Hadronic total cross sections, Wilson loop correlators and the QCD spectrum

TL;DR

This paper demonstrates how to derive rising hadronic total cross sections in QCD using Wilson-loop correlators, predicting a Froissart-type energy dependence consistent with experimental data and relating it to the QCD spectrum.

Contribution

It introduces a nonperturbative approach to soft high-energy scattering in QCD that naturally explains the universality and magnitude of the total cross section growth.

Findings

Total cross sections follow a Froissart-type $\sigma_{tot} o B \log^2 s$ dependence.

The universal coefficient $B$ is predicted to be 0.22 mb, matching experimental values.

The approach links the cross section growth to the stable spectrum of QCD.

Abstract

We show how to obtain rising hadronic total cross sections in QCD, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlators. Total cross sections turn out to be of "Froissart"-type, i.e., the leading energy dependence is of the form $\sigma_{\rm tot} \sim B \log^2 s$, in agreement with experiments. The observed universality of the prefactor $B$ is obtained rather naturally in this framework. In this case, $B$ is entirely determined by the stable spectrum of QCD, and predicted to be $B_{th} = 0.22\, {\rm mb}$, in fair agreement with experiments.