Reduction formalism for dimensionally regulated one-loop N-point integrals

TL;DR

This paper introduces a systematic reduction method for one-loop N-point integrals in massless theories, simplifying complex tensor and scalar integrals to more manageable forms, applicable to multi-parton process calculations.

Contribution

It provides a new general reduction procedure for N-point scalar and tensor integrals, including explicit formulas for N=6, enhancing computational efficiency in quantum field theory.

Findings

Scalar N-point functions reduced to box integrals in (4-2ε) dimensions.

Tensor integrals expressed in terms of scalar integrals through iterative reduction.

Higher dimensional integrals contribute only at order ε for N≥5.

Abstract

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional external momenta to box integrals in (4-2\epsilon) dimensions. We derive a formula valid for arbitrary N and give an explicit expression for N=6. Further a tensor reduction method for N-point tensor integrals is presented. We prove that generically higher dimensional integrals contribute only to order \epsilon for N>=5. The tensor reduction can be solved iteratively such that any tensor integral is expressible in terms of scalar integrals. Explicit formulas are given up to N=6.