Efficient contraction of 1-loop N-point tensor integrals

TL;DR

This paper introduces an efficient method for reducing 1-loop N-point tensor integrals using a standard decomposition, enabling faster calculations of cross sections and supporting a new numerical package.

Contribution

The paper presents a novel reduction technique for tensor integrals that simplifies contractions and improves computational efficiency in cross section calculations.

Findings

Efficient contraction method for tensor integrals.

Development of the OLEC numerical package.

Initial numerical results demonstrate effectiveness.

Abstract

A new approach for the reduction of tensor integrals is described. The standard decomposition \`{a} la Davydychev is applied. Integrals with higher indices are then expressed in terms of scalar higher-dimensional integrals with generic indices. The approach allows to perform contractions with external momenta in a particularly efficient manner. This is due to the possibility to perform analytically the resulting sums over the indices of products of signed minors and scalar products of chords. Advantages of this approach for the calculation of cross sections are described. We are preparing the numerical package OLEC (\texttt{O}ne \texttt{L}oop \texttt{E}xternal \texttt{C}ontractions) with interfaces in Mathematica for algebraic and in C++ for numerical calculations. First numerical results are discussed.