NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part

TL;DR

This paper calculates the imaginary part of two-loop vertex corrections in QCD factorization for B -> pi pi decays, advancing the precision of direct CP asymmetry predictions by completing NNLO contributions.

Contribution

It provides the first complete NNLO calculation of the imaginary part of topological tree amplitudes in charmless hadronic B decays, including charm mass dependence.

Findings

Soft and collinear divergences cancel at 2-loop order, confirming factorization.

NNLO corrections significantly enhance the strong phase of the color-suppressed amplitude.

Results are obtained analytically, including charm quark mass effects.

Abstract

We compute the imaginary part of the 2-loop vertex corrections in the QCD Factorization framework for hadronic two-body decays as B -> pi pi. This completes the NNLO calculation of the imaginary part of the topological tree amplitudes and represents an important step towards a NNLO prediction of direct CP asymmetries in QCD Factorization. Concerning the technical aspects, we find that soft and collinear infrared divergences cancel in the hard-scattering kernels which demonstrates factorization at the 2-loop order. All results are obtained analytically including the dependence on the charm quark mass. The numerical impact of the NNLO corrections is found to be significant, in particular they lead to an enhancement of the strong phase of the colour-suppressed tree amplitude.