The Effect of $D-\bar{D}$ Mixing on the Measurement of $\gamma$ in $B\to DK$ Decays

Abstract

$D-\bar{D}$ 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 $D-\bar{D}$ 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.

8 pages, no figures