Cross sections, multiplicity and moment distributions at the LHC

TL;DR

This paper investigates hadron-hadron scattering at the LHC by applying unitarity constraints, incorporating non-perturbative QCD effects, and providing predictions for multiplicity distributions and moments consistent with experimental data.

Contribution

It introduces a unitarity-based framework with non-perturbative QCD effects to connect various scattering observables and predicts multiplicity moments at high energies.

Findings

Reproduces experimental oscillations in $H_q$ moments.

Provides predictions for total and elastic cross sections.

Analyzes theoretical uncertainties due to gluon mass scale.

Abstract

The unitarity of the $S$-matrix requires that the absorptive part of the elastic scattering amplitude receives contributions from both the inelastic and the elastic channels. We explore this unitarity condition in order to describe, in a connected way, hadron-hadron observables like the total and elastic differential cross sections, the ratio of the real to imaginary part of the forward scattering amplitude and the inclusive multiplicity distributions in full phase space, over a large range of energies. We introduce non-perturbative QCD effects in the forward scattering amplitude by using the infrared QCD effective charge dependent on the dynamical gluon mass. In our analysis we pay special attention to the theoretical uncertainties in the predictions due to this mass scale variation. We also present quantitative predictions for the $H_{q}$ moments at high energies. Our results reproduce the moment oscillations observed in experimental data, and are consistent with the behavior predicted by QCD.