Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight

TL;DR

This paper analytically computes higher-order epsilon-expansion terms for three-loop master integrals relevant to form factors and g-2, reaching weights typical of four-loop calculations using advanced mathematical techniques.

Contribution

It introduces a combined method leveraging sector decomposition, Mellin-Barnes representation, and PSLQ to evaluate epsilon-expansions up to high transcendentality weights.

Findings

Achieved epsilon-expansions up to weight eight for form factors.

Extended known results to higher transcendentality weights.

Demonstrated effectiveness of combined computational techniques.

Abstract

We evaluate analytically higher terms of the epsilon-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g-2 in QED up to the transcendentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm.