Analytic properties of different unitarization schemes

TL;DR

This paper compares the analytic properties of eikonal and U-matrix unitarization schemes, showing their fundamental similarities and differences in asymptotic behavior and phase relations, with implications for scattering amplitude unitarization.

Contribution

It demonstrates that eikonal and U-matrix schemes share core properties and explores conditions for their equivalence, including phase bounds in the U-matrix scheme.

Findings

Both schemes can fill the full unitarity circle.

They can produce standard and non-standard asymptotic ratios.

A phase bound in the U-matrix scheme is derived.

Abstract

The analytic properties of the eikonal and U-matrix unitarization schemes are examined. It is shown that the basic properties of these schemes are identical. Both can fill the full circle of unitarity, and both can lead to standard and non-standard asymptotic relations for the ratio of the elastic cross section to the total cross section. The relation between the phases of the unitarized amplitudes in each scheme is examined, and it is shown that demanding equivalence of the two schemes leads to a bound on the phase in the U-matrix scheme.