Effect of D − D ¯ mixing on the measurement of γ in B → D K decays

$D\ensuremath{-}\overline{D}$ mixing is the source of the largest theoretical uncertainty in the extraction of $\ensuremath{\gamma}$ from $B\ensuremath{\rightarrow}DK$ decays. In the standard model, the mixing can have a rate close to its current experimental upper bound and is $CP$ conserving to an excellent approximation. We show that neglecting $CP$-conserving $D\ensuremath{-}\overline{D}$ mixing leads to an error in the determination of $\ensuremath{\gamma}$ only at second order in the small parameters $\ensuremath{\Delta}{m}_{D}/{\ensuremath{\Gamma}}_{D}$ and $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{D}/{\ensuremath{\Gamma}}_{D}$ and is therefore very small and can be safely neglected.