A Ginzburg-Landau model of knotted flux-tube and glueball-like $f_{J}$ mesons

TL;DR

This paper models knotted flux-tubes in QCD using a Ginzburg-Landau framework, predicting glueball-like meson spectra and confirming the vacuum as a type-II superconductor consistent with lattice data.

Contribution

It introduces a dual Ginzburg-Landau model for knotted flux-tubes in QCD, linking topological knot structures to meson spectra and vacuum properties.

Findings

SU(2) QCD vacuum is a type-II superconductor with κ=√3

Predicted low-lying $f_J$ meson states are linked to specific knot topologies

Model results align with lattice data and experimental meson masses

Abstract

A dual Ginzburg-Landau model of the knotted chromo-electric flux-tube is revisited, in which the covariant decomposition of gluon field and the random phase approximation are used. It is shown that the SU(2) QCD vacuum is of type-II superconductor, with the Ginzburg-Landau parameter $\kappa = \sqrt{3}$, being independent of the magnetic condensate and strong coupling used, and consistent with the lattice data. The mass spectrum of a number of $f_{J}$ meson states with $J\leq 2$, which are taken to be of glue dominate, are computed with help of the energies of the knotted(linked) QCD fluxtubes. The low-lying $f_{J}$ states ($leq 1.7GeV$) are shown to be associated with the string excitations of the types $2_{1}^{2}$ and $K=3_{1}^{{}}$ in knot topologies.