The Effect of $D-\bar D$ Mixing on the Measurement of $γ$ in $B\to D K$ Decays

Abstract

$D-\bar D$ mixing is the source of the largest theoretical uncertainty in the extraction of $γ$ from $B\to D K$ 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 $γ$ only at second order in the small parameters, $Δm_D/Γ_D$ and $ΔΓ_D/Γ_D$, and is therefore very small and can be safely neglected.