Nonperturbative Results for Yang-Mills Theories

TL;DR

This paper explores nonperturbative features of SU(3) Yang-Mills theory using a modified beta function with a pole, linking it to the mass gap and comparing results with lattice calculations.

Contribution

It introduces a specific form of the beta function with a pole to analyze nonperturbative aspects of Yang-Mills theories and estimates the mass gap.

Findings

Mass gap estimated at 1.67 GeV, aligning with lattice results.

Behavior of physical quantities is smooth across the beta function pole.

Application to supersymmetric Yang-Mills theory with an exact beta function.

Abstract

Some non perturbative aspects of the pure SU(3) Yang-Mills theory are investigated assuming a specific form of the beta function, based on a recent modification by Ryttov and Sannino of the known one for supersymmetric gauge theories. The characteristic feature is a pole at a particular value of the coupling constant, g. First it is noted, using dimensional analysis, that physical quantities behave smoothly as one travels from one side of the pole to the other. Then it is argued that the form of the integrated beta function g(m), where m is the mass scale, determines the mass gap of the theory. Assuming the usual QCD value one finds it to be 1.67 GeV, which is in surprisingly good agreement with a quenched lattice calculation. A similar calculation is made for the supersymmetric Yang-Mills theory where the corresponding beta function is considered to be exact.