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Scattering amplitudes to all orders in meson exchange

Conference ·
OSTI ID:6360737
;

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
Country of Publication:
United States
Language:
English

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Related Subjects

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