The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals. (4th November 2022)

• Record Type: Journal Article
• Authors: Blümlein, Johannes; Schneider, Carsten
• Is Part Of: Journal of physics. Volume 55:Number 44(2022)
• Publication Date: 2022-11-04
• Subjects: multi-loop Feynman integrals -- computer algebra -- special functions; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac8086
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the standard model of elementary particles. In this survey article the most recent and relevant computer algebra and special function algorithms are presented that are currently used or that may play an important role to perform such challenging precision calculations in the future. They are discussed in the context of analytic zero, single and double scale calculations in the quantum field theories of the standard model and effective field theories, also with classical applications. These calculations play a central role in the analysis of precision measurements at present and future colliders to obtain ultimate information for fundamental physics.