A Systematic Expansion of Running Couplings and Masses

TL;DR

This paper introduces a new method for expanding running couplings and masses in quantum field theory using logarithmic series and renormalization group summation, applicable across different schemes.

Contribution

It presents a systematic expansion approach for running couplings and masses, offering an alternative to direct integration and relating different renormalization schemes.

Findings

Provides explicit expansion formulas for $a()$ and $m()$

Demonstrates the use of renormalization group summation in the expansion

Shows how to relate couplings and masses across schemes

Abstract

As an alternative to directly integrating their defining equations to find the running coupling $a(\mu)$ and the running mass $m(\mu)$, we expand these quantities in powers of $\ln\left(\frac{\mu}{\mu^\prime}\right)$ and their boundary values $a(\mu^\prime)$ and $m(\mu^\prime)$. Renormalization group summation is used to partially sum these logarithms. We consider this approach using both the $\overline{MS}$ and 't Hooft renormalization schemes. We also show how the couplings and masses in any two mass independent renormalization schemes are related.