Nonlocal theory of single pion photoproduction

Abstract

A nonlocal interaction theory is formulated for photoproduction processes by introducing a form function. An effective nonlocal, Lorentz invariant and gauge invariant Lagrangian density for the four-field interaction that gives rise to a production amplitude is constructed. The general structure of the form function is investigated by using some restrictions of the form function. For low energy π0 photoproduction an explicit form of the Fourier component of the form function is obtained. The physical model of the present formalism is to assume, similar to the strong absorption model, that the system in intermediate states is confined in a finite domain of space. For π0 production the linear dimension of this domain is obtained to beω0 = 3·88F. It is important to observe that the extent of electromagnetic distribution in a nucleon is also nearly the size ofω0. This is believed to be the reason that in low energy pion photoproduction the effects of electromagnetic structure of a nucleon are irrelevant. The unpolarized differential and total cross sections are calculated forπ0 production in helicity representation and the predictions are found to be in good agreement with experiments.