Partial fractioning reduction of perturbative amplitudes

TL;DR

This paper introduces a novel partial fractioning method to simplify complex loop integrals in perturbative quantum field theory, reducing the number of denominators and simplifying calculations for diagrams with many external lines.

Contribution

The paper presents a new partial fractioning technique that reduces the complexity of loop integrals with many propagators, improving computational efficiency in perturbative calculations.

Findings

Reduces the number of denominators in loop integrals with many external lines.

Simplifies multiloop diagram calculations by further reducing linear denominators.

Handles integrals with numerator momenta, up to d+1 linear factors.

Abstract

A new method is presented for the simplification of loop integrals in one particle irreducible diagrams with large numbers of external lines, based on the partial fractioning of products of propagators. Whenever a loop diagram in $d$ dimensions has $d+1$ or more lines that carry the same linear combination of loop momenta, its integral can be reexpressed as a linear combination of integrals with no more than $d+1$ denominators for each such set of lines, of which $d$ are linear in the loop momenta and only one quadratic. In multiloop diagrams, the total number of linear denominators can be reduced further. In integrals with numerator momenta there may also be up to $d+1$ linear factors in the numerator.