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}}^0to {pi}^{+}{mathrm{ell}}^{-}{overline{nu}}_{mathrm{ell}} . From the world average of the latter we obtain |Vub| = (3.77 ± 0.15) · 10−3, which is in agreement with the most recent inclusive determination at the 1 σ level.
Highlights
The most recent inclusive determination by the Belle collaboration [10] finds the tension reduced, with the central value dropping closer to the exclusive one, while simultaneously increasing the uncertainty
We study the B → π form factors and use their numerical results from QCD-based methods to update the exclusive determination of |Vub| from B → π semileptonic decays and the SM predictions of a number of phenomenologically interesting observables
We begin by revisiting the determination of the form factors using light-cone sum rules with π distribution amplitudes
Summary
Our setup follow the usual approach to calculate both the B-meson decay constant fB in two-point QCD sum rules and the B → π form factors in LCSR within a simultaneous analysis [16, 21, 30]. While the input parameters for the light quark masses mu and md change only slightly, this change has a large numerical effect on μ2π, which normalises the twistthree two-particle contributions to the sum rules. It affected the value of qq condensate density. A recent lattice QCD analysis [26] of the shape of the leading-twist pion LCDA has provided for the first time a determination of the leading Gegenbauer moment a2 from first principles We use this result as a Gaussian prior in our analysis.
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