Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations

TL;DR

This paper introduces a novel method combining recurrence relations and dispersive techniques to efficiently evaluate complex multi-loop Feynman diagrams for precision electroweak calculations.

Contribution

It develops a new approach that reduces computational complexity by expressing multi-point functions in a two-point basis and using shifted dimensions with recurrence relations.

Findings

Reduces the number of dispersive integrals needed for calculations.

Minimizes computation time for one- and two-loop diagrams.

Enables more precise and efficient multi-loop Feynman diagram evaluations.

Abstract

Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method in order to evaluate complex multi-loop Feynman diagrams. By expressing multi-point Passarino-Veltman functions in a two-point basis and using shifted space-time dimensions with recurrence relations, we minimize the number of required dispersive integrals. This approach reduces computation time and enables a precise and efficient analysis of one- and two-loop diagrams.