Analytic Computing Methods for Precision Calculations in Quantum Field Theory

TL;DR

This paper reviews current mathematical methods for high-precision multi-loop calculations in quantum field theory, highlighting achievements and challenges for future theoretical developments in particle physics.

Contribution

It provides a comprehensive overview of the state-of-the-art analytical computation techniques for multi-loop corrections in quantum field theory, emphasizing the need for extensions to meet future experimental precision.

Findings

Massless single scale quantities computed to 4-loop order in QCD

Single and double mass quantities calculated to 3-loop order

Zero scale quantities achieved 5-loop order calculations

Abstract

An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present massless single scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.