Scattering amplitudes to all orders in meson exchange

Conference · Mon Jan 01 00:00:00 EST 1990

OSTI ID:6360737

Silbar, R R; Mattis, M P

As the number of colors in QCD, N{sub C}, becomes large, it is possible to sum up all meson-exchange contributions, however arbitrarily complicated, to meson-baryon and baryon-baryon scattering. A semi-classical structure for the two-flavor theory emerges, in close correspondence to vector-meson-augmented Skyrme models. In this limit, baryons act as extended static sources for the classical meson fields. This leads to non-linear differential equations for the classical meson fields which can be solved numerically for static radial (hedgehog-like) solutions. The non-linear terms in the equations of motion for the quantized meson fields can then be simplified, to leading order in 1/N{sub C}, by replacing all factors of the meson field but one by the previously-found classical field. This results in linear, Schroedinger-like equations, which are easily solved. For the meson-baryon case the solution can be subsequently analyzed to obtain the phase shifts for the scattering and, from these, the baryon resonance spectrum of the model. As the warm-up, we have carried out this calculation for the simple case of {sigma} mesons only, finding sensible results. 8 refs., 3 figs.

• Research Organization: Los Alamos National Lab., NM (USA)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6360737
• Report Number(s): LA-UR-90-3579; CONF-9009285-1; ON: DE91001952; TRN: 91-000335
• Resource Relation: Conference: From fundamental fields to nuclear phenomenon conference, Boulder, CO (USA), 19-22 Sep 1990
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON-EXCHANGE MODELS
SCATTERING AMPLITUDES
LAGRANGIAN FUNCTION
MESON-BARYON INTERACTIONS
PHASE SHIFT
QUANTUM CHROMODYNAMICS
SKYRME POTENTIAL
AMPLITUDES
FIELD THEORIES
FUNCTIONS
HADRON-HADRON INTERACTIONS
INTERACTIONS
MATHEMATICAL MODELS
NUCLEON-NUCLEON POTENTIAL
PARTICLE INTERACTIONS
PARTICLE MODELS
PERIPHERAL MODELS
POTENTIALS
QUANTUM FIELD THEORY
645204* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties