Proton–proton total cross-sections at VHE from accelerator data

Up-to-date estimates of proton–proton total cross-sections, σtotpp, at very high energies in the literature were obtained from cosmic rays (>1017 eV) by approximations using the measured proton–air cross-section at these energies. As σtotpp are measured with present day high energy colliders up to nearly 2 TeV in the centre of mass (∼1015 eV in the laboratory), several proven theoretical, empirical and semi-empirical parametrizations for interpolation at accelerator energies were used to extrapolate these measured values to get reasonable estimates of cross-sections at higher cosmic ray energies (∼1017 eV). The cross-section estimates from these two methods disagree by a discrepancy beyond statistical error. Here we use a phenomenological model based on the ‘multiple diffraction’ approach to successfully describe data at accelerator energies. Using this model, we then estimate σtotpp at cosmic ray energies. The model free-parameters used in the fit depend on only two physical observables: the differential cross-section and the parameter ρ. The model estimates of σtotpp are then compared with total cross-section data. Using regression analysis, we determine confidence error bands, analysing the sensitivity of our predictions to the data used in the extrapolations. This work reduces the width of the confidence band around ‘multiple diffraction’ model fits of accelerator data. With the data at 546 GeV and 1.8 TeV, our extrapolations are compatible with only the Akeno cosmic ray data, predicting a slower rise with energy than do other cosmic ray results and other extrapolation methods. We discuss our results within the context of constraints expected from future accelerator and cosmic ray experimental results.