Unitarity and Finkelstein-Kajantie problem in diffraction hadron production

TL;DR

This paper addresses the Finkelstein-Kajantie problem in diffraction hadron production by developing a unitarization model based on Dyson-Schwinger equations, ensuring cross sections do not violate the Froissart-Martin bound.

Contribution

It introduces a unitarization approach using Dyson-Schwinger equations with Froissaron propagators and a 3-froissaron vertex, resolving the Finkelstein-Kajantie problem in diffraction production.

Findings

The model successfully resolves the Finkelstein-Kajantie problem.

Cross sections are kept within the Froissart-Martin bound.

Provides a consistent unitarization framework for diffraction processes.

Abstract

The diffraction production of many hadron showers separated by large rapidity gaps, when calculated within the standard pomeron approach, lead to cross sections rising much faster than Froissart-Martin bound. This is the point of Finkelstein-Kajantie problem. We consider the unitarization procedure based on Dyson-Schwinger equations with input froissaron propagators and 3-froissaron vertex (3f-vertex) depending on angular momenta of froissarons in it. The developed diffraction production model allows to resolve Finkelstein-Kajantie problem.