Connection Between Regge Behavior and Fixed-Angle Scattering

Abstract

The physical origins and dynamical details of Regge behavior are studied by examining a general class of theories which are capable of describing the observed large-momentum-transfer data and extending them into the intermediate-t range. The mechanism responsible for the smooth connection between the deep-scattering region and the Regge region is discussed in detail. We derive a convenient new form of the exact integral equation which describes generalized ladder graphs containing irreducible scattering amplitudes as the rungs. The limiting behavior of the Regge trajectories and residues are then calculated in both the single-channel and the more realistic coupled-channel cases. The trajectories are found to approach negative constants for large negative momentum transfer and the residues fall as powers in the same limit. Furthermore, since the forward and backward Regge regimes must join smoothly onto the same fixed-angle behavior, there are relations between a priori unrelated trajectory functions and residues. The standard properties of Regge poles, in particular factorization and signature, are shown to be present even though the basic, fixed-angle interaction possesses neither of these properties. These general considerations are then applied to the more specific constituent-interchange model. Here we find that the asymptotic behavior of the trajectories and residues are controlled by the form factors of the particles involved in the scattering. Finally, we elucidate the relationship between the constituent-interchange diagrams and the Harari-Rosner duality diagrams.