Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams

TL;DR

This paper introduces symbolic summation techniques based on difference fields to transform complex multi-sums into simpler nested sums, successfully applied to compute 2- and 3-loop massive Feynman diagrams with local operator insertions.

Contribution

It presents a general strategy using difference field theory to evaluate multi-sums in Feynman diagram calculations, advancing computational methods in quantum field theory.

Findings

Successfully computed 2-loop and 3-loop massive Feynman diagrams

Transformed multi-sums into nested sums and products

Demonstrated the effectiveness of symbolic summation methods

Abstract

By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2--loop and 3--loop massive single scale Feynman diagrams with local operator insertion.