A Ginzburg-Landau model of knotted flux-tube and glueball-like $f_J$ mesons

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 $J\le 2$, 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 ($leq1.7GeV$) are shown to be associated with the string excitations of the types $2_1^2$ and $K=3_1^{}$ in knot topologies.