$D-\overline{D}$ mixing is the source of the largest theoretical uncertainty in the extraction of $\gamma$ from $B\to DK$ 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 $D-\overline{D}$ mixing leads to an error in the determination of $\gamma$ only at second order in the small parameters $\Delta m_D/{\Gamma }_D$ and $\Delta {\Gamma }_D/{\Gamma }_D$ and is therefore very small and can be safely neglected.

• Received 13 June 2005

DOI:https://doi.org/10.1103/PhysRevD.72.031501