$CP$ asymmetries in singly-Cabibbo-suppressed $D$ decays to two pseudoscalar mesons

$C P$ asymmetries in singly-Cabibbo-suppressed $D$ decays to two pseudoscalar mesons

Bhubanjyoti Bhattacharya, Michael Gronau, and Jonathan L. Rosner

Phys. Rev. D 85, 054014 – Published 20 March 2012; Erratum Phys. Rev. D 85, 079901 (2012)

Abstract

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