Factorizable amplitude inB0→π+π−

Using the measured spectrum shape for $\overrightarrow{B}\pi \mathcal{l}\nu ,$ the rate for $B^{+}\to {\pi }^{+}{\pi }^0,$ information on the Cabibbo-Kobayashi-Maskawa matrix element $|V_{\mathrm{ub}}|,$ and theoretical inputs from factorization and lattice gauge theory, we obtain an improved estimate of the “tree” contribution to $B^0\to {\pi }^{+}{\pi }^{-}.$ We find the branching ratio $\mathcal{B}{(B}^0\to {\pi }^{+}{\pi }^{-}\left){|}_{\mathrm{tree}}{=(5.25\mathrm{}}_{-0.50}^{+1.67\mathrm{}}\right)\times {10}^{-6}$ to be compared with the experimental value $\mathcal{B}{(B}^0\to {\pi }^{+}{\pi }^{-})=(4.55\mathrm{}\pm 0.44)\times {10}^{-6}.$ The fit implies $|V_{\mathrm{ub}}|=(3.62\mathrm{}\pm 0.34)\times {10}^{-3}.$ Implications for tree-penguin interference in $B^0\to {\pi }^{+}{\pi }^{-}$ and for other charmless B decays are discussed.