Unitarization of elastic amplitude on SO_mu(2.1) group

TL;DR

This paper generalizes the eikonal representation for elastic scattering amplitudes using SO_mu(2.1) group expansion, addressing small impact parameters, large transverse momenta, and backward scattering effects.

Contribution

It introduces a group-theoretic approach to unitarize elastic amplitudes, extending the eikonal model to more complex scattering scenarios.

Findings

Modified unitarity relation with backward scattering included

Models of profile functions for reflection and absorption cases

Generalized framework for elastic amplitude unitarization

Abstract

We obtain the solution of the unitarity equation for the elastic processes in terms of the expansion coefficients of the amplitude as a function on the SO_mu(2.1) group. This approach is a generalization of the eikonal representation to the case of small impact parameters and large transverse momenta. We show how the unitarity relation is modified when the contributions of the backward scattering are taken into account. We discuss the simplest models of the profile functions in the following cases: full reflection, full absorption and the combination of these two cases.