The → π form factors from QCD and their impact on |V |

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

The online version contains supplementary material available at 10.1007/JHEP07(2021)036.