Partial next-to-next-to-leading-order corrections to the B → π form factors from light-cone sum rules

A

bstract

By incorporating the available leading-power results at

and next-to-leading-power corrections at tree level, we compute the

$$ \mathcal{O}\left({\alpha}_s^2{\beta}_0\right) $$ O α s 2 β 0

contribution to the B → π form factors 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

$$ \mathcal{O}\left({\alpha}_s^2{\beta}_0\right) $$ O α s 2 β 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 → π form factors across the full kinematic range. Utilizing these form factors, we update the branching ratios, lepton-flavor-universality ratio R _π , forward-backward asymmetry

$$ {\mathcal{A}}_{\mathrm{FB}} $$ A FB

, flat term

$$ {\mathcal{F}}_{\mathrm{H}} $$ F H

and polarization asymmetry

$$ {\mathcal{A}}_{\lambda_{\ell }} $$ A λ ℓ

of

$$ B\to \pi \mu {\overline{\nu}}_{\mu } $$ B → πμ ν ¯ μ

and

$$ B\to \pi \tau {\overline{\nu}}_{\tau } $$ B → πτ ν ¯ τ

decays. We also extract the Cabibbo-Kobayashi-Maskawa matrix element | V _ub | = 3.73(14) × 10 ⁻³ . We find that the resulting shifts are generally small and remain within the uncertainties of previous analyses.