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Journal of Particle Physics
JPP > Volume 3, Number 1, October 2019

A Physical Version of the QCD Confinement Scale(s)

Download PDF  (209.6 KB)PP. 1-4,  Pub. Date:November 8, 2019
DOI: 10.22606/jpp.2019.31001

Author(s)
Herbert M. Fried, Peter H. Tsang
Affiliation(s)
Department of Physics, Brown University, Providence, Rhode Island, United States
Department of Physics, Brown University, Providence, Rhode Island, United States
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 μ, and a “deformation parameter” ξ, which shrinks the transverse-quarkcoordinate separation distribution φ(b) away from Gaussian. With the mass scale μ defined as equal to the mass of each quark bound state, we show that ξ decreases with increasing bound state mass, mBS, using order-of-magnitude estimates which agree with obvious intuition. Our ξ-values, including a calculation for the recently detected 4-quark system, display the predicted behavior: ξ decreases with increasing mBS. Our results for φ(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.
Keywords
QCD, confinement, hadron spectrum, light front QCD
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