Systematic approximation of multi-scale Feynman integrals

TL;DR

The paper introduces an algorithm for systematically approximating multi-scale Feynman integrals analytically, enabling fast and accurate numerical evaluation across all kinematic regions, which is crucial for high-precision particle physics calculations.

Contribution

It presents a new algorithm that provides algebraic expressions for multi-scale Feynman integrals, valid in all kinematic regions and to arbitrary order in the dimensional regulator.

Findings

Algorithm successfully approximates two-loop integrals with internal mass scales.

Results enable efficient numerical evaluation in Higgs+jet production.

Demonstrates applicability to complex multi-scale Feynman integrals.

Abstract

An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman integrals, allowing for fast numerical evaluation. The results are valid in all kinematical regions, both above and below thresholds, up to in principle arbitrary orders in the dimensional regulator. The scope of the algorithm is demonstrated by presenting results for selected two-loop three-point and four-point integrals with an internal mass scale that appear in the two-loop amplitudes for Higgs+jet production.