The B¯ → π form factors from QCD and their impact on |Vub|

Abstract

We revisit light-cone sum rules with pion distribution amplitudes to determine the full set of local $\overline{B}$ → 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 q², are extrapolated to large q² 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 q² 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 q² spectrum of the semileptonic decay ${\overline{B}}^0\to {\pi }^{+}{\mathrm{\ell }}^{-}{\overline{\nu }}_{\mathrm{\ell }}$. 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.