Determine Arbitrary Feynman Integrals by Vacuum Integrals

TL;DR

The paper introduces a new representation for Feynman integrals using an auxiliary parameter, transforming their computation into an analytical continuation problem, and develops a more efficient reduction method for multi-loop integrals.

Contribution

It presents a novel representation of Feynman integrals via vacuum integrals and a new reduction technique that outperforms existing methods.

Findings

Successfully reduced complex two-loop integrals in key particle processes

Demonstrated efficiency of the new reduction method over traditional IBP methods

Provided a conceptual framework linking Feynman integrals to vacuum integrals

Abstract

By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore conceptually translates the problem of computing Feynman integrals to the problem of performing analytical continuations. As an application of the new representation, we use it to construct a novel reduction method for multi-loop Feynman integrals, which is expected to be more efficient than known integration-by-parts reduction method. Using the new method, we successfully reduced all complicated two-loop integrals in $gg\to HH$ process and $gg\to ggg$ process.