Infrared Gluon Resummation and pp total cross-sections

TL;DR

This paper develops an eikonal model incorporating infrared-resummed soft gluons and a singular strong coupling constant to describe proton-proton total and elastic cross-sections, addressing key scattering features and high-energy saturation effects.

Contribution

It introduces a novel approach linking IR singularity of alpha_s to asymptotic freedom within an eikonal framework for hadron scattering.

Findings

Successfully models the optical point, forward peak, dip, and descent in differential cross-sections.

Explores the impact of IR singular alpha_s on high-energy saturation.

Identifies challenges in applying one-channel eikonal models to LHC data.

Abstract

We address here the problem of describing both the total and the elastic proton-proton cross-section, through the four outstanding features of hadron scattering: (i) the optical point; (ii) the forward peak, (iii) the dip and (iv) the subsequent descent at larger momentum transfers. These issues are discussed through an eikonal model for the elastic amplitude where the matter distribution in impact parameter space is given by resummed soft gluons down into the infrared (IR) region. The asymptotic growth of the total cross-section is obtained in a mini-jet model and the taming (saturation) at high energies is related to confinement realized here through an IR singular strong coupling constant alpha_s(Q^2). We present an ansatz that links the IR singularity of alpha_s(Q^2) to that of asymptotic freedom (AF) (at lowest order). Through this model, we illustrate the problems that arise in a generic one-channel eikonal model employed for a description of the measured differential elastic cross-section at LHC7.