High-Energy Large-Momentum-Transfer Processes and Analyticity in Coordinate Space

Abstract

In nonrelativistic scattering theory, analytic potentials lead to exponentially decreasing differential cross sections for large momentum transfers. We attempt to adopt this connection for strong interactions. Since the differential cross section for proton-proton elastic scattering with large momentum transfers decreases exponentially with the momentum transfer, we postulate that the wave functions of strongly interacting particles are analytic functions of the coordinate variables. This assumption leads in a natural way to an exponential dependence on the transverse momentum transfer. On the basis of this, we speculate about various scattering processes involving a total of four strongly interacting particles, two incoming and two outgoing. The results are, in some cases, less specific than those of the previous consideration. Since it is natural to consider not only two-particle but also three-particle wave functions, the speculation is also extended to some processes where three particles are produced.