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

TL;DR

This paper examines how direct CP violation in charm decays affects the measurement of the unitarity triangle angle gamma from B -> DK decays, proposing conditions for accurate extraction despite CPV.

Contribution

It demonstrates that gamma can be accurately determined even with charm CPV if certain conditions are met and highlights potential shifts when neglecting CPV effects.

Findings

Gamma extraction remains feasible with charm CPV if one D decay has negligible CPV.

Neglecting charm CPV can cause a shift in gamma of order r_D/r_B.

The shift can be significant for B -> Dπ decays, but modest for B -> DK.

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.