Shape of the primary proton spectrum in the multi-TeV region from data on the vertical muon flux

It is shown, that the primary proton spectrum, reconstructed from sea-level and underground data on the muon spectrum using the QGSJET 01, QGSJET II, NEXUS 3.97 and SIBYLL 2.1 interaction models, demonstrates not only a model-dependent intensity, but also a model-dependent form. For a correct reproduction of the muon spectrum shape the primary proton flux should have a non-constant power index for all considered models, except SIBYLL 2.1, with a break at energies around 10–15 TeV and a value of the exponent before the break close to that obtained in the ATIC-2 experiment.