Simple Lévy α-Stable Model Analysis of Elastic pp and pp¯ Low-|t| Data from SPS to LHC Energies

A simple Lévy α-stable (SL) model is used to describe the data on elastic pp and pp¯ 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 α parameter of the model has an energy-independent value of 1.959 ± 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 pp¯ 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 ≲s≲ 4 GeV.