Non-leptonic B-decays at two-loops in QCD

TL;DR

This paper reviews the progress in calculating two-loop QCD corrections to non-leptonic B-decays, focusing on analytical results for key amplitudes in heavy-to-light and heavy-to-heavy transitions.

Contribution

It provides new analytical expressions for master integrals and amplitudes in two-loop QCD corrections to B-decays within the QCD factorisation framework.

Findings

Analytical results for master integrals obtained.

Explicit expressions for penguin amplitudes a_4^u and a_4^c.

Analytical form of amplitude a_1(D* pi) derived.

Abstract

I review the status of the calculation of two-loop QCD corrections to non-leptonic B-decays in the framework of QCD factorisation. In the case of heavy-to-light decays I will cover the leading penguin amplitudes a_4^u and a_4^c. For heavy-to-heavy transitions I will discuss the amplitude a_1(D^(*) pi). In both cases I will present some computational details, especially on how to obtain analytical results for the master integrals in a canonical basis, which in turn enables us to derive analytical expressions for almost all terms in the amplitudes.