Quasi-eikonal and quasi-U-matrix unitarization schemes beyond the Black Disk Limit

TL;DR

This paper examines quasi-eikonal and quasi-U-matrix unitarization schemes beyond the Black Disk Limit, revealing unitarity violations and oscillation structures, and discusses parameter choices to restore unitarity.

Contribution

It analyzes the unitarity properties of generalized unitarization models beyond the Black Disk Limit and proposes ways to restore unitarity through parameter adjustments.

Findings

Unitarity violations occur at high energies in both models.

Oscillation structures are observed in the imaginary part of the amplitude at large impact parameters.

Parameter tuning can potentially restore unitarity in these models.

Abstract

Quasi-eikonal and quasi-U-matrix unitarization of the standard Regge-pole amplitude for ${\alpha}(0)>1$ have been considered. We show that some violation of unitarity even at high energy exists in both models. We have found in quasi-eikonal model a bump-oscillation structure of ${\rm Im}H(s,b)$ at large values of impact parameter $b$ but where ${\rm Im}H(s,b)$ is closed to the maximal value. We argue that it is possible to choose the parameter regulating deviation of generalized models from pure eikonal or U-matrix modes in order to restore unitarity.