ASYMPTOTIC BEHAVIOUR OF π-π SCATTERING AMPLITUDE AND SINGULARITIES IN COMPLEX L-PLANE IN STRIP APPROXIMATION

Abstract

The contribution of inelastic intermediate states to the singularities in complex l-planc and to the asymptotic behaviour of crossed channel are investigated in the strip approximation. The procedure is to solve the simultaneous equations suggested by Chew, Frautschi and Mandelstam by means of iteration method. The general iteration expressions for the s channel high energy amplitude f(s,t) and the t channel partial wave amplitude ft (t) are derived. It is shown that the divergence difficulty mentioned by Chew, Frautschi and Mandelstam is not present in the iteration results of the above f(s,t). The main results of first iteration are as follows: i) The total cross section falls slowly for not very high energies, but at the end tends to a constant. ii) The diffraction angular distribution will have a long tail. As the energy increases, this long tail extends towards the small angle region. iii) In the t channel a cut will appear along the real axis in complex l-plane; the right ending point of the cut is at l=1 when t=0, and moves to the left as t decreases, with a speed nearly half that of the vacuum pole. Higher order iterations are also investigated; the results are qualitatively analogous to those of first order.