Construction of π± photoproduction amplitudes at high energy from dispersion relations and local duality

Abstract

We investigate the charged-pion photoproduction amplitudes at all energies. We first show that low-energy s-channel helicity amplitudes exhibit, in most cases, a Bessel-function structure of zeroes. At high energy we therefore parametrize the imaginary parts of helicity amplitudes according to the Harari model, and compute the real parts using fixed- t dispersion relations as proposed recently. Such an evaluation of scattering amplitudes presents some very nice properties. In particular, it allows one to understand from duality arguments how the Born contribution may survive with full strength in the forward direction but not at large t-values. Furthermore FESR are identically satisfied by the model.