair of pseudoscalar mesons. Nonzero $CP$ asymmetries are expected for ${D}^{+}\ensuremath{\rightarrow}{K}^{+}{\overline{K}}^{0}$ (the most promising channel for which a nonzero $CP$ asymmetry has not yet been reported), as well as ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}^{0}$, and ${D}_{s}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{K}^{+}$. No $CP$ asymmetry is predicted for ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ or ${D}^{0}\ensuremath{\rightarrow}{K}^{0}{\overline{K}}^{0}$ in this framework.