Glueball States in a Constituent Gluon Model

Abstract

In a model with dynamical gluon mass, we investigate the bound states of two and three gluons via a Schrödinger 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 {\it 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 $M_{0^{++}}$ 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 3-gluon glueballs $0^{-+}$, $1^{--}$ and $3^{--}$ states are nearly degenerate, and their mass ratio with $2^{++}$ is largely independent of all parameters and consistent with lattice calculations. We estimate the mass of $1^{--}$ glueball to be $3.1-3.7$ GeV, which is close to the mass of $J/\psi$ and ${\psi }^{\prime }$.

Revtex, 7 pages with 7 eps figures

References in corpus (1)

• Partial wave analysiss of pbar-p -> piminus-piplus, pizero-pizero, eta-eta and eta-etaprime

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