2006/09/29 by C. B. Compean, Compean, C. B., M. Kirchbach +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Mathematical Physics (math-ph) #Nuclear Theory (nucl-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum Physics (quant-ph) #hep-ph #math-ph #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.48550/arxiv.nucl-th/0610001
Invited talk given by one of us (M.K.) at the Mini-Workshop Bled 2006, "Progress in Quark Models", Bled, Slovenia, July 10-17, 2006. 8 figures
arxiv created 2006/09/29 · openalex publication_date 2006/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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_μ1...μK. 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.