Can Froissart Bound Explain Hadron Cross-Sections at High Energies?

TL;DR

This paper examines whether the Froissart bound can explain the slow increase of hadron cross-sections at high energies, concluding it is unlikely due to energy scale limitations.

Contribution

The paper reanalyzes the derivation of the Froissart bound in QCD and argues it cannot account for the experimentally observed slow growth of hadron cross-sections.

Findings

Froissart bound becomes restrictive only at energies above 10^5-10^6 GeV.

Standard derivation of Froissart bound does not justify observed cross-section behavior.

Small pion masses limit the bound's applicability at current energies.

Abstract

Experimentally observed slow growth of hadron cross-sections at high energies is a very intriguing but poorly understood property of QCD. It is tempting to explain the slow growth by saturation of Froissart bound or another similar universal mechanism. We reconsider derivation of Froissart bound in QCD in chiral limit and argue it can not justify experimentally observed behavior. Although the conventional Froissart-Martin bound should impose non-trivial constraint on the growth of hadron cross-sections, because of the small value of pion masses it will become restrictive only at currently unaccessible center-of-mass energies exceeding $10^5-10^6$ GeV.