Models for differential cross section in proton-proton scattering and their implications at ISR and LHC energies

Abstract

A few composite exponential models for the differential cross section (\(\frac{d\sigma }{d|t|}\)) are proposed to analyse the proton-proton (pp) elastic scattering at several energies. The parameters of these proposed models are found by fitting these models to the data for pp elastic differential cross section reported at CERN-ISR, LHC, and extrapolated energies of other models. Plots of the data have important features, including dip-bump structure and shrinkage of the forward peak. Dips produced by our proposed models overlap the dips produced by data for a broad energy range of \(\sqrt{s}\) = 23 GeV, 23.5 GeV, 27.23 GeV, 30.7 GeV, 44.7 GeV, 52.8 GeV, 62.5 GeV, 200 GeV, 800 GeV, 2.76 TeV, 7 TeV, 8 TeV, 13 TeV, 14 TeV, 15 TeV, and 28 TeV. Employing these proposed models, elastic cross section \({(\sigma _{\text {el}})}\), inelastic cross section \({(\sigma _{\text {inel}})}\), and total cross section \({(\sigma _{\text {tot}})}\) are calculated at all the energies. Calculated results are compared with experimental data and theoretical results of other models. Implications of these results (obtained by models) related to the structure and dynamics of the proton are discussed. The findings of this study emphasize the significance of combining theoretical and phenomenological approaches to accurately describe pp elastic scattering at high energies and provide significant information to future LHC experiments for the investigation of the differential cross section.