Glueball Calculations in Large-NcGauge Theory

Abstract

We use the light-front Hamiltonian of transverse lattice gauge theory to compute from first principles the glueball spectrum and light-front wave functions in the leading order of the 1͞N c color expansion. We find 0 11 , 2 11 , and 1 12 glueballs having masses consistent with N c 3 data available from Euclidean lattice path integral methods. The wave functions exhibit a light-front constituent gluon structure. [S0031-9007(98) PACS numbers: 12.39. Mk, 11.15.Pg, 12.38.Gc, 12.38.Lg There is growing experimental evidence that glueballs, bound states of gluons in the SU(3) gauge theory quantum chromodynamics (QCD), have been discovered in the mass range 1.5-1.7 GeV [1][2][3]. But the confinement feature of QCD-interactions grow stronger as the energy of a process decreases-complicates any first principles calculation of the bound state problem. Until now, the most successful bound state calculations use a Euclidean spacetime lattice and simulate the path integral by Monte Carlo methods. These difficult calculations are now roughly consistent with the experimental signatures of glueballs [2,4], although much detail remains to be clarified. Therefore, it is important to have some independent method of calculating the properties of glueballs from first principles in gauge theory. In this Letter, we present our first results on this problem using an effective light-front Hamiltonian quantization (canonical quantization on a null plane in spacetime). This is the transverse lattice method, suggested originally by Bardeen and Pearson [5,6], which we have developed to the extent that quantitative calculations are now feasible [7,8].Although this work is ostensibly about glueballs, we have a more general motivation for developing the lightfront Hamiltonian formulation of gauge theory. A lightfront Hamiltonian has Lorentz-frame-independent wave functions. Together with the simplicity of the light-front vacuum, this leads to a field-theoretic realization of the parton model for hadrons on which so much understanding is based. The rich phenomenology in hadronic and nuclear physics that would follow from knowledge of the light-front wave functions is surveyed in the lectures of Brodsky [9]. We will use the glueball problem in QCD, which is especially difficult computationally, as a quantitative test of our light-front formalism.A detailed account of our methods and various quantitative tests that we have performed, mostly in 2 1 1 dimensions, can be found in Refs. [7,8], but we will briefly review the salient points below. We will work in the leading order of the 1͞N c expansion of SU͑N c ͒ gauge theory, which omits the 1͞N 2 c -suppressed glue configurations. It also removes "sea" quarks from our theory, an approximation also used in the Euclidean lattice calculations. We work on a coarse transverse lattice, using an effective potential tuned to minimize discretization errors. The ground state J P C 0 11 glueball mass is M 3.3 6 0.2 p s, where s ഠ 0.1936 GeV 2 is the string tension, and is consistent with SU(2) and SU(3) re...

Mesons on a transverse lattice

“…The colourdielectric hypothesis suggests that the renormalised trajectory [13], on which sufficiently long-distance observables take the same values as in the continuum limit, passes into this region at sufficiently large a [5,14]. Since weak-coupling perturbation theory is unlikely to be reliable for the construction of this trajectory at large a, it was suggested to use symmetry to reconstruct it [7,11]. In the case of a transverse lattice regulator, it is plausible that with the most general cut-off L, gauge and Poincaré symmetry are sufficient to identify a unique trajectory associated to QCD.…”

“…In this work, the light-cone Hamiltonian for a version of lattice QCD with quarks is investigated. It builds upon previous work of the author with B. van de Sande on the pure gauge theory [5][6][7], following an original idea of Bardeen et. al.…”

A study of heavy-light mesons on the transverse lattice

“…The degrees of freedom that enter the Hamiltonian are quark and antiquark creation operators at each site and link-fields (which, in the spirit of the color-dielectric approach [8], we take as general matrix fields) on the transverse links connecting the sites. For simplicity, we work in the large N C limit.…”

“…[7] and for glueball spectra in Ref. [8]). More recent applications of the color dielectric transverse lattice formulation to mesons at large N C can be found in Refs.…”

An Approximate Light Cone Method to Investigate Meson Structure

“…Transverse lattice techniques were employed quite successfully to pure glue calculations 5,6 . Encouraged by these results, the femtoworm approximation, which we describe briefly in the next section, was conceived to include the fermions on the transverse lattice, as well.…”