The factorizable amplitude in $B^0\to {\pi }^{+}{\pi }^{-}$

Abstract

Using the measured spectrum shape for $B\to \pi \ell \nu$, the rate for $B^{+}\to {\pi }^{+}{\pi }^0$, information on the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{ub}|$, 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 $\text{b}(B^0\to {\pi }^{+}{\pi }^{-}){|}_{\mathrm{tree}}=(5.25_{-0.50}^{+1.67})\times 10^{-6}$, to be compared with the experimental value $\text{b}(B^0\to {\pi }^{+}{\pi }^{-})=(4.55\pm 0.44)\times 10^{-6}$. The fit implies $|V_{ub}|=(3.62\pm 0.34)\times 10^{-3}$. Implications for tree-penguin interference in $B^0\to {\pi }^{+}{\pi }^{-}$ and for other charmless $B$ decays are discussed.

Comments: 11 pages, LaTeX, 3 figures, to be submitted to Phys. Rev. D