Systematization of Basic Divergent Integrals in Perturbation Theory and Renormalization Group Functions

TL;DR

This paper demonstrates that at any loop order, the divergent parts of Feynman amplitudes can be expressed using a finite set of basic integrals, simplifying the calculation of renormalization group functions.

Contribution

It introduces a systematic method to relate divergent integral coefficients across loop orders, reducing the complexity of renormalization calculations.

Findings

Divergent content is spanned by basic integrals at each loop order.

Coefficients of basic integrals determine renormalization group functions.

Relations between coefficients across loops are established.

Abstract

We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals which need not be evaluated. Only the coefficients of the basic divergent integrals are necessary to determine renormalization group functions. Relations between these coefficients of different loop orders are derived.