Spherical Quantum Chromodynamics of Heavy Quark Systems

Abstract

We propose a model for Quantum Chromodynamics, obtained by ignoring the angular dependence of the gluon fields, which could qualitatively describe systems containing one heavy quark. This leads to a two dimensional gauge theory which has chiral symmetry and heavy quark symmetry. We show that in a light cone formalism, the Hamiltonian of this spherical QCD can be expressed entirely in terms of color singlet variables. Furthermore, in the large $N_c$ limit, it tends to a classical hadron theory. We derive an integral equation for the masses and wavefunctions of a heavy meson. This can be interpreted as a relativistic potential model. The integral equation is scale invariant, but renormalization of the coupling constant generates a scale. We compute the approximate beta function of the coupling constant, which has an ultraviolet stable fixed point at the origin.

20 pages (The theory has been shown to be asymptotically free by explicitly computing the beta function in a nonperturbative fashion)

References in corpus (3)

• Heavy Mesons in Two Dimensions
• Two dimensional baryons in the large N limit
• Two Dimensional Quantum Chromodynamics on a Cylinder

Cited by in corpus (2)

• Temperature- and Curvature Dependence of the Chiral Symmetry Breaking in 2D Gauge Theories
• The Thomas-Fermi approximation for gauge theories