Glueballs in a Hamiltonian Light-Front Approach to Pure-Glue QCD

Abstract

We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it. The renormalization procedure is designed to produce a Hamiltonian that will yield physical states that rapidly converge in an expansion in free-particle Fock-space sectors. To make this possible, we use light-front field theory to isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to force its free-state matrix elements to quickly decrease as the difference of the free masses of the states increases. The cutoff violates a number of physical principles of light-front pure-glue QCD, including Lorentz covariance and gauge covariance. This means that the operators in the Hamiltonian are not required to respect these physical principles. However, by requiring the Hamiltonian to produce cutoff-independent physical quantities and by requiring it to respect the unviolated physical principles of pure-glue QCD, we are able to derive recursion relations that define the Hamiltonian to all orders in perturbation theory in terms of the running coupling. We approximate all physical states as two-gluon states, and use our recursion relations to calculate to second order the part of the Hamiltonian that is required to compute the spectrum. We diagonalize the Hamiltonian using basis-function expansions for the gluons' color, spin, and momentum degrees of freedom. We examine the sensitivity of our results to the cutoff and use them to analyze the nonperturbative scale dependence of the coupling. We investigate the effect of the dynamical rotational symmetry of light-front field theory on the rotational degeneracies of the spectrum and compare the spectrum to recent lattice results. Finally, we examine our wave functions and analyze the various sources of error in our calculation.

75 pages, 17 figures, 1 table

References in corpus (11)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• The glueball spectrum from an anisotropic lattice study
• Glueball masses and other physical properties of SU(N) gauge theories in D=3+1: a review of lattice results for theorists
• A Weak-Coupling Treatment of Nonperturbative QCD Dynamics to Heavy Hadrons
• Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
• Glueball Spectrum from an Effective Hamiltonian
• Effects of Massive Gluons on Quarkonia in Light-Front QCD
• Systematic Renormalization in Hamiltonian Light-Front Field Theory
• Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
• Flow equations for the quantum electrodynamics on the light-front
• Light-cone Hamiltonian flow for positronium. The numerical solutions

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• Proximity of $f_0(1500)$ and $f_0(1710)$ to the scalar glueball
• Special relativity constraints on the effective constituent theory of hybrids
• Spontaneously broken quark helicity symmetry
• Mesons in (2+1) Dimensional Light Front QCD. II. Similarity Renormalization Approach
• Light-front Hamiltonians for heavy quarks and gluons