Shift in weak phase $\gamma$ 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 $D^0\to {\pi }^{+}{\pi }^{-}$. 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$D$isasuperpositionof$D^0$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 $\gamma$ of several degrees and pinpoint measurements which would reduce uncertainties to an acceptable level.