Two-loop master integrals for non-leptonic heavy-to-heavy decays

TL;DR

This paper analytically computes two-loop master integrals for non-leptonic heavy-to-heavy decays using a canonical basis, facilitating their use in QCD factorization frameworks.

Contribution

It introduces a new canonical basis for two-loop integrals with two different internal masses, simplifying their analytical solution.

Findings

Derived a basis that disentangles kinematics from space-time dimension.

Solved differential equations in terms of iterated integrals up to weight four.

Provides integrals suitable for convolution with light-cone distribution amplitudes.

Abstract

We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that disentangles the kinematics from the space-time dimension in the differential equations, and subsequently solve the latter in terms of iterated integrals up to weight four. The solution constitutes another valuable example of the finding of a canonical basis for two-loop master integrals that have two different internal masses, and assumes a form that is ideally suited for a subsequent convolution with the light-cone distribution amplitude in the framework of QCD factorisation.