Angular Momentum Dependent Quark Potential of QCD Traits and Dynamical O(4) Symmetry

Abstract

A common quark potential that captures the essential traits of the QCD quark-gluon dynamics is expected to (i) interpolate between a Coulomb-like potential (associated with one-gluon exchange) and the infinite wall potential (associated with trapped but asymptotically free quarks), (ii) reproduce in the intermediary region the linear confinement potential (associated with multi-gluon self-interactions) as established by lattice QCD calculations of hadron properties. We first show that the exactly soluble trigonometric Rosen-Morse potential possesses all these properties. Next we observe that this potential, once interpreted as angular momentum dependent, acquires a dynamical O(4) symmetry and reproduces exactly quantum numbers and level splittings of the non-strange baryon spectra in the SU(2)_I* O(4) classification scheme according to which baryons cling on to multi-spin parity clusters of the type (K/2,K/2)*[(1/2,0) + (0, 1/2)], whose relativistic image is ψ_{μ_{1}...μ_{K}}. Finally, we bring exact energies and wave functions of the levels within the above potential and thus put it on equal algebraic footing with such common potentials of wide spread as are the harmonic-oscillator- and the Coulomb potentials.