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

• Published in: The journal of high energy physics Vol. 2023; no. 1; pp. 96 - 34
• Main Authors: Henn, Johannes M., Matijašić, Antonela, Miczajka, Julian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 18.01.2023; Springer Nature B.V; SpringerOpen
• Subjects: Algebra; Amplitudes; Classical and Quantum Gravitation; Differential and Algebraic Geometry; Differential equations; Elementary Particles; Function space; Helicity; High energy physics; Higher-Order Perturbative Calculations; Integrals; Kinematics; Partial differential equations; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Regularization; Relativity Theory; Scattering Amplitudes; String Theory; Scattering Amplitudes; Differential and Algebraic Geometry; Higher-Order Perturbative Calculations
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2023)096

A bstract 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.