Estimating $r_B^{D\ddot{I}€}$ as an input to the determination of the CKM angle ${\hat{I}}^3$

Abstract

The interference between Cabibbo-favoured and Cabibbo-suppressed $B\to D\ddot{I}€$ decay amplitudes provides sensitivity to the CKM angle ${\hat{I}}^3$. The relative size of the interfering amplitudes is an important ingredient in the determination of ${\hat{I}}^3$. Using branching fractions from various $B\to Dh$ decays, and the measured value for $r_B^{DK}$, the magnitude of the amplitude ratio of $B^{+}\to D^0\ddot{I}{€}^{+}$ and $B^{+}\to {\bar{D}}^0\ddot{I}{€}^{+}$ decays is estimated to be $r_B^{D\ddot{I}€}=0.0053\pm 0.0007$.

4 pages, 4 figures