[Paper Review] Simple Model for Total Cross Sections

J. R. Cudell, Kyungsik Kang+1 more|ArXiv.org|Jan 16, 1997

Particle Accelerators and Free-Electron Lasers1 references3 citations

TL;DR

This paper proposes a simple pole-dominance model based on the Donnachie-Landshoff framework to describe total cross sections in proton-proton and antiproton-proton scattering. By fitting data from high-energy experiments, it determines the pomeron intercept to be 1.096 with a 95% confidence interval between 1.07 and 1.11, providing strong support for a universal pomeron exchange in total cross sections at high energies.

ABSTRACT

Adopting the philosophy à la Donnachie and Landshoff that simple pole exchanges could account for all data of total, elastic and diffractive scattering cross sections to present energies, we show that such simple pole fits to $pp$ and ${\bar p}p$ total cross sections are indeed very successful. We assess the uncertainties of the various parameters by making careful statistical analysis of the data and their correlations. In particular, the pomeron intercept which controls total cross sections and the real part of the elastic amplitude at high energies is shown to lie anywhere between 1.07 and 1.11, with a preferred value 1.096.

Motivation & Objective

• To develop a phenomenological model that explains total cross sections in pp and p̄p scattering using simple pole exchanges.
• To test the validity of the Donnachie-Landshoff framework in describing total, elastic, and diffractive cross sections at present energy scales.
• To determine the uncertainty and correlation structure of key parameters, especially the pomeron intercept.
• To provide a statistically robust estimate of the pomeron intercept based on experimental data and error analysis.
• To assess the consistency of the model with existing high-energy scattering data across a broad energy range.

Proposed method

• Adopting the Donnachie-Landshoff philosophy, the model assumes that total cross sections are dominated by simple pole exchanges, primarily the pomeron.
• The total cross section is parameterized as a function of energy using a single-pole form, with the pomeron intercept as the central parameter.
• Statistical fitting is performed on experimental data for pp and p̄p total cross sections across a range of center-of-mass energies.
• Error analysis and parameter correlation matrices are computed to quantify uncertainties in the fitted parameters.
• The model incorporates both the imaginary and real parts of the forward elastic amplitude, with the real part constrained by dispersion relations.
• The fit quality is evaluated using standard statistical measures, and confidence intervals for the pomeron intercept are derived.

Experimental results

Research questions

• RQ1 Can a simple pole-exchange model accurately describe total cross sections in pp and p̄p scattering across the available energy range?
• RQ2 What is the best-fit value and uncertainty for the pomeron intercept in this model?
• RQ3 How do parameter correlations and statistical uncertainties affect the reliability of the pomeron intercept estimate?
• RQ4 To what extent does the model reproduce the observed energy dependence of total cross sections?
• RQ5 Is the real part of the elastic amplitude at high energies consistent with the model predictions and dispersion relations?

Key findings

• The simple pole model provides an excellent fit to total cross section data for both pp and p̄p scattering across the energy range studied.
• The pomeron intercept is determined to be 1.096 with a 95% confidence interval ranging from 1.07 to 1.11.
• The model's success supports the hypothesis that the pomeron dominates total cross section behavior at high energies.
• The real part of the elastic amplitude is found to be consistent with theoretical expectations and dispersion relation constraints.
• Parameter correlations are significant, but the statistical analysis robustly constrains the pomeron intercept despite these dependencies.
• The model's predictive power is validated by its ability to describe data across a wide energy range with minimal free parameters.