Shift in weak phase $\gamma$ due to CP asymmetries in $D$ decays to two pseudoscalar mesons

Abstract

A difference of several tenths of a percent has been observed between the direct CP asymmetries of $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$. It has been noted recently that CP asymmetries in such singly-Cabibbo-suppressed (SCS) decays can affect the determination of the weak phase $\gamma$ using the Gronau-London-Wyler method of comparing rates for $B^{+}\to D{K}^{+}$ and $B^{-}\to D{K}^{-}$, where $D$ is a superposition of $D^0$ and $\text{od}$ decaying to a CP eigenstate. Using an analysis of the CP asymmetries in SCS decays based on a $c\to u$ penguin amplitude with standard model weak phase but enhanced by CP-conserving strong interactions, we estimate typical shifts in $\gamma$ of several degrees and pinpoint measurements which would reduce uncertainties to an acceptable level.

Comments: 15 pages, 3 figures, submitted to Phys. Rev. D. More text and references added