NNLO vertex corrections to non-leptonic B decays: Tree amplitudes

TL;DR

This paper computes NNLO vertex corrections to non-leptonic B decay amplitudes, providing analytical results with charm mass dependence, and updates theoretical predictions that align well with experimental data for certain decay modes.

Contribution

It presents the first complete analytical calculation of two-loop NNLO vertex corrections to B decay amplitudes, including charm mass effects, improving theoretical precision.

Findings

Good agreement with experimental data for most observables.

Updated predictions for pi pi, pi rho, and rho rho final states.

Discrepancy observed in pi^0 pi^0 branching fraction.

Abstract

The colour-suppressed tree amplitude in non-leptonic B decays is particularly sensitive to perturbative and non-perturbative corrections. We calculate the two-loop (NNLO) vertex corrections to the colour-suppressed and colour-allowed tree amplitudes in QCD factorization. Our results are given completely analytically, including the full dependence on the charm quark mass. We then update theoretical predictions for a range of interesting observables derived from pi pi, pi rho, and rho rho final states that do not depend (significantly) on penguin contributions, and hence are now available with NNLO accuracy. We observe good agreement with experimental data within experimental and theoretical errors, except for observables involving the pi^0 pi^0 branching fraction.