[Paper Review] Analytic Amplitude Models for Forward Scattering

K. Kang, J. R. Cudell+6 more|ArXiv.org|Nov 28, 2001

Advanced SAR Imaging Techniques3 citations

TL;DR

This paper develops and applies a set of statistical indicators to evaluate analytic amplitude models for forward hadronic scattering, favoring models with a universal log²s Pomeron term that extend fits down to √s = 4 GeV. The analysis identifies the PL2 Pomeron model as the most consistent with data, satisfying theoretical constraints and fitting total cross sections and real parts across multiple reactions.

ABSTRACT

We report on fits of a large class of analytic amplitude models for forward scattering against the comprehensive data for all available reactions. To differentiate the goodness of the fits of many possible parametrizations to a large sample of data, we developed and used a set of quantitative indicators measuring statistical quality of the fits over and beyond the typical criterion of the $\Chi^2 /dof$. These indicators favor models with a universal $ log^2 s$ Pomeron term, which enables one to extend the fit down to $\sqrt s = 4$ GeV.

Motivation & Objective

• To develop a systematic, quantitative framework for comparing the goodness of fit of diverse analytic amplitude models for forward scattering.
• To address the limitations of the standard χ²/dof criterion by introducing additional statistical indicators for model ranking.
• To test whether models with a universal log²s Pomeron term can consistently describe total cross sections and real parts across all available hadronic and electromagnetic reactions.
• To identify the most phenomenologically and theoretically consistent model among competing analytic amplitude parameterizations.
• To assess the applicability of the PL2 Pomeron model, which incorporates two types of Pomeron with distinct intercepts, across the full energy range down to √s = 4 GeV.

Proposed method

• The authors apply a comprehensive set of statistical indicators beyond χ²/dof to evaluate model fits across a large dataset of total cross sections and real parts of forward amplitudes.
• They use dispersion relations and the substitution rule s → s e^(-iπ/2) to relate the real part of the amplitude to its imaginary part, ensuring analyticity and unitarity.
• The models are tested against data from pp, p̄p, πp, Kp, γp, and γγ scattering across energies from √s = 4 GeV up to high energies.
• The PL2 Pomeron model is evaluated based on its ability to incorporate both the BFKL-like Pomeron (intercept >1) and a C=+1 three-gluon exchange Pomeron (intercept=1), ensuring theoretical consistency.
• The fitting procedure includes constraints from unitarity, crossing symmetry, and positivity, with model performance ranked using the new statistical indicators.
• The analysis extends to non-forward regions by considering the potential for future extension to differential cross sections and diffractive scattering.

Experimental results

Research questions

• RQ1 Which analytic amplitude model best describes the total cross section and real part of the forward scattering amplitude across all available reactions and down to √s = 4 GeV?
• RQ2 Can a universal log²s Pomeron term provide a consistent and unitarized description of forward scattering data across multiple hadronic and electromagnetic processes?
• RQ3 How do the new statistical indicators improve model discrimination beyond the standard χ²/dof criterion?
• RQ4 Does the PL2 Pomeron model, with two distinct Pomeron components, offer a better fit and theoretical consistency than simpler Regge or log s models?
• RQ5 To what extent can the current model framework be extended to include non-forward scattering and deep inelastic scattering data?

Key findings

• The statistical indicators developed in this work successfully differentiate between competing analytic amplitude models, favoring those with a universal log²s Pomeron term.
• Models incorporating the log²s Pomeron term provide a consistent fit to data down to √s = 4 GeV, extending the reach of previous analyses.
• The PL2 Pomeron model, which includes both a BFKL-like Pomeron (intercept >1) and a C=+1 three-gluon exchange Pomeron (intercept=1), is found to be the most consistent with data and theoretical constraints.
• The model satisfies unitarity by construction, respects the degeneracy of lower trajectories, and correctly describes the factorization of cross sections: (Hγp)² ≈ Hγγ × Hpp.
• The fit to the ρ parameter in pp and π⁺p scattering remains challenging, indicating a need for simultaneous fits to total cross sections and differential cross sections in the Coulomb-nuclear interference and diffractive cone regions.
• The study paves the way for future extensions to non-forward amplitudes and deep inelastic scattering, with the potential to generalize the ranking scheme for periodic model-data cross-assessment.