# L\'evy imaging of elastic hadron-hadron scattering: Odderon and inner structure of the proton

## TL;DR

This paper introduces a model-independent Le9vy imaging method to analyze elastic hadron-hadron scattering, revealing differences between proton-proton and proton-antiproton interactions, evidence of the Odderon, and insights into proton substructure at various energies.

## Contribution

The paper develops a novel Le9vy imaging technique for reconstructing scattering amplitudes, providing new evidence of the Odderon and detailed proton substructure.

## Key findings

- Differences in B(t) and a3(t) between pp and pe1p collisions indicating Odderon effects.
- Identification of two distinct proton substructures at different energies.
- Extraction of the shadow profile P(b) from experimental data.

## Abstract

A novel model-independent L\'evy imaging method is employed for reconstruction of the elastic $pp$ and $p\bar p$ scattering amplitudes at low and high energies. The four-momentum transfer $t$ dependent elastic slope $B(t)$, the nuclear phase $\phi(t)$ as well as the excitation function of the shadow profile $P(b)$ have been extracted from data at ISR, Tevatron and LHC energies. We found qualitative differences in properties of $B(t)$ and $\phi(t)$ between $pp$ and for $p\bar p$ collisions, that indicate an Odderon effect. A proton substructure has also been identified and found to have two different sizes, comparable to that of a dressed quark at the ISR and of a dressed diquark at the LHC energies, respectively.