One-loop hexagon integral to higher orders in the dimensional regulator

• DOI: 10.48550/arxiv.2210.13505
• Publication Date: 2023-01-18
• Authors: Henn, Johannes M.; Matijašić, Antonela; Miczajka, Julian
• Keywords: High Energy Physics - Theory; FOS: Physical sciences; QC770-798; 01 natural sciences; High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Higher-Order Perturbative Calculations; Differential and Algebraic Geometry; Scattering Amplitudes

Abstract The state-of-the-art in current two-loop QCD amplitude calculations is at five-particle scattering. Computing two-loop six-particle processes requires knowledge of the corresponding one-loop amplitudes to higher orders in the dimensional regulator. In this paper we compute analytically the one-loop hexagon integral via differential equations. In particular we identify its function alphabet for general D-dimensional external states. We also provide integral representations for all one-loop integrals up to weight four. With this, the one-loop integral basis is ready for two-loop amplitude applications. We also study in detail the difference between the conventional dimensional regularization and the four-dimensional helicity scheme at the level of the master integrals and their function space.