HQET vertex diagram: $\varepsilon$ expansion

TL;DR

This paper develops a method to compute the epsilon expansion of the one-loop HQET vertex diagram with arbitrary insertions and residual energies, using differential equations reduced to epsilon form and expressed via Goncharov polylogarithms.

Contribution

The authors derive a systematic approach to obtain the epsilon expansion of complex HQET vertex diagrams employing differential equations in epsilon form and Goncharov polylogarithms, advancing computational techniques in quantum field theory.

Findings

Epsilon expansion expressed in Goncharov polylogarithms.

Differential equations reduced to epsilon form for arbitrary insertions.

Method applicable to complex HQET vertex diagrams.

Abstract

Differential equations for the one-loop HQET vertex diagram with arbitrary self-energy insertions and arbitrary residual energies are reduced to the $\varepsilon$ form and used to obtain the $\varepsilon$ expansion in terms of Goncharov polylogarithms.