The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals

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.

42 pages, see also the overview article arXiv:2203.13011.v3: journal version

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Cited by in corpus (9)

• The SAGEX Review on Scattering Amplitudes
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Tree-level amplitudes from the pure spinor superstring
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• ALPs, the on-shell way
• Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations