Applicability of a Representation for the Martin's Real-Part Formula in Model-Independent Analyses

TL;DR

This paper introduces a new representation for Martin's real-part formula, enabling a largely model-independent analysis of high-energy proton-proton scattering data, revealing peripheral effects and sign changes in the opacity function.

Contribution

It presents a novel representation for Martin's formula that allows for model-independent analysis of scattering data without requiring full scaling properties.

Findings

Peripheral inelastic overlap function above 2 fm

Zero in the opacity function in momentum transfer space

Analytical parametrization of empirical results

Abstract

Using a novel representation for the Martin's real-part formula without the full scaling property, an almost model-independent description of the proton-proton differential cross section data at high energies (19.4 GeV - 62.5 GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted inelastic overlap function presents a peripheral effect (tail) above 2 fm and the extracted opacity function is characterized by a zero (change of sign) in the momentum transfer space, confirming results from previous model-independent analyses. Analytical parametrization for these empirical results are introduced and discussed. The importance of investigations on the inverse problems in high-energy elastic hadron scattering is stressed and the relevance of the proposed representation is commented. A short critical review on the use of Martin's formula is also presented.