Measurement of $\mathcal{B}{(B}^{-}\to D^0{\pi }^{-})$ and $\mathcal{B}(B^0\to D^{+}{\pi }^{-})$ and isospin analysis of $\overline{B}\to D\pi$ decays

We present new measurements of branching fractions for the color-favored decays $B^{-}\to D^0{\pi }^{-}$ and $B^0\to D^{+}{\pi }^{-}.$ Using $9.67\times {10}^{6}B\overline{B}$ pairs collected with the CLEO detector, we obtain the branching fractions $\mathcal{B}{(B}^{-}\to D^0{\pi }^{-})=(49.7\mathrm{}\pm 1.2\pm 2.9\pm 2.2)\times {10}^{-4}$ and $\mathcal{B}(B^0\to D^{+}{\pi }^{-})=(26.8\mathrm{}\pm 1.2\pm 2.4\pm 1.2)\times {10}^{-4}.$ The first error is statistical, the second is systematic, and the third is due to the experimental uncertainty on the production ratio of charged and neutral B mesons in ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ decays. These results, together with the current world average for the color-suppressed branching fraction $\mathcal{B}(B^0\to D^0{\pi }^0),$ are used to determine the cosine of the strong phase difference ${\delta }_I$ between the $I=1/2\mathrm{}$ and $I=3/2\mathrm{}$ isospin amplitudes. We find $\cos {\delta }_I{=0.863\mathrm{}}_{-0.023-0.035-0.030}^{+0.024+0.036+0.038\mathrm{}},$ and obtain a $90\%$ confidence interval of $16.5°<{\delta }_I<38.1\mathrm{}°.$ This nonzero value of ${\delta }_I$ suggests the presence of final state interactions in the $D\pi$ system.