Spherical Quantum Chromodynamics of Heavy Quark Systems

Details Spherical Quantum Chromodynamics of Heavy Quark Systems Spherical Quantum Chromodynamics of Heavy Quark Systems

1993-01-05

arxiv.org/abs/hep-ph/9301208v2

Phys.Rev.D48:3354-3363,1993

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevD.48.3354

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.

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