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Dynamical equations for a Regge theory with crossing symmetry and unitarity. I. Introduction, and the case of weak coupling

Journal Article · · Phys. Rev., D; (United States)
;
A program for construction of a crossing-symmetric unitary Regge theory of meson-meson scattering is proposed. The construction proceeds through solution of a nonlinear functional equation, psi = G (psi), for certain partial-wave scattering functions psi. The functional equation is analogous to a conventional dynamical equation, in that the scattering amplitude is generated from input functions which describe the primary forces between mesons and possible inelastic effects. A solution of the equation provides a scattering amplitude having Mandelstam analyticity, exact crossing symmetry, exact unitarity below the production threshold, and meromorphy of partial waves in the right-half l plane, with the consequent Regge asymptotics. Inelastic unitarity (0 < or = eta (l,s) < or = 1) is not guaranteed, but may perhaps be achieved through constraints on inputs. In any case, the partial waves are bounded throughout the physical region; such a bound was not ensured in earlier schemes based on the Mandelstam iteration. In this first paper of a series, the equations are formulated for the case of weak coupling, in which no Regge poles enter the right-half l plane. Inelastic effects are described by crossed two-particle processes and assigned input functions. Later papers will treat the case of strong coupling, in which Regge trajectories are generated dynamically, and the extension of the formalism to include many coupled channels.
Research Organization:
Illinois Institute of Technology, Chicago, Illinois 60616
OSTI ID:
7304581
Journal Information:
Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 15:8; ISSN PRVDA
Country of Publication:
United States
Language:
English

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Related Subjects

645205* -- High Energy Physics-- Particle Interactions &amp; Properties-Theoretical-- Strong Interactions
Baryon No. = 0-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
COMPOSITE MODELS
CROSSING SYMMETRY
FIELD THEORIES
HADRON-HADRON INTERACTIONS
INTERACTIONS
MATHEMATICAL MODELS
MATRICES
MESON-MESON INTERACTIONS
NUCLEAR MODELS
PARTIAL WAVES
PARTICLE INTERACTIONS
PARTICLE MODELS
PERTURBATION THEORY
QUARK MODEL
REGGE POLES
S MATRIX
SCATTERING AMPLITUDES
SYMMETRY
UNITARITY
WEAK-COUPLING MODEL