On the High Energy Behaviour of The Total Cross Section in the QCD Dipole Model

TL;DR

This study numerically investigates high energy QCD scattering amplitudes using the dipole model, incorporating fluctuations, saturation, and confinement effects, showing the total cross section saturates the Froissart-Martin bound with realistic coefficients.

Contribution

It extends previous dipole model analyses by including fluctuations, wave function saturation, and nonperturbative effects, demonstrating the saturation of the Froissart-Martin bound in a comprehensive numerical framework.

Findings

Total cross section grows proportional to the square of the logarithm of energy.

Inclusion of confinement effects leads to saturation of the Froissart-Martin bound.

Saturation and non-leading effects influence the proportionality coefficient.

Abstract

In this paper we perform a numerical study of the tranverse expansion of hadronic scattering amplitudes in the dipole picture of high energy QCD. We go beyond the mean field approximation by including fluctuations and also wave function saturation effects, and the evolution with both a fixed and a running coupling is investigated. We also study the nonperturbative aspects, and as has been predicted earlier, our results indicate that the Froissart-Martin bound is saturated once confinement effects are included in the evolution. Thus the total cross section increases proportional to the square of the logarithm of the cms energy. Furthermore it is seen that we obtain a reasonable value for the proportionality coefficient. The impact of saturation and non-leading effects on this coefficient is also studied.