A Systematic Expansion of Running Couplings and Masses

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.

Comments: 16 pages, 3 figures, LaTeX; this version is accpeted publication at Modern Physics Letters A