The $$ \overline{B} $$ → π form factors from QCD and their impact on |Vub|
Domagoj Leljak, Blaženka Melić, Danny van Dyk
Abstract
A bstract We revisit light-cone sum rules with pion distribution amplitudes to determine the full set of local $$ \overline{B} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> → 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 $$ {\overline{B}}^0\to {\pi}^{+}{\mathrm{\ell}}^{-}{\overline{\nu}}_{\mathrm{\ell}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>0</mml:mn> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:math> . 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.