General One-loop Reduction in Generalized Feynman Parametrization Form

TL;DR

This paper enhances a recent one-loop integral reduction method by Chen, demonstrating its effectiveness through explicit examples and completing previous computations with missing tadpole coefficients.

Contribution

It introduces improvements to Chen's reduction method, effectively canceling unwanted terms and dimension shifts, with explicit examples for various loop integrals.

Findings

Successful reduction of bubble, triangle, box, and pentagon integrals with doubled propagators.

Explicit demonstration of the method's effectiveness in canceling unwanted terms.

Completion of previous computations by including missing tadpole coefficients.

Abstract

Recently there is an alternative reduction method proposed by Chen in [1,2]. In this paper, using the one-loop scalar integrals with propagators having higher power, we show the power of the improved version of Chen's new method in which we used some tricks to cancel the dimension shift and the terms we do not want. We present the explicit examples of bubble, triangle, box and pentagon with one propagators doubled. With these results, we have completed our previous computations in \cite{wang} with the missed tadpole coefficients.