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 onegluon-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 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 0 −+ , 1 −− and 3 −− three gluon glueball 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 the 1 −− glueball to be around 3.1−3.7 GeV, which is close to the mass of J/ψ and ψ ′ .

Constituent Gluons in Hybrid Mesons: A Group Theoretical Analysis

“…Table 2: Possible number of constituent gluons corresponding to the number of hybrid mesons upto multiplicityThe predictions discussed above do not give any information about the relationship between the number of constituent gluons and the masses of the observed hybrids since in exact SU (3) C symmetry, gluons are massless. However, there are specific models in literature, where the constituent gluons have effective mass of the order of 0.7 GeV [16,17] resulting in the following degenerate mass relation:…”

Short-range potentials from QCD at orderg2

“…Logically, the same kind of models -linear confinement and Coulomb term at long-and short-range respectively -has since been applied to describe exotic hadrons, like glueballs [4,5,6,7,8,9] and hybrids [12,13,14]. However, if the derivation of the Fermi-Breit potential between two quarks is a standard procedure, it is not the case for the interactions between two gluons (see for example the discrepancies between refs.…”

“…Since it is not the case in some approaches (see refs. [4,7]), we then discuss in sec. VII the influence of a possible nonzero mass for the exchanged gluons.…”

“…However, if the derivation of the Fermi-Breit potential between two quarks is a standard procedure, it is not the case for the interactions between two gluons (see for example the discrepancies between refs. [4,5,7]). Moreover, to our knowledge, the equivalent of the Fermi-Breit potential between a quark and a gluon…”

“…These bound states of two, three or more gluons are called glueballs. The theoretical computation of the glueball spectrum is a problem which currently deserves much interest, either in lattice QCD [3], or within the framework of effective models [4,5,6,7,8,9]. Other so-called "exotic" hadrons are hybrid mesons:…”