Heavy quarks and strong binding: A field theory of hadron structure

Abstract

We investigate in canonical field theory the possibility that quarks may exist in isolation as very heavy particles, ${M}_{\mathrm{quark}}>>1$ GeV, yet form strongly bound hadronic states, ${M}_{\mathrm{hadron}}\ensuremath{\sim}1$ GeV. In a model with spin-\textonehalf{} quarks coupled to scalar gluons we find that a mechanism exists for the formation of bound states which are much lighter than the free constituents. Following Nambu, we introduce a color interaction mediated by gauge vector mesons to quarantee that all states with nonvanishing triality have masses much larger than 1 GeV. The possibility of such a solution to a strongly coupled field theory is exhibited by a calculation employing the variational principle in tree approximation. This procedure reduces the field-theoretical problem to a set of coupled differential equations for classical fields which are just the free parameters of the variational state. A striking property of the solution is that the quark wave function is confined to a thin shell at the surface of the hadronic bound state. Though the quantum corrections to this procedure remain to be investigated systematically, we explore some of the phenomenological implications of the trial wave functions so obtained. In particular, we exhibit the low-lying meson and baryon multiplets of SU(6); their magnetic moments, charge radii, and radiative decays, and the axial charge of the baryons. States of nonvanishing momenta are constructed and the softness of the hadron shell to deformations in scattering processes is discussed qualitatively along with the implications for deep-inelastic electron scattering and dual resonance models.