Next-to-Next-to-Leading-Order Corrections to the $B\to \pi$ Form Factors from Light-Cone Sum Rules

Abstract

By incorporating the available leading-power results at $\mathcal{O}({\alpha }_s)$ and next-to-leading-power corrections at tree level, we improve the precision of the theoretical predictions for $B\to \pi$ form factors to the $\mathcal{O}({\alpha }_s^2{\beta }_0)$ level in the large-recoil region using the light-cone sum rule approach with $B$-meson light-cone distribution amplitudes. We find that the QCD corrections at $\mathcal{O}({\alpha }_s^2{\beta }_0)$ contribute approximately $+6.1\%$ compared to the tree-level result. Combining the light-cone sum rule predictions in the large-recoil region, lattice QCD results in the small-recoil region, we perform a combined fit for the $B\to \pi$ form factors across the full kinematic range. Utilizing these form factors, we calculate the branching ratios, lepton-flavor-universality ratio $R_{\pi }$, forward-backward asymmetry ${\mathcal{A}}_{\mathrm{FB}}$, flat term ${\mathcal{F}}_{\mathrm{H}}$ and polarization asymmetry ${\mathcal{A}}_{{\lambda }_{\mathrm{\ell }}}$ of $B\to \pi \mu {\bar{\nu }}_{\mu }$ and $B\to \pi \tau {\bar{\nu }}_{\tau }$ decays. Using the experimentally measured $q^2$-binned differential branching ratios of $B\to \pi \mu {\bar{\nu }}_{\mu }$ decay as input, employing the Bourrely-Caprini-Lellouch parametrization, we extract the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|=3.73(14)\times 10^{-3}$.

Comments: 30 pages, 8 figures