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We revisit light-cone sum rules with pion distribution amplitudes todetermine the full set of local $B \to \pi$ form factors. To this end, wedetermine all duality threshold parameters from a Bayesian fit for the firsttime. Our results, obtained at small momentum transfer $q^2$, are extrapolatedto large $q^2$ where they agree with precise lattice QCD results. We find thata modification to the commonly used BCL parametrization is crucial tointerpolate the scalar form factor between the two $q^2$ regions. We providenumerical results for the form factor parameters -- including their covariance-- based on simultaneous fit of all three form factors to both the sum rule andlattice QCD results. Our predictions for the form factors agree well withmeasurements 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 recentinclusive determination at the $1\,\sigma$ level.

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