Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$
Résumé
We propose a new parametrization of the $B\to\pi$ vector form factor, $f_+(q^2)$, as an expansion in powers of a conformal mapping variable, which satisfies the analyticity and perturbative scaling properties of the form factor, as well as unitarity. By using the available theoretical and experimental information on exclusive $B\to\pi l\nu$ decays, we obtain an accurate description of $f_+(q^2)$ in the physical region, with only three parameters. We also obtain $|V_{ub}|=(3.36 \pm 0.23) \times 10^{-3}$, where the uncertainty includes the statistical error and the systematic error associated with the use of our parameterization, the latter being negligible. In obtaining these results, we make a conservative estimate of the effects of correlations in the systematic and statistical errors of the lattice results used.
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