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.