Higher Cumulants in the Cluster Expansion in QCD

TL;DR

This paper extends the stochastic vacuum model in QCD by including higher cumulants, specifically fourth cumulants, to analyze their effects on quark-antiquark potentials, flux tube formation, and scattering cross sections.

Contribution

It introduces higher cumulants into the cluster expansion in QCD, providing new insights into flux tube formation and scattering without altering the overall Gaussian model results.

Findings

Fourth cumulants can contribute to chromomagnetic flux tubes.

Fourth cumulants do not significantly change the total cross section in high-energy scattering.

The extended model offers a more detailed understanding of non-Gaussian effects in QCD.

Abstract

In this work an extension of the Gaussian model of the stochastic vacuum is presented. It consists of including higher cumulants than just the second one in the cluster expansion in QCD. The influence of nonabelian fourth cumulants on the potential of a static quark-antiquarkpair is examined and the formation of flux tubes between a static $q\bar{q}$-pair is investigated. It is found that the fourth cumulants can contribute to chromomagnetic flux tubes. Furthermore the contribution of fourth cumulants to the total cross section of soft high energy hadron-hadron scattering is examined and it is found that the fourth cumulants do not change the general picture obtained in the Gaussian model.