# Convergence properties of L\'evy expansions: implications for Odderon and proton structure

## TL;DR

This paper investigates the convergence properties of the Levy expansion method for analyzing elastic hadron-hadron scattering, demonstrating its stability and effectiveness in revealing proton sub-structures and Odderon effects.

## Contribution

It introduces a new model-independent Levy expansion technique and shows its convergence and stability in analyzing differential cross sections in hadron scattering.

## Key findings

- Levy expansion converges and is stable for analyzing scattering data.
- Reveals sub-structures inside protons.
- Detects Odderon effects in proton scattering.

## Abstract

We detail here the convergence properties of a new model-independent imaging method, the L\'evy expansion, that seems to play an important role in the analysis of the differential cross section of elastic hadron-hadron scattering. We demonstrate, how our earlier results concerning the Odderon effects in the differential cross-section of elastic proton-proton and proton-antiproton scattering as well as those related to apparent sub-structures inside the protons were obtained in a convergent and stable manner.