Estimating $r_{B}^{Dπ}$ as an input to the determination of the CKM angle $γ$

The interference between Cabibbo-favoured and Cabibbo-suppressed $B\to Dπ$ decay amplitudes provides sensitivity to the CKM angle $γ$. The relative size of the interfering amplitudes is an important ingredient in the determination of $γ$. Using branching fractions from various $B\to Dh$ decays, and the measured value for $r_{B}^{DK}$, the magnitude of the amplitude ratio of $B^+\to D^0π^+$ and $B^+\to \bar{D}^0π^+$ decays is estimated to be $r_{B}^{Dπ} = 0.0053 \pm 0.0007$.

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