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

Abstract

The LHCb Collaboration has recently reported evidence for a CP asymmetry approaching the percent level in the difference between $D^0\to {\pi }^{+}{\pi }^{-}$ 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 $D^{+}\to K^{+}\text{ok}$ (the most promising channel for which a non-zero CP asymmetry has not yet been reported), as well as $D^0\to {\pi }^0{\pi }^0$, $D_s^{+}\to {\pi }^{+}\text{ko}$, and $D_s\to {\pi }^0{K}^{+}$. No CP asymmetry is predicted for $D^{+}\to {\pi }^{+}{\pi }^0$ or $D^0\to \text{ko}\text{ok}$ in this framework.

Comments: 14 pages, 9 figures, final version to be published in Phys. Rev. D. Some text updated