The Froissart bound for inelastic cross-sections

TL;DR

This paper establishes a tighter bound on the inelastic cross-section at high energies, showing it is at most one-quarter of the total cross-section bound, refining our understanding of scattering limits.

Contribution

It proves that the inelastic cross-section is bounded by a quarter of the Froissart bound for total cross-sections, providing a new theoretical limit.

Findings

Inelastic cross-section bound is one-fourth of the total Froissart bound.

Implications for high-energy scattering processes.

Refines theoretical constraints on particle interactions.

Abstract

We prove that while the total cross{}-section is bounded by $(\pi/m_\pi^2) \ln^2 s$, where $s$ is the square of the c.m. energy and $m_\pi$ the mass of the pion, the total inelastic cross{}-section is bounded by $(1/4)(\pi/m_\pi^2) \ln^2 s$, which is 4 times smaller. We discuss the implications of this result on the total cross{}-section itself.