Froissart Bounds for Amplitudes and Cross Sections at High Energies

TL;DR

This paper discusses the high-energy behavior of total cross sections, explaining the Froissart bounds, their origin, and their implications, including the possibility of their violation without breaching unitarity.

Contribution

It clarifies the origin and meaning of Froissart bounds and challenges the common belief about their violation implying unitarity breach.

Findings

Froissart bounds are rooted in fundamental principles.

Violation of log-squared bounds does not necessarily violate unitarity.

High-energy amplitudes can increase rapidly in nonphysical regions.

Abstract

High-energy behavior of total cross sections is discussed in experiment and theory. Origin and meaning of the Froissart bounds are described and explained. Violation of the familiar log-squared bound appears to not violate unitarity (contrary to the common opinion), but correspond to rapid high-energy increase of the amplitude in nonphysical regions.