The $\bar{B}\to \pi$ form factors from QCD and their impact on $|V_{ub}|$

TL;DR

This paper refines the determination of $B o \pi$ form factors using QCD sum rules and lattice data, leading to an improved extraction of the CKM matrix element |V_{ub}| with consistent results.

Contribution

It introduces a Bayesian approach to determine duality thresholds and modifies the BCL parametrization for better interpolation of form factors.

Findings

Form factors agree with lattice QCD at high $q^2$

Predicted $|V_{ub}|$ aligns with inclusive measurements

Provides covariance matrix for form factor parameters

Abstract

We revisit light-cone sum rules with pion distribution amplitudes to determine the full set of local $B \to \pi$ form factors. To this end, we determine all duality threshold parameters from a Bayesian fit for the first time. Our results, obtained at small momentum transfer $q^2$, are extrapolated to large $q^2$ where they agree with precise lattice QCD results. We find that a modification to the commonly used BCL parametrization is crucial to interpolate the scalar form factor between the two $q^2$ regions. We provide numerical results for the form factor parameters -- including their covariance -- based on simultaneous fit of all three form factors to both the sum rule and lattice QCD results. Our predictions for the form factors agree well with measurements of the $q^2$ spectrum of the semileptonic decay $\bar{B}^0\to \pi^+\ell^-\bar\nu$. From the world average of the latter we obtain $|V_{ub}| = (3.77 \pm 0.15)\cdot 10^{-3}$, which is in agreement with the most recent inclusive determination at the $1\,\sigma$ level.