Chinese Magic in Loop Integrals

TL;DR

This paper introduces a novel approach using Chinese magic to simplify higher point loop integrals in quantum field theory, reducing computational complexity and potentially improving numerical stability.

Contribution

It presents a new method for directly reducing five-point loop integrals to scalar functions, bypassing traditional tensor reduction techniques.

Findings

Reduced five-point integrals to scalar functions directly

Avoided tensor Passarino-Veltman reduction

Potential for enhanced numerical stability

Abstract

We present an approach to higher point loop integrals using Chinese magic in the virtual loop integration variable. We show, using the five point function in the important e^+e^-\to f\bar{f}+\gamma process for ISR as a pedagogical vehicle, that we get an expression for it directly reduced to one scalar 5-point function and 4-, 3-, and 2- point integrals, thereby avoiding the computation of the usual three tensor 5-pt Passarino-Veltman reduction. We argue that this offers potential for greater numerical stability.