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.

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