Glueballs on a transverse lattice

Abstract

Accurate non-perturbative calculations of glueballs are performed using light-front quantised SU(N) gauge theory, to leading order of the 1/N expansion. Based on early work of Bardeen and Pearson, disordered gauge-covariant link variables M on a coarse transverse lattice are used to approximate the physical gauge degrees of freedom. Simple energetics imply that, at lattice spacings of order the inverse QCD scale, the effective light-front Hamiltonian can be expanded in gauge-invariant powers of M: a colour-dielectric expansion. This leads to a self-consistent constituent structure of boundstates. We fix the couplings of this expansion by optimising Lorentz covariance of low-energy eigenfunctions. To lowest non-trivial order of the expansion, we have found a one-parameter trajectory of couplings that enhances Lorentz covariance. On this trajectory the masses of nearly-covariant glueball states exhibit approximate scaling, having values consistent with large-N extrapolations of continuum results from other methods. There is very little variation with N in pure Yang-Mills theory: the lightest glueball mass changes by only a few percent between SU(3) and SU(infinity). The corresponding light-front wavefunctions show an unconventional structure. We also examine restoration of rotational invariance in the heavy-source potential.Comment: 24 pages, 21 figure

Generalized Parton Distributions of the Pion on the Transverse Lattice

“…values of Q at ξ = 0. H(x, 0, 0) is the conventional structure function [3], which exhibits rising Regge behaviour at small x characteristic of a system with gluonic degrees of freedom. It falls to zero precipitously near x → 1.…”

“…where, on the right hand side, the wavefunction is convoluted with a kernel K [3] that exchanges lightcone momentum, creates, and annihilates partons. Typically the kernel is singular when one or more momentum fractions x i vanish in this equation.…”

“…Following earlier work [2], van de Sande and the author [3] recently computed numerically the lightcone wavefunctions of the pion in transverse lattice gauge theory at large N c [4,5] (see also [6]). In this talk, these wavefunctions will be applied to deduce the generalised quark parton distributions in both transverse momentum and position space [7].…”

“…[3], which contains details of the construction of the lightcone Hamiltonian and Fock space, the renormalisation and the determination of various residual couplings appearing in the lightcone hamiltonian. The couplings were constrained by optimizing covariance of low-lying meson and glueball wavefunctions, rotational invariance of the heavy source potential, and fitting two phenomenological parameters in the meson sector, conveniently taken to be f π and the ρ meson mass.…”

“…[3] were subject to a number of cutoffs. Firstly, the transverse lattice spacing is held fixed at a ≈ 300MeV −1 , representing the renormalisation scale.…”