A New Scenario of Confinement and Hadron Spectra

TL;DR

This paper proposes a phenomenological model of the QCD vacuum with a constant background field, deriving hadron mass relations and predicting masses of exotic states, providing a new perspective on confinement and hadron spectra.

Contribution

It introduces a novel QCD vacuum model with a constant background field, deriving mass formulas and relations that align with observed hadron spectra and suggest four-quark states.

Findings

Derives a Regge relation from the model.

Predicts hadron mass bounds based on the background field.

Suggests four-quark states for certain mesons.

Abstract

This work presents a new phenomenological description of QCD vacuum where the color background field is depicted by a constant parallel vector with amplitude proportional to $\sigma\sim 0.28 GeV^2$. The familiar Regge relation can be derived directly in a classic meaning. A new mass formula of hadrons are conjectured to give a very consistent description of hadron mass spectra. The lower bounds of the baryon mass are determined to be $\sqrt{3\sigma}$ for nucleon and $\sqrt{5\sigma}$ for isospin-3/2 baryon. In the meanwhile, the mass-square differences of $1 {}^3 S_1$ and $1 {}^1 S_0$ meson states are obtained to be $2 \sigma$. We also predict the mass of the lowest four-quark state to be $\sqrt{4\sigma}$, which favors the $a_0(980)$ and $f_0(980)$ to be four-quark candidates. On the other hand, the effective heavy quark confinement potential is a direct result of this model.