B^\pm -> D K^\pm with direct CP violation in charm

Abstract

We investigate the implications of direct CP violation (CPV) on the determination of the unitarity triangle angle \gamma\ from B -> DK decays. We show that \gamma\ can still be extracted even with the inclusion of direct CPV in charm if (i) at least one of the D decays has negligible CP violation; and (ii) data from charm factory at threshold are used. If approximate expressions without including direct CP violation in charm are used, this can result in a shift in \gamma\ that is O(r_D/r_B). It is modest for B -> DK but can be O(1) for B -> D\pi. We illustrate the size of the shift on an example of Gronau-London-Wyler method.