Information onB→ππprovided by the semileptonic processB→πlν

Analysis of the present data on the semileptonic process $\overrightarrow{B}\pi l\nu$ indicates that they have not yet reached the precision to provide adequate information on the $\overrightarrow{B}\pi$ form factor $F_{+}{(q}^2),$ which for $q^2{=m}_{\pi }^2$ is known to be related to the factorized color-favored $(“T,”$ or “tree”) contribution to $B^0\to {\pi }^{+}{\pi }^{-}.$ It is shown here that with around 500 $\overrightarrow{B}\pi l\nu$ events in which rate and spectrum are measured one can improve the accuracy of T by a significant amount. A recent CLEO determination of the $D^{*}D\pi$ coupling constant is compared with an earlier prediction, and its role in the description of the $\overrightarrow{B}\pi$ form factors is noted. When combined with an estimate of the penguin amplitude $\left(“P”\right)$ obtained using flavor SU(3) symmetry from $\overrightarrow{B}K\pi$ decays, information on T allows one to gauge the effects of the penguin amplitude on extraction of the weak phase $\alpha ={\phi }_2$ from the time-dependent CP-violating rate asymmetry in $B^0\to {\pi }^{+}{\pi }^{-}.$ The constraint on $\alpha$ implied by a recent experimental result on this asymmetry is described.