Glueball spectrum from an effective hamiltonian

Abstract

Using simple and general arguments we propose an effective Hamiltonian for the description of low-energy pure QCD. The Hamiltonian is a function of spatially constant collective modes. Its eigenstates can be organized into bands classified by the irreducible representations of an O(8) group. The latter also determine parity and charge conjugation of the states. The energy spectrum agrees well with the glueball spectrum as measured on the lattice, and in particular the level ordering with respect to spin is naturally explained.

Constituent gluon interpretation of glueballs and gluelumps

“…It is worth mentioning Ref. [33], in which a fully group-theoretical classification of glueballs is performed following a SU (3) × SU (2) scheme. But, the influence of gluon helicity through the helicity formalism has, to our knowledge, never been taken into account and leads to interesting and new results as we will see through this paper.…”

Schematic model for QCD. III. Hadronic states

“…Herewith we summarize, for completeness, the configurations which may appear in the gluon sector of the theory. In the model [8] the basic building blocks are effective gluons with color (1,1) and spin 1. The detailed group structure and the model Hamiltonian used is discussed in Ref.…”

“…For the notation of the groups, which appear in the many-gluons states, and their irreps see Ref. [8], where the general classification, i.e. with open color, can be deduced.…”

“…Concerning the use of symmetry principles, the work of [8] shows how the ordering of levels of many gluon states may be understood. In [8], the predictive power of the model, based on the microscopical treatment of gluons configurations, was tested by means of the spectrum related to exotic quantum numbers.The purpose of this work is to extend the model of Ref.[1] to describe the main structure of the hadronic spectrum of QCD. The essentials of the model are the following: a)color, flavor and spin degrees of freedom are taken explicitly into account to built the configurations, both in the quark and gluon sectors of the model; b)the quarks and antiquarks are placed in a s-state; c)the interaction of the quarks with the gluons proceeds via gluon pairs coupled to spin and color zero, only.…”

“…Its position is fixed as it was done in Ref. [8]. The coupling between quarks and antiquarks and gluons proceeds via this gluon-pair configurations.…”