Odderon and proton substructure from a model-independent Levy imaging of elastic $pp$ and $p\bar p$ collisions

TL;DR

This paper introduces a model-independent Levy imaging method to analyze elastic scattering data, revealing differences in proton substructure and evidence for the Odderon effect in high-energy collisions.

Contribution

The paper develops a novel Levy imaging technique that directly reconstructs scattering amplitudes and identifies proton substructure and Odderon effects without relying on specific models.

Findings

Differences in $B(t)$ for $pp$ and $par p$ suggest Odderon presence.

Proton substructure sizes vary between ISR and LHC energies.

Model-independent sizes and cross-sections of proton substructure are provided.

Abstract

We describe a new and model-independent L\'evy imaging method of quality fits to the published datasets and reconstruct the amplitude of high-energy $pp$ and $p\bar p$ elastic scattering processes. This method allows us to determine the excitation function of the shadow profile $P(b)$, the elastic slope $B(t)$ and the nuclear phase $\phi(t)$ functions of $pp$ and $p\bar p$ collisions directly from the data. Surprisingly, notable qualitative differences in $B(t)$ for $pp$ and for $p\bar p$ collisions point towards an Odderon effect. As a by-product, we clearly identify the proton substructure with two different sizes at the ISR and LHC energies, that has striking similarity to a dressed quark (at the ISR) and a dressed diquark (at the LHC). We present model-independent results for the corresponding sizes and cross-sections for such a substructure for the existing data at different energies.