[Paper Review] The Total Cross Section at the LHC: Models and Experimental Consequences

J. R. Cudell|ArXiv.org|Nov 18, 2009

High-Energy Particle Collisions Research16 references3 citations

TL;DR

This paper evaluates theoretical models of the total proton-proton cross section at the LHC, emphasizing that unitarization schemes and pomeron structure significantly affect predictions. It shows that standard experimental analyses may introduce systematic errors of 10–15 mb due to incorrect assumptions about the t-dependence of the slope and the real part of the amplitude, necessitating refined measurements of these observables to achieve 1% precision.

ABSTRACT

I review the predictions of the total cross section for many models, and point out that some of them lead to the conclusion that the standard experimental analysis may lead to systematic errors much larger than expected.

Motivation & Objective

• To assess the impact of different theoretical models of the total cross section on LHC experimental predictions.
• To identify systematic errors in standard total cross section measurements arising from incorrect assumptions about the t-dependence of the differential cross section and the ρ parameter.
• To evaluate how unitarization schemes—especially two-pomeron models with saturation or eikonal unitarization—affect total cross section predictions.
• To determine the implications of these models for achieving 1% precision in total cross section measurements at the LHC.
• To explore whether multiple-pole or two-pomeron structures in the complex j-plane better describe soft hadronic scattering data.

Proposed method

• The paper analyzes a wide range of models, including simple, double, and triple poles in the complex j-plane, to describe the total cross section.
• It uses the COMPETE collaboration's cleaned dataset of soft hadronic scattering data (pp, p̄p, π±p, K±p, γp, γγ) from √s ≥ 4 GeV to fit various parametrizations.
• The study applies unitarization schemes such as the saturation scheme and the standard one-channel eikonal to ensure partial-wave unitarity in high-energy predictions.
• It simulates LHC-like data using a unitarized two-pomeron model with Coulomb-nuclear interference and standard binning, then performs standard analysis to extract σ_tot.
• The paper compares the extracted σ_tot to the input model value to quantify systematic biases in conventional methods.
• It evaluates the t-dependence of the slope B and the real part of the amplitude (ρ) under different models, particularly in the saturation scheme.

Experimental results

Research questions

• RQ1 How do different pomeron models—simple pole, multiple poles, or two-pomeron systems—affect predictions of the total cross section at LHC energies?
• RQ2 To what extent do standard experimental assumptions about constant slope B and small ρ parameter introduce systematic errors in total cross section measurements?
• RQ3 What is the impact of unitarization schemes such as eikonal or saturation on the predicted total cross section and its energy dependence?
• RQ4 Can a two-pomeron model with a hard pomeron (intercept ≈1.4) and small coupling reproduce soft data while remaining consistent with LHC predictions?
• RQ5 What experimental corrections are necessary to achieve 1% precision in σ_tot, given the model-dependent t-dependence of B and ρ?

Key findings

• The COMPETE fit predicts a total cross section of 84–112 mb at √s = 10 TeV and 90–117 mb at 14 TeV, based on parametrizations with χ²/per point ≤ 1.
• A two-pomeron model with a hard pomeron (intercept ≈1.4) and small coupling (≤7% at √s < 200 GeV) provides a good fit to soft data and matches DIS results.
• Unitarization of the two-pomeron model via the saturation or eikonal scheme leads to total cross sections as high as 150 mb, depending on the scheme.
• Standard experimental analysis methods systematically overestimate σ_tot by about 10 mb (luminosity-dependent) or 15 mb (luminosity-independent) due to incorrect assumptions about t-dependence of B and ρ.
• The differential cross section cannot be approximated by e^{Bt} with constant B; the slope B and ρ parameter exhibit strong t-dependence, especially in the two-pomeron model.
• Achieving 1% precision in σ_tot requires dedicated studies of the t-dependence of B and ρ, as current assumptions lead to significant systematic biases.