Eikonalization and Unitarity Constraints

TL;DR

This paper extends eikonal models for proton-proton and antiproton-proton scattering, incorporating multiparticle states and unitarity constraints, revealing that the Odderon intercept must be ≤ 1 unless specific coupling conditions are met.

Contribution

It introduces a generalized eikonal formalism with up to three parameters for crossing even and odd Reggeon states, analyzing unitarity effects on scattering amplitudes.

Findings

Unitarity constrains the Odderon intercept to be ≤ 1.

The formalism accounts for all relevant intermediate multiparticle states.

Specific coupling conditions are required for the Odderon intercept to exceed unity.

Abstract

An extensive generalization of the ordinary and quasi-eikonal methods is presented for the $pp$ and $\bar pp$ elastic scattering amplitudes, which takes into account in a phenomenological way all intermediate multiparticle states involving the crossing even and crossing odd combinations of Reggeons. The formalism in this version involves a maximum of three parameters corresponding to the intermediate states which are possible in this configuration. The unitarity restriction is investigated and particular cases are discussed. An interesting result that emerges concerns the Odderon trajectory intercept: we find that unitarity dictates that this quantity {\it must} be below or equal unity unless a very peculiar equality exists between the coupling of the particles to the Pomeron and the Odderon.