The B ¯ → π form factors from QCD and their impact on |V ub |.

We revisit light-cone sum rules with pion distribution amplitudes to determine the full set of local B ¯ → π 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 B ¯ 0 → π + ℓ - ν ¯ ℓ . From the world average of the latter we obtain |V ub | = (3.77 ± 0.15) · 10 -3, which is in agreement with the most recent inclusive determination at the 1 σ level. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/JHEP07(2021)036.

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