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

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.

Comments: 33 pages, 8+1 figures, 9+1 tables; In the resubmitted version - an integrated LCSR form factor prediction is presented, several clarifications are made concerning pole masses, and typos corrected