Glueball states in a constituent gluon model

In a model with a dynamical gluon mass, we investigate the bound states of two and three gluons via a Schrodinger equation. The short distance potential is approximated by one-gluon exchange while the long distance part is assumed to be of a breakable string. We estimate the masses and in particular the sizes of low-lying bound states with no orbital angular momentum. By considering quantum-mechanical smearing of the gluon fields and normalizing to lattice results on M-o++ and M-2++, we find that the 0(++) glueball is rather small in size compared with the others. The fitted gluon mass is of order 600 to 700 MeV, which is reasonable. The 0(-+), 1(--), and 3(--) three gluon glueball states are nearly degenerate, and their mass ratio with 2(++) is largely independent of all the parameters and consistent with lattice calculations. We estimate the mass of the 1(--) glueball to be around 3.1-3.7 GeV, which is close to the mass of J/psi and psi'.