Sign of the color-hyperfine splitting in charmonium P states as a test of perturbative QCD

• Published in: Physical review. D, Particles and fields Particles and fields, 1992-05, Vol.45 (9), p.3268-3271
• Main Authors: LICHTENBERG, D. B, PREDAZZI, E, RONCAGLIA, R
• Format: Article
• Language: English
• Subjects: 662230 - Quantum Chromodynamics- (1992-); 662240 - Models for Strong Interactions- (1992-); 662440 - Properties of Other Particles Including Hypothetical Particles- (1992-); ANGULAR MOMENTUM; BOSONS; BOTTOMONIUM; CHARMONIUM; Classical and quantum physics: mechanics and fields; COLOR MODEL; COMPOSITE MODELS; COULOMB FIELD; COUPLING CONSTANTS; ELECTRIC FIELDS; ELECTRODYNAMICS; ELEMENTARY PARTICLES; ENERGY LEVELS; Exact sciences and technology; FERMIONS; FIELD THEORIES; HADRONS; HYPERFINE STRUCTURE; MATHEMATICAL MODELS; MESONS; P STATES; PARTICLE MODELS; PARTICLE PROPERTIES; PERTURBATION THEORY; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; POSTULATED PARTICLES; QUANTUM CHROMODYNAMICS; QUANTUM ELECTRODYNAMICS; QUANTUM FIELD THEORY; QUARK MODEL; QUARKONIUM; QUARKS; SPIN; TESTING; Theory of quantized fields
• ISSN: 0556-2821; 1089-4918
• DOI: 10.1103/PhysRevD.45.3268

The sign of the difference in energy between the center of gravity of the {sup 3}{ital P} levels and the {sup 1}{ital P} level in heavy quarkonium is a test of the {alpha}{sub {ital s}}{sup 2} terms in perturbative QCD with a fixed coupling constant. Whereas this energy difference is zero in the Fermi-Breit approximation and greater than zero in a generalized Fermi-Breit approximation with asymptotically free potentials, the energy difference is negative in perturbative QCD calculations to one-loop order with a fixed {alpha}{sub {ital s}}. For potentials which reasonably agree with the spin-averaged data, the absolute magnitude of the splitting is calculated to be about 4 MeV or less in charmonium and 2 MeV or less in bottomonium. Since the energy of the {sup 3}{ital P} center of gravity in charmonium is known, a measurement of the energy of the {sup 1}{ital P} level is needed to discriminate between these different schemes. Although the {sup 1}{ital P} levels in bottomonium will probably be harder to measure, we also present results for bottomonium.