Model-Independent Femtoscopic Lévy Imaging for Elastic Proton-Proton Scattering

Abstract

A model independent Lévy expansion method is introduced to describe nearly Lévy shaped squared moduli of Fourier transforms. We apply this method to precisely characterize the most recent elastic scattering data of proton-proton collisions at √ s = 13 TeV. The results reveal a substructure of protons, which is found to be significantly larger and darker in high energy proton-proton collisions at the TeV scale, as compared to a rather faint and apparently overlooked substructure, that we also identify in elastic proton-proton scattering at the ISR energy range of √ s = 23 − 62 GeV.

Evidence of Odderon-exchange from scaling properties of elastic scattering at TeV energies

“…For example, as we have shown in Refs. [9,12], at low |t|, a stretched exponential form with α 0.9 describes the elastic scattering data from ISR to LHC energies reasonably well in a very broad energy range from 23.5 GeV to 13 TeV.…”

“…[31], and are also described above: a new domain may be indicated by a sudden change of B(s) in between 2.76 and 7 TeV and, similarly, the crossing of the critical σ el (s)/σ tot (s) = 1/4 line in multi-TeV range of energies, somewhere between 2.76 and 7 TeV. From the theoretical side, we have previously noted such as drastic change in the size of the proton substructure between the ISR and LHC energy domains from a dressed quark-like to a dressed di-quark type of a substructure [9,12] which may be, in principle, connected to such a dramatic change in the scaling behaviour of the elastic cross section. However, in this work we are focused on the scaling properties of the experimental data, and we are not intended to draw any model-dependent conclusions here.…”

“…Finally, let us note that the exponential shape of H(x) ≈ exp(−x) can be derived as a consequence of the analyticity of T el (s, ∆ ) at ∆ = 0 corresponding to the t = 0 optical point. However, our recent analysis of the differential elastic cross sections in the LHC energy range [9,12] suggests that this approximation breaks down since the TOTEM experiment observed a significant non-exponential behaviour already in the diffractive cone. In this case, at low values of |t|, nearly Lévy stable source distributions can be introduced, that lead to an approximate H(x) ∝ exp(−x α ) behaviour, where α = α Levy /2 ≤ 1.…”

“…In earlier studies of Refs. [12,13], the Odderon signatures have been identified and qualitatively described in a model-independent way using the power of the so-called Lévy imaging technique [9]. One of such signatures concern the presence of a dip-and-bump structure in the differential cross section of elastic pp collisions and the lack of such a structure in elastic p p collisions.…”

“…[9,[12][13][14] a substructure of the two distinct sizes has been identified in the low (a few tens of GeV) and high (a few TeV) energy domains, respectively. Besides, a new statistically significant feature in the b-dependent shadow (or inelasticity) profile has been found at the maximal available energy √ s = 13 TeV and represents a long-debated hollowness, or "black-ring" effect that emerges instead of the conventionally anticipated "black-disk" regime [12,14].…”