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

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 $\overline{MS}$ $b$-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 $f_{B\pi }^{+}(0)=0.26_{-0.03}^{+0.04}$. 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 $f_{B\pi }^0(q^2)$ and $f_{B\pi }^T(q^2)$ are calculated.

33 pages, 7 figures, one figure and a few comments added, version to appear in JHEP

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