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Branching fraction measurement of B0 --> D(*)- pi+, B- --> D(*)0 pi- and isospin analysis of B --> D(*) pi decays

Using 65 million $Υ(4S)\to B\bar{B}$ 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 ${\cal B}(\bar{B^{0}} \to D^{+} π^{-}) = (2.55 \pm 0.05 \pm 0.16)\times 10^{-3}$, ${\cal B}(\bar{B^{0}} \to D^{*+} π^{-}) = (2.79 \pm 0.08 \pm 0.17)\times 10^{-3}$, ${\cal B}(B^{-} \to D^{0} π^{-}) = (4.90 \pm 0.07 \pm 0.22)\times 10^{-3}$ and ${\cal B}(B^{-} \to D^{*0} π^{-}) = (5.52 \pm 0.17 \pm 0.42)\times 10^{-3}$, 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 $\bar{B^{0}} \to D^{(*)0}π^{0}$, the cosines of the strong phase difference $δ$ between the $I=1/2$ and $I=3/2$ isospin amplitudes are determined to be $ \cos δ= 0.872^{+0.008+0.031}_{-0.007-0.029}$ for the $\bar{B} \to Dπ$ process and $ \cos δ= 0.924^{+0.019+0.063}_{-0.017-0.054}$ for the $\bar{B} \to D^{*}π$ process. Under the isospin symmetry, the results for $\cos δ$ suggest that final-state interactions are present in the $Dπ$ system.