Shape of primary proton spectrum in multi-TeV region from data on   vertical muon flux
  It is shown, that primary proton spectrum, reconstructed from sea-level and underground data on muon spectrum with the use of QGSJET 01, QGSJET II, NEXUS 3.97 and SIBYLL 2.1 interaction models, demonstrates not only model-dependent intensity, but also model-dependent form. For correct reproduction of muon spectrum shape primary proton flux should have non-constant power index for all considered models, except SIBYLL 2.1, with break at energies around 10-15 TeV and value of exponent before break close to that obtained in ATIC-2 experiment. To validate presence of this break understanding of inclusive spectra behavior in fragmentation region in p-air collisions should be improved, but we show, that it is impossible to do on the basis of the existing experimental data on primary nuclei, atmospheric muon and hadron fluxes. 
A.V. Yushkov and A. A. Lagutin