Simple Lévy-$\alpha$ stable model analysis of elastic $pp$ and $p\bar{p}$ low-$|t|$ data from SPS to LHC energies

Abstract

A simple Lévy-$\alpha$ stable (SL) model is used to describe the data on elastic $pp$ and $p\bar{p}$ scattering at low-$|t|$ from SPS energies up to LHC energies. The SL model is demonstrated to describe the data with a strong non-exponential feature in a statistically acceptable manner. The energy dependence of the parameters of the model is determined and analyzed. The Lévy $\alpha$ parameter of the model has an energy-independent value of 1.959 $\pm$ 0.002 following from the strong non-exponential behavior of the data. We strengthen the conclusion that the discrepancy between TOTEM and ATLAS elastic $pp$ differential cross section measurements arises only in the normalization and not in the shape of the distribution of the data as a function of $t$. We find that the slope parameter has different values for $pp$ and $p\bar{p}$ elastic scattering at LHC energies. This may be the effect of the odderon exchange or the jump in the energy dependence of the slope parameter in the energy interval 3 GeV $\lesssim \sqrt{s}\lesssim$ 4 GeV.

arXiv comment30 pages, 5 figures, 1 table; presented at ISMD 2023; an extended introduction and an appendix are added

References in corpus (38)

• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Soft diffraction and the elastic slope at Tevatron and LHC energies: a multi-Pomeron approach
• Measurement of the total cross section from elastic scattering in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector
• Evidence for non-exponential elastic proton-proton differential cross-section at low |t| and sqrt(s) = 8 TeV by TOTEM
• Measurement of the total cross section from elastic scattering in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector
• Hadronic forward scattering: Predictions for the Large Hadron Collider and cosmic rays
• Bose-Einstein correlations for Levy stable source distributions
• Elastic differential cross-section measurement at $\sqrt{s}=13$ TeV by TOTEM
• Lévy-stable two-pion Bose-Einstein correlations in $\sqrt{s_{{}_{NN}}}=200$ GeV Au$+$Au collisions
• Hollowness in $pp$ and $p\bar{p}$ scattering in a Regge model
• The Interest of Large-t Elastic Scattering
• Measurement of the total cross section and $\rho$-parameter from elastic scattering in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Odderon and proton substructure from a model-independent Levy imaging of elastic $pp$ and $p\bar{p}$ collisions
• Test of the \boldmath{$\tau$}-Model of Bose-Einstein Correlations and Reconstruction of the Source Function in Hadronic Z-boson Decay at LEP
• Constituent quark and diquark properties from small angle proton-proton elastic scattering at high energies
• The soft and the hard pomerons in hadron elastic scattering at small t
• Excitation function of elastic $pp$ scattering from a unitarily extended Bialas-Bzdak model
• Excitation function of elastic $pp$ scattering from a unitarily extended Bialas-Bzdak model
• Proton structure and hollowness from Lévy imaging of $pp$ elastic scattering
• Shape of Proton and the Pion Cloud
• Elastic $pp$ and $\bar{p}p$ scattering in the models of unitarized pomeron
• Unified Model for Small-t and High-t Scattering at High Energies: Predictions at RHIC and LHC
• Parametrization of Bose-Einstein Correlations and Reconstruction of the Space-Time Evolution of Pion Production in e+e- Annihilation
• Coulomb Corrections for Bose-Einstein Correlations from One- And Three-Dimensional Lévy-Type Source Functions
• Proton (antiproton) elastic scattering at energies from FNAL to LHC in the tripole pomeron-odderon model
• Observation of Odderon Effects at LHC energies -- A Real Extended Bialas-Bzdak Model Study
• Asymptotic Energy Dependence of Hadronic Total Cross Sections from Lattice QCD
• Pion interferometry with Lévy-stable sources in $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions at STAR
• Hadronic total cross sections at high energy and the QCD spectrum
• Centrality dependent Lévy-stable two-pion Bose-Einstein correlations at the PHENIX experiment
• The interplay of hadronic amplitudes and Coulomb phase in LHC measurements at 13 $\mathrm{TeV}$
• Femtoscopic correlation measurement with symmetric Lévy-type source at NA61/SHINE
• Do we understand near-forward elastic scattering up to TeV energies?
• Fine structure of the diffraction cone: from ISR to the LHC
• Lévy $\alpha$-stable model for the non-exponential low-$|t|$ proton-proton differential cross section
• The ReBB model and its $H(x)$ scaling version at 8 TeV: Odderon exchange is a certainty
• Levy analysis of Bose-Einstein correlation in pp collisions at s 7 TeV measured with the ATLAS
• Levy HBT results at NA61/SHINE