Solving for tadpole coefficients in one-loop amplitudes

TL;DR

This paper presents a method to relate one-point integral coefficients to higher-point coefficients in one-loop amplitudes by introducing an unphysical propagator, simplifying the calculation of scalar integral coefficients.

Contribution

It introduces a novel approach to connect different scalar integral coefficients through the addition of an unphysical propagator, enhancing computational techniques in quantum field theory.

Findings

Established a relation between one-point and higher-point integral coefficients

Provided a method to incorporate unphysical propagators in amplitude calculations

Simplified the process of extracting scalar integral coefficients

Abstract

One-loop amplitudes may be expanded in a basis of scalar integrals multiplied by rational coefficients. We relate the coefficient of the one-point integral to the coefficients of higher-point integrals, by considering the effects of introducing an additional, unphysical propagator, subject to certain conditions.