Quark confinement and hadronic interactions

• Published in: Annals of physics 1986-08, Vol.170 (1), p.65-254
• Main Authors: Lenz, F, Londergan, J.T, Moniz, E.J, Rosenfelder, R, Stingl, M, Yazaki, K
• Format: Article
• Language: English
• Subjects: 645204 - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties; 645205 - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions, Baryon No. = 0- (-1987); ASYMPTOTIC SOLUTIONS; BOUND STATE; BOUNDARY CONDITIONS; COLOR MODEL; COMPOSITE MODELS; DIFFERENTIAL EQUATIONS; ELASTIC SCATTERING; EQUATIONS; EXCHANGE INTERACTIONS; FORM FACTORS; FUNCTIONS; GREEN FUNCTION; HADRON-HADRON INTERACTIONS; HAMILTONIANS; INTERACTIONS; LIE GROUPS; MANY-BODY PROBLEM; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATRICES; MOMENTUM TRANSFER; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE INTERACTIONS; PARTICLE MODELS; PARTICLE PROPERTIES; PHASE SHIFT; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM OPERATORS; QUARK MODEL; RESONANCE; S MATRIX; SCATTERING; SCHROEDINGER EQUATION; SU GROUPS; SUM RULES; SYMMETRY GROUPS; U GROUPS; U-1 GROUPS; WAVE EQUATIONS; WAVE FUNCTIONS
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/0003-4916(86)90088-6

A study of quark models for many-hadron systems is presented. The starting point in the construction of these nonrelativistic models is a proper formal definition of the concept of color singlet and nonsinglet clusters in a multiquark system which respects the exchange symmetry of the quarks. This definition provides a natural way to impose saturation of the confining forces. As a consequence, the resulting models are free from unphysical van der Waals forces whose presence is a characteristic difficulty in the conventional models based on superposition of two-body confining forces. The dynamics of the multiquark system are specified by defining the color projections of the Hamiltonian. These models make explicit the role of the color hidden dynamics in multihadron systems. The properties of these models are investigated in a study of the s-wave q 2− q 2 system. We develop new analytical methods appropriate for the study of many-body systems in the presence of confining interactions. These methods allow us to extract a variety of analytical results as well as exact numerical solutions, and they are employed to clarify the relation between the simple structure of the multiquark Hamiltonian and the wide variety of the resulting hadronic phenomena. The properties of bound and scattering states are studied for various models of the color hidden dynamics. Although the Hamiltonian contains only the confining force which determines the hadronic scale, phenomena are exhibited at a much lower energy scale. We investigate descriptions of the multiquark system in terms of hadronic degrees of freedom. Ambiguities in the formulation of such effective hadronic theories are discussed as well as their limitations in describing various physical observables. The fine tuning of the hadronic effective forces needed to generate the model phenomena which appear at a low-energy scale is understood from the underlying quark dynamics. Different signatures of quark degrees of freedom are studied, such as the appearance of threshold resonances or color hidden resonances, “EMC”-like modifications of the quark momentum distribution in hadronic bound states, or changes in the asymptotic behaviour of form-factors. The interdependence of these phenomenologically unrelated signatures is established, as well as their relation to properties of the color hidden dynamics.