New analytic unitarization schemes

TL;DR

This paper compares two unitarization schemes for hadron elastic scattering amplitudes, showing their fundamental properties are similar and proposing an interpolating scheme that bridges both methods.

Contribution

It introduces a unified unitarization approach that combines the standard eikonal and U matrix schemes, highlighting their shared properties and extending their applicability.

Findings

Both schemes share core properties regardless of functional form

U matrix and eikonal schemes can be extended to similar frameworks

A new interpolating unitarization scheme is proposed

Abstract

We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black disk limit includes the standard eikonal representation, while the other class, which goes beyond the black-disk limit to reach the full unitarity circle, includes the U matrix. It is shown that the basic properties of these schemes are independent of the functional form used for the unitarisation, and that U matrix and eikonal schemes can be extended to have similar properties. A common form of unitarisation is proposed interpolating between both classes. The correspondence with different nonlinear equations are also briefly examined.