Analysis of pion nucleon scattering at high energies

Abstract

A phenomenological analysis of Pion Nucleon scattering data at high and intermediate energies and at all angles has been undertaken. At high energies say above 5 GeV/c the differential cross sections are strongly peaked in the forward and backward directions and these peaks can be adequately explained by a small number of leading Regge poles in t channel (for the forward peak) and u channel (for the backward peak). In this work new Regge fits are performed to all available recent high energy data, to obtain the Regge parameters. Below 5 GeV/c down up to 2 GeV/c the forward and backward peaks are still very conspicuous and can still be explained by the Regge poles used in the high energy fits. So it is thought to be convenient to define an amplitude Fp(s,t,u) which is the difference between the total and the Regge amplitudes. A parametric form of this amplitude (viz, Fg) was taken to fit all data between 2 to 5 GeV/c simultaneously, while the parameters of the Regge Amplitudes are held fixed to their values obtained from high energy fits. First all Π-p scattering data were fitted to get I = 3/2 amplitude then Π- p and charge exchange data were fitted to obtain I = 1/2 amplitudes. Two different ways of parameterising Fg (s,t,u) have been attempted. The first was based on the direct channel Regge pole model with Khuri modification, and the second was of a simpler and less sophisticated phenomenological form, the amplitudes being expressed as a power series in Cos 0 ( being scattering angle) with energy dependent coefficients', the second method was found particularly successful in the present work. Partial Wave projections of both T = 1/2 and T = 3/2 amplitudes were made and the phase shifts were obtained for both the isospin amplitudes. Possibilities of the existence of resonances in the energy region 2 to 5 GeV are discussed.