Effect of D-Dbar mixing in the extraction of gamma with B- -> D0 K- and B- -> D0 pi- decays

Abstract

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.

References in corpus (8)

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• Measurement of the CKM angle gamma from a combination of B->Dh analyses
• A model-independent Dalitz plot analysis of $B^{\pm }\to D{K}^{\pm }$ with $D\to K_{\mathrm{S}}^0{h}^{+}{h}^{-}$ ($h=\pi ,K$) decays and constraints on the CKM angle $\gamma$
• Observation of the suppressed ADS modes $B^{\pm }\to [{\pi }^{\pm }{K}^{\mp }{\pi }^{+}{\pi }^{-}{]}_D{K}^{\pm }$ and $B^{\pm }\to [{\pi }^{\pm }{K}^{\mp }{\pi }^{+}{\pi }^{-}{]}_D{\pi }^{\pm }$
• Determining the unitarity triangle angle $\gamma$ with a four-body amplitude analysis of ${\mathrm{B}}^{\pm }\to ({\mathrm{K}}^{+}{\mathrm{K}}^{-}{\pi }^{+}{\pi }^{-}{)}_{\mathrm{D}}{\mathrm{K}}^{\pm }$ decays
• Search for b --> u Transitions in B^{+-} --> [K^{-+} pi^{+-} pi0]_D K^{+-} Decays
• CP violation effects on the measurement of $\gamma$ from $B\to DK$
• Shift in weak phase $\gamma$ due to CP asymmetries in $D$ decays to two pseudoscalar mesons

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