Experimental study of structure functions and sum rules in charge-changing interactions of neutrinos and antineutrinos on nucleons

High-energy exclusive and inclusive cross sections are discussed in terms of their dependence on the transverse-position variables (impact parameters) of incident and outgoing particles. The objective is to clarify the points of conflict and agreement of various models with each other and with intuitive ideas based on macroscopic collisions. First the impact parameter representation of states and amplitudes is reviewed. New impact parameter conservation laws and sum rules are derived from Lorentz invariance. The generalized optical theorem of Mueller is extended to give the impact parameter distribution of produced particles. Mueller-Regge behaviour is shown to imply three-dimensional limiting fragmentation in (impact parameter, rapidity)- space and a specific linear structure of the final-state particle density in the central region of this space. The predictions of weak- and strong-coupling multiperipheral models, the φ³ ladder eikonal model and the dual resonance model are presented, with emphasis on the dependence of average multiplicity on impact parameter and the dependence of mean square impact parameter on multiplicity. Special techniques for strong-coupling multiperipheral models are used to study the breakdown of the random-walk impact-parameter structure of the weak-coupling case, and to show explicitly that the average multiplicity is a decreasing function of impact parameter in the strongly coupled ABFST model.