Reggeon field theory (Schlögl's first model) on a lattice: Monte Carlo calculations of critical behaviour: P. Grassberger and A. de la Torre. Faculty of Physics, University of Wuppertal, Germany

Abstract

A method is suggested for calculating the elastic amplitude as the shadow of multiparticle processes. This does not require explicit formulae for the production amplitudes, but depends only on the following assumptions: (a) Regge behaviour, (b) semi-local duality, (c) exchange degeneracy. The system is multiperipheral in general structure but because of the assumption (a)-(c), it incorporates such features as the clustering of final particles and provides a proper treatment of quantum numbers, phases, and resonance spins. As a result, the unitarity sum separates automatically into two components corresponding respectively to pomeron and ordinary reggeon exchange, each of which is seen to have the correct qualitative dependence on the quantum numbers, the energy s, and the momentum transfer t. Quantitatively, the elastic amplitude is given in terms of a triple-Regge vertex, for which we suggest a simple parametization based on a detailed study of existing experiment and the Veneziano model. The method is then applied to calculate the elastic amplitudes for π±p, K±p and pp within the range 6 < s < 50 and 0 > t > −0.5 GeV2. Semi-quantitative agreement is obtained with experiment with essentially no free parameter. Although the investigation is restricted at present to elastic scattering as the shadow of only the non-diffractive component satisfying (a)-(c), the method is believed to apply also to other diffractive processes, and may be regarded as the first step in an iterative solution of the full unitarity equation.