Effect of D-Dbar mixing in the extraction of gamma with B- -> D0 K- and B- -> D0 pi- decays
We examine the impact of D-Dbar mixing in the extraction of the angle gamma of the unitarity triangle with B- ->D(*)K(*)- and B- ->D(*)pi- decays. We point out that the leading corrections, linear in the small mixing parameters x=Delta m/Gamma and y=Delta Gamma/2Gamma, depend on how the signal selection efficiency varies as a function of the D proper time, and we estimate the scale factor in a simplified case. We note that the charm mixing effect is suppressed in the GLW method. We discuss the case where the leading corrections become quadratic in x and y, and we point out some limitations of this scenario. We compute the bias Delta_gamma when D-Dbar mixing is ignored in the rates of B- ->D(*)K(*)- but not in the measurement of the D decay parameters. We find |Delta_gamma|<~1 deg for all B- ->D(*)K(*)- decays, limited by the measured value of the strong phase difference between the b-> u cbar s and b->c ubar s decay amplitudes. The effect in B- ->D(*)pi- decays cannot be neglected.