Four-loop HQET propagators from the DRA method

TL;DR

This paper advances the calculation of four-loop propagator integrals in heavy-quark effective theory using the DRA method, introducing a new technique for fixing solutions and providing epsilon expansions near four and three dimensions.

Contribution

It presents a novel approach to fixing homogeneous solutions in the DRA method using pole parts from integrals in different dimensions, enhancing multi-loop integral computations.

Findings

Calculated four-loop master integrals in HQET.

Provided epsilon expansions near d=4 and d=3.

Introduced a new technique for fixing homogeneous solutions.

Abstract

We use dimensional recurrence relations and analyticity to calculate four-loop propagator-type master integrals in the heavy-quark effective theory. Compared to previous applications of the DRA method, we apply a new technique of fixing homogeneous solutions from pole parts of integrals evaluated in different rational space-time dimension points. The latter were calculated from the integration-by-parts reduction of finite integrals in shifted space-time dimension and/or with increased propagators powers. We provide results for epsilon expansions of master integrals near $d = 4$ and $d = 3$ using constructed alternative sets of integrals with expansion coefficients having conjectural uniform transcendental weight.