Glueball as a bound state in the self-dual homogeneous gluon field

Abstract

Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex $p^2$--plane) and the weak coupling constant lead to the Regge behaviour of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the self-dual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless $0^{++}$ two-gluon state from the QCD generating functional in the one-gluon exchange approximation. The mass of this bound state is defined by the Bethe-Salpeter equation. The glueball mass is $1765\mathrm{MeV}$ for ${\alpha }_s=0.33$ if the gluon condensate is $<({\alpha }_s/\pi )GG>=0.012{\mathrm{GeV}}^4$.

Comments: 3 pages. Parallel talk given at the 5rd International Conference on Quark Confinement and the Hadron Spectrum (Confinement V), Gargnano, Italy, September 10-14, 2002. To appear in the proceedings