[Paper Review] Predictions for proton-proton interaction cross-sections at LHC

A.B. Kaidalov, M. G. Poghosyan|arXiv (Cornell University)|Sep 16, 2011

Black Holes and Theoretical Physics2 references3 citations

TL;DR

This paper presents predictions for proton-proton total, elastic, single-diffractive, and double-diffractive cross-sections at LHC energies using a Regge field theory model based on Gribov's reggeon calculus with eikonalized multi-Pomeron exchange. The model successfully describes unitarity and Froissart bound saturation, predicting a logarithmic rise in total cross-sections, with total cross-sections reaching ~108 mb at √s = 14 TeV.

ABSTRACT

This is a short communication with a summary of results obtained with a model based on Gribov's reggeon calculus, which was proposed and applied to processes of soft diffraction at high energies. We present a brief description of the model and its predictions for various LHC energies.

Motivation & Objective

• To predict total, elastic, single- and double-diffractive cross-sections for proton-proton collisions at LHC energies.
• To describe high-energy soft hadronic interactions using a Regge field theory framework based on Gribov's reggeon calculus.
• To ensure unitarity and compliance with the Froissart bound by including multi-Pomeron exchange via eikonalization.
• To fit and describe experimental data on total and elastic cross-sections using contributions from Pomeron, f, and ω Reggeons.
• To extend the model to predict single- and double-diffraction dissociation cross-sections across LHC energy ranges.

Proposed method

• Uses Gribov’s reggeon calculus to model high-energy soft hadronic processes, focusing on Pomeron and Reggeon exchange.
• Applies eikonalization to multi-Pomeron exchange diagrams to restore unitarity and suppress unphysical growth of cross-sections.
• Parametrizes the elastic scattering amplitude using diagrams involving single Regge-pole exchange and multi-Pomeron exchange (branch points).
• Incorporates non-enhanced absorptive corrections to triple-Regge vertices and loop diagrams to describe diffraction dissociation.
• Fits triple-Regge coupling constants to experimental data on double-differential single-diffractive cross-sections.
• Uses the matrix element saturation condition with contributions from Pomeron, f-, and ω-Reggeons for pp and p̄p collisions.

Experimental results

Research questions

• RQ1 How do total and elastic proton-proton cross-sections scale with energy at LHC energies within a unitary Regge field theory model?
• RQ2 To what extent does eikonalized multi-Pomeron exchange reproduce the Froissart bound and ensure unitarity in high-energy pp scattering?
• RQ3 What are the predicted cross-sections for single- and double-diffractive dissociation at √s = 7, 10, and 14 TeV?
• RQ4 How well do the model’s predictions for the elastic slope B compare with experimental data across the LHC energy range?
• RQ5 What is the relative contribution of Pomeron and Reggeon exchanges to diffraction dissociation processes in pp collisions?

Key findings

• The model predicts a total cross-section of 108 mb at √s = 14 TeV, with a 3% uncertainty, consistent with the logarithmic rise expected from the Froissart bound.
• The elastic cross-section increases to 29.5 mb at √s = 14 TeV, with a predicted slope B of 20.5 GeV⁻², indicating a rise in forward scattering strength.
• Single-diffractive cross-sections rise to 14.3 mb for M² < 0.05s at √s = 14 TeV, with a 10% uncertainty, showing a slow growth with energy.
• Double-diffractive cross-sections reach 6.4 mb at √s = 14 TeV for Δη > 3, indicating a weak energy dependence consistent with Pomeron dominance.
• The model successfully describes existing data on total and elastic cross-sections for pp and p̄p collisions across the energy range from 0.9 to 14 TeV.
• The predictions for all cross-sections are stable and consistent with unitarity and the Froissart bound, with controlled uncertainties across the LHC energy spectrum.