Glueball Spectroscopy in a Relativistic Many-Body Approach to Hadronic Structure

Abstract

A comprehensive, relativistic many-body approach to hadron structure is advanced based on the Coulomb gauge QCD Hamiltonian. Our method incorporates standard many-body techniques which render the approximations amenable to systematic improvement. Using BCS variational methods, dynamic chiral symmetry breaking naturally emerges and both quarks and gluons acquire constituent masses. Gluonia are studied both in the valence and in the collective, random phase approximations. Using representative values for the strong coupling constant and string tension, calculated quenched glueball masses are found to be in remarkable agreement with lattice gauge theory.Typeset using REVT E X 1 Our knowledge of the standard model cannot be considered complete until explicit gluonic degrees of freedom are found and understood [1]. In an effort to address this issue we advance a comprehensive framework for consistently describing and understanding hadron structure -including the glueball and hybrid sectors. The model is motivated in part by our previous studies of relativistic [4] The idea is to build on the known successes of the constituent quark model for heavy quarks by considering a many-body relativistic Hamiltonian in a quasiparticle basis where dynamical chiral symmetry breaking and massive gluon modes are explicit. Such a model incorporates an extensive Fock space but reduces to the simple quark model in the valence approximation. Furthermore, the simultaneous presence of quark and gluon degrees of freedom permits studying their mixture in hybrid and glueball states. This is especially important since glueball searches tend to occur in meson-rich regions of the hadron spectrum and also because it may be years before lattice gauge calculations provide significant insight. This letter focuses on the gluonic sector of the model Hamiltonian, presenting the glueball spectrum calculation and a discussion of the associated approximation schemes. In the summary we comment on other issues regarding applications to mesons, baryons and hybrids.There have been a variety of previous glueball studies: the Bag Model [6][7][8], QCD

Glueball spectrum from an effective hamiltonian

“…In Ref. [6] a phenomenological QCD Hamiltonian is combined with a BCS type vacuum, which leads to an effective mass for the constituent gluons. Results are given for the masses of the 0 ++ , 2 ++ , 0 −+ and 2 −+ glueballs including excited states.…”

“…[1]- [6]), or that use effective field theory descriptions such as working directly with the meson and baryon fields and adjusting the interaction parameters to experimental data [7]. The fundamental question remains however: how does one derive the effective theory consistently from the underlying more fundamental theory?…”

Schematic model for QCD at finite temperature

“…The observed sequence of levels cannot be explained by lattice gauge calculations and alternative methods have to be develop to explain the ordering [3]. Many effective models have achieved some success in describing the low energy regime of QCD [4,5]. These models have in common that only quarks and antiquarks are taken into account in the fermionic sector, while effective gluon potentials or states with a fix number of gluons are considered.…”

“…The parameters used in the calculations are: Ω = 9 (i.e., n c = 3 and n f l = 3), ω f = 1 3 GeV and ω b = 1.6 GeV. For V 1 = 0 GeV we obtain the first state at 4 3 GeV, corresponding to two quark-antiquark pairs. The next state is the glueball at 1.6 GeV.…”

Casimir scaling, glueballs, and hybrid gluelumps

“…This mechanism can be tested for instance in two-gluon glueballs. Direct evidence for such a system is still controversial, but several models [5][6][7][8] predict similar masses with values close to some of the experimental candidates [9,10]. The Casimir scaling hypothesis can also be tested in another system whose colour-spin structure is similar to the one of a glueball.…”