The fundamental scale of QCD

TL;DR

This paper unifies various fundamental scales in QCD, such as the vacuum condensate, nucleon mass, string tension, and perturbative scale, using the field correlator method and background perturbation theory.

Contribution

It establishes connections among key QCD scales through the field correlator approach and demonstrates the resolution of IR singularities within this framework.

Findings

All QCD scales are connected via vacuum condensates.

IR singularities and renormalons are resolved in BPT.

The string tension relates to local condensates and perturbative scales.

Abstract

There are several scales in the QCD as the theory of strong interaction: the vacuum gluonic condensate (as the divergence of the dilatation current), the nucleon mass as the basic mass scale in our universe, which is connected to the string tension $\sigma$, and the perturbative QCD scale $\Lambda_{\rm QCD}$, which defines the scale of the renormalized perturbative expansions. In this paper we connect all these scales to the vacuum condensate, using the field correlator method, where the string tension is expressed in terms of nonlocal field correlators, which are connected to the local condensates, while the perturbative $\Lambda_V$ is connected to $\sigma$ in the framework of the Background Perturbation Theory (BPT). We also demonstrate how the IR singularities and IR renormalons disappear in BPT making the resulting theory internally consistent.