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

The LHCb Collaboration has recently reported evidence for a CP 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 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. Non-zero CP asymmetries are expected for $D^+ \to K^+ \ok$ (the most promising channel for which a non-zero CP asymmetry has not yet been reported), as well as $D^0 \to π^0 π^0$, $D_s^+ \to π^+ \ko$, and $D_s \to π^0 K^+$. No CP asymmetry is predicted for $D^+ \to π^+ π^0$ or $D^0 \to \ko \ok$ in this framework.

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