Branching fraction measurement of $\bar{B}^0 \to D^{()-} \pi^+$, $B^- \to D^{()^0} \pi^-$ and isospin analysis of $\bar{B} \to D^{()} \pi$ decays

Using 65 million $\Upsilon(4S)\to B\bar{B}$ events collected with the BABAR detector at the PEP-II $e^{+}e^{-}$ storage ring at the Stanford Linear Accelerator Center, we measure the color-favored branching fractions ${\cal B}(\bar{B^{0}} \to D^{+} \pi^{-}) = (2.63 \pm 0.05 \pm 0.22)\times 10^{-3}$, ${\cal B}(\bar{B^{0}} \to D^{*+} \pi^{-}) = (2.79 \pm 0.08 \pm 0.18)\times 10^{-3}$, ${\cal B}(B^{-} \to D^{0} \pi^{-}) = (4.90 \pm 0.07 \pm 0.23)\times 10^{-3}$ and ${\cal B}(B^{-} \to D^{*0} \pi^{-}) = (5.52 \pm 0.17 \pm 0.43)\times 10^{-3}$, where the first error is statistical and the second is systematic. With these results and the current world average for the branching fraction for the color-suppressed decay $\bar{B^{0}} \to D^{(*)0}\pi^{0}$, the cosines of the strong phase difference $\delta$ between the $I=1/2$ and $I=3/2$ isospin amplitudes are determined to be $ \cos \delta = 0.860^{+0.007+0.029}_{-0.006-0.028}$ for the $\bar{B} \to D\pi$ process and $ \cos \delta = 0.917^{+0.018+0.059}_{-0.016-0.051}$ for the $\bar{B} \to D^{*}\pi$ process. The results for $\cos \delta$ suggest that final-state interactions are present in the $D\pi$ system.