Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals

TL;DR

This paper introduces an iterative reduction method for one-loop Feynman integrals using module intersection in the Baikov representation, resulting in a uniform formula that simplifies IBP relations through Gram determinants.

Contribution

It presents a novel iterative sector-level reduction strategy for one-loop integrals based on module intersection and auxiliary vectors, leading to a compact, uniform reduction formula.

Findings

Developed an iterative reduction strategy for general one-loop integrals.

Organized IBP relations into Gram determinants for simplicity.

Provided a uniform formula applicable to all one-loop integrals.

Abstract

In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the reduction of general one-loop integrals, i.e., integrals having arbitrary tensor structures and arbitrary power for propagators. Inspired by these studies, a uniform and compact formula that iteratively reduces all one-loop integrals has been written down, where messy polynomials in integration-by-parts (IBP) relations have organized themselves to Gram determinants.