Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$

TL;DR

This paper introduces a new model-independent parametrization of the $B\to\pi$ form factor using a conformal mapping expansion, enabling a precise determination of $|V_{ub}|$ with minimal systematic error.

Contribution

The authors develop a novel, systematic, and unitarity-consistent expansion for the $B\to\pi$ form factor, improving the extraction of $|V_{ub}|$ from decay data.

Findings

The new parametrization accurately fits experimental and lattice data.

The systematic error in the form factor is negligible across the entire semileptonic region.

The determined value of $|V_{ub}|$ is $(3.54 \pm 0.30) \times 10^{-3}$.

Abstract

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 unitarity, analyticity and perturbative QCD scaling. The unitarity constraint is used also for defining the systematic error of the expansion. We fit with the new parametrization the available experimental and theoretical information on exclusive $B\to\pi l\nu$ decays, making a conservative estimate of the effects of correlations in the systematic and statistical errors of the lattice results. With four parameters to describe $f_+(q^2)$, the systematic error is negligible in the whole semileptonic region. We also obtain $|V_{ub}|=(3.54 \pm 0.30) \times 10^{-3}$ where, in our approach, the uncertainty is predominantly statistical.