A solution for tensor reduction of one-loop N-point functions with N >= 6

TL;DR

This paper presents an analytical recursive method for tensor reduction of one-loop N-point Feynman integrals with N ≥ 6, facilitating automation and precise calculations in high-energy physics.

Contribution

It provides a new analytical approach to tensor reduction for N ≥ 6 point functions, improving efficiency and suitability for automation.

Findings

Coefficients derived analytically from metric tensor representations

Efficient expressions for contractions with external momenta

Enhanced potential for automated calculations

Abstract

Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop $N$-point corrections are needed. We study here the tensor reduction for Feynman integrals with $N \ge 6$. A general, recursive solution by Binoth et al. expresses $N$-point Feynman integrals of rank $R$ in terms of $(N-1)$-point Feynman integrals of rank $(R-1)$ (for $N\ge 6$). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization.