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

A difference of several tenths of a percent has been observed between the direct CP asymmetries of $D^0\to K^+K^-$ and $D^0\to π^+π^-$. It has been noted recently that CP asymmetries in such singly-Cabibbo-suppressed (SCS) decays can affect the determination of the weak phase $γ$ 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 $\od$ 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 $γ$ of several degrees and pinpoint measurements which would reduce uncertainties to an acceptable level.