Light-cone sum rules for $B \to \pi$ form factors revisited

TL;DR

This paper updates QCD light-cone sum rules for B to pi form factors by including gluon radiative corrections, using the MSbar b-quark mass, and fitting to experimental data to refine predictions of form factors and CKM matrix element |V_ub|.

Contribution

It provides revised calculations of B to pi form factors with higher-order corrections and employs the MSbar scheme, improving the precision of theoretical predictions.

Findings

Predicted f^+_{Bπ}(0) = 0.26^{+0.04}_{-0.03}

Extracted |V_{ub}| = (3.5 ± 0.4 ± 0.2 ± 0.1) × 10^{-3}

Calculated scalar and penguin form factors for B to pi transitions.

Abstract

We reconsider and update the QCD light-cone sum rules for $B\to \pi$ form factors. The gluon radiative corrections to the twist-2 and twist-3 terms in the correlation functions are calculated. The $\bar{MS}$ $b$-quark mass is employed, instead of the one-loop pole mass used in the previous analyses. The light-cone sum rule for $f^+_{B\pi}(q^2)$ is fitted to the measured $q^2$-distribution in $B\to \pi l \nu_l$, fixing the input parameters with the largest uncertainty: the Gegenbauer moments of the pion distribution amplitude. For the $B\to \pi$ vector form factor at zero momentum transfer we predict $f^+_{B\pi}(0)= 0.26^{+0.04}_{-0.03}$. Combining it with the value of the product $|V_{ub}f^+_{B\pi}(0)|$ extracted from experiment, we obtain $|V_{ub}|=(3.5\pm 0.4\pm 0.2\pm 0.1) \times 10^{-3}$. In addition, the scalar and penguin $B\to \pi$ form factors $f^0_{B\pi}(q^2)$ and $f^T_{B\pi}(q^2)$ are calculated.