Regge behavior and fixed-angle scattering

Abstract

It is shown that, if one expresses the hadronic scattering amplitude as a sum of contributions from individual quark diagrams, each of these quark diagram contributions will obey a logarithmic scaling law in the high-energy fixed-angle limit. The ingredients of the proof are the linear motion of singularities in the complex angular-momentum plane and certain analyticity assumptions. The logarithmic scaling law emerges from the requirement of consistency of the behaviors of the individual quark diagram amplitude in the fixed-angle high-energy regime and in the Regge regime. Each quark diagram is found to have an intrinsic scale set by the slope of the «dominant» singularity in the complex angular-momentum plane of any one of its channels,i.e. the singularity whose trajectory lies highest for large negative values of that channel's Mandelstam variable. Complex angular-momentum plane singularities that are dominant in different channels of the same quark diagram must therefore have the same slope. As the Pomeranchuk singularity and Regge-Regge cuts are dominant in different channels of the same (twisted loop) quark diagram, it follows that they must have the same slope of ∼0.42 (GeV)−2. If one assumes a small number of quark diagrams to dominate the physical scattering amplitude at present energies and fixed angles, the differential cross-section is found also to obey a logarithmic scaling law which agrees with the wide-angle pp scattering data.