Convergence properties of Lévy expansions: implications for Odderon and proton structure

T Csörgő,A Ster,R Pasechnik

doi:10.1051/epjconf/201920606007

Abstract

We detail here the convergence properties of a new model-independent imaging method, the Lévy 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.

Highlights

The model-independent Lévy imaging technique [1,2,3] has recently become a useful, simple and unambiguous tool for extracting the physics information from the elastic hadron-hadron scattering data in a statistically acceptable manner
Indirect signatures of the Odderon exchange in differential elastic pp and ppcross-sections have been identified by using the Lévy imaging technique, known as the model-independent Lévy expansion method
A remarkable feature of the Lévy expansion of the elastic amplitude is that the diffractive cone is described fairly well by the Lévy-stable distribution in terms of two free parameters only, the Lévy scale parameter R characterising the length-scale of the

Summary

Introduction

The model-independent Lévy imaging technique [1,2,3] has recently become a useful, simple and unambiguous tool for extracting the physics information from the elastic hadron-hadron scattering data in a statistically acceptable manner. Given a power of the Lévy imaging technique operating with very few initial assumption for description of a large amount of data, a natural question arises about the stability and convergence of the associated Lévy series that are used for mapping the elastic amplitude with this method. In this contribution, we attempt to give a short description of the main results of the method, as well as demonstrate its convergence properties for a large variety of data sets at different scattering energies. The main results were summarized recently in two short contributions [2, 3], the convergence properties of this model-independent Lévy expansion method were not yet detailed in the literature before

Model-independent Lévy expansion of the scattering amplitude

Observables

Odderon

Findings

Summary and conclusions