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Analysis of the present data on the semileptonic process $B \to \pi \ell \nu$indicates that they have not yet reached the precision to provide adequateinformation on the $B \to \pi$ 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 witharound 500 $B \to \pi \ell \nu$ events in which rate and spectrum are measuredone can improve the accuracy of $T$ by a significant amount. A recent CLEOdetermination of the $D^* D \pi$ coupling constant is compared with an earlierprediction, and its role in the description of the $B \to \pi$ form factors isnoted. When combined with an estimate of the penguin amplitude (``$P$'')obtained using flavor SU(3) symmetry from $B \to K \pi$ decays, information on$T$ allows one to gauge the effects of the penguin amplitude on extraction ofthe weak phase $\alpha = \phi_2$ from the time-dependent CP-violating rateasymmetry in $B^0 \to \pi^+ \pi^-$. The constraint on $\alpha$ implied by arecent experimental result on this asymmetry is described.Comment: 17 pages, LaTeX, 7 figures, revised version resubm. to Phys. Rev. D.  Further modifications in abstract, text, and reference

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Information on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>provided by the semileptonic process<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></…

Information onB→ππprovided by the semileptonic processB→