Extrapolation and unitarity bounds for the $B \to \pi$ form factor

Understand

We address the problem of extrapolating the vector form factor $f_{B\pi}^+$, which is relevant to $B\to \pi\ell \nu_\ell$ decays, from the region of small to the region of large momentum transfer.

• As input, we use the QCD light-cone sum rule at small momentum transfer.
• We carry out a comprehensive Bayesian uncertainty analysis and obtain correlated uncertainties for the normalization and shape parameters of the form factor.
• The $z$-series parametrization for $f_{B\pi}^+$ is employed to extrapolate our results to large momentum transfer, and to compare with the lattice QCD results.