Can one improve the Froissart bound?

TL;DR

The paper explores potential improvements to the Froissart bound by leveraging unitarity principles, especially elastic unitarity, and discusses the importance of averaging the cross-section for a well-defined problem.

Contribution

It proposes that the Froissart bound can be improved through better utilization of unitarity, emphasizing the role of elastic unitarity and averaging techniques.

Findings

Elastic unitarity can be key to improving the Froissart bound.

A suitable averaging of the cross-section is necessary for a well-defined problem.

The approach preserves the Lukaszuk--Martin bound.

Abstract

We explain why we hope that the Froissart bound can be improved, either qualitatively or, more likely, quantitatively, by making a better use of unitarity, in particular elastic unitarity. In other instances (Gribov's theorem) elastic unitarity played a crucial role. A preliminary requirement for this is to work with an appropriate average of the cross-section, to make the problem well defined. This is possible, without destroying the Lukaszuk--Martin bound.