A physical version of the QCD confinement scale(s)

TL;DR

This paper proposes a physical definition of the QCD confinement scale using a gauge-invariant non-perturbative approach, introducing parameters that describe confinement and showing their behavior aligns with physical intuition and recent holographic results.

Contribution

It introduces a novel physical framework for defining the QCD confinement scale with two parameters, linking the confinement mass scale to bound state properties and transverse quark fluctuations.

Findings

The deformation parameter $\xi$ decreases with increasing bound state mass.

The model's predictions for $\xi$ align with physical intuition and recent holographic analyses.

Results support a consistent physical picture of confinement in QCD.

Abstract

We suggest a physical definition of the confinement mass scale in QCD in the framework of non-perturbative, gauge invariant QCD, where all possible gluons exchanged between any pair of quark lines are included; and we insist that a stable, quark bound state should not and must not have transverse quark fluctuations larger than the Compton wavelength of the bound state particle itself. This is possible in our QCD formulation because there are two parameters which describe confinement, a mass scale $\mu$, and a "deformation parameter" $\xi$, which shrinks the transverse-quark-coordinate separation distribution $\varphi(b)$ away from Gaussian. With the mass scale $\mu$ defined as equal to the mass of each quark bound state, we show that $\xi$ decreases with increasing bound state mass, $m_{BS}$, using order-of-magnitude estimates which agree with obvious intuition. Our $\xi$-values, including a calculation for the recently detected 4-quark system, display the predicted behavior: $\xi$ decreases with increasing $m_{BS}$. Our results for $\varphi(b)$, when the quark bound state is a nucleon or heavier, then show agreement with the form of Gaussian momentum-space fall-offs in recent Light-Front holographic analyses.