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.

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

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