Calculating contracted tensor Feynman integrals

TL;DR

This paper presents a new algebraic method for efficiently calculating contracted tensor Feynman integrals, simplifying the evaluation of one-loop contributions in high-energy collider physics.

Contribution

It introduces compact algebraic expressions for tensor integral contractions, enhancing computational efficiency for multi-particle production processes.

Findings

Derived compact algebraic expressions for tensor contractions.

Facilitated efficient evaluation of one-loop integrals.

Applicable to massless and massive particle processes.

Abstract

A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.