NNLO vertex corrections in charmless hadronic B decays: Real part

TL;DR

This paper calculates the real part of 2-loop vertex corrections in charmless B decays, completing NNLO topological amplitude calculations in QCD factorization, and finds moderate numerical impact with reduced scale dependence.

Contribution

It provides the first complete NNLO calculation of the real part of vertex corrections in charmless B decays, ensuring infrared divergence cancellation and improving theoretical precision.

Findings

Infrared divergences are canceled at 2-loop level.

Numerical corrections are moderate in size.

Factorization scale dependence is significantly reduced.

Abstract

We compute the real part of the 2-loop vertex corrections for charmless hadronic B decays, completing the NNLO calculation of the topological tree amplitudes in QCD factorization. Among the technical aspects we show that the hard-scattering kernels are free of soft and collinear infrared divergences at the 2-loop level, which follows after an intricate subtraction procedure involving evanescent four quark operators. The numerical impact of the considered corrections is found to be moderate, whereas the factorization scale dependence of the topological tree amplitudes is significantly reduced at NNLO. We in particular do not find an enhancement of the phenomenologically important ratio |C/T| from the perturbative calculation.