Comment on form factor shape and extraction of |V_ub| from B --> pi l nu

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Abstract
We point out that current experimental data for partial B --> pi l nu branching fractions reduce the theoretical input required for a precise extraction of |V_ub| to the form factor normalization at a single value of the pion energy. We show that the heavy-quark expansion provides a bound on the form factor shape that is orders of magnitude more stringent than conventional unitarity bounds. We find |V_ub| = (3.7 +/- 0.2 +/- 0.1) x [0.8/F_+(16 GeV^2)]. The first error is from the experimental branching fractions, and the second is a conservative bound on the residual form factor shape uncertainty, both of which will improve with additional data. Together with current and future lattice determinations of the form factor normalization this result gives an accurate, model independent determination of |V_ub|. We further extract semileptonic shape observables such as |V_ub F_+(0)| = 0.92 +/- 0.11 +/- 0.03 and show how these observables can be used to test factorization and to determine low-energy parameters in hadronic B decays.

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