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

TL;DR

This paper investigates the primary proton spectrum in the multi-TeV range using muon flux data and finds that the spectrum's shape depends on the interaction model, with a break around 10-15 TeV necessary for accurate reproduction.

Contribution

It demonstrates the model-dependent nature of the primary proton spectrum and highlights the need for improved understanding of p-air collisions to confirm spectral features.

Findings

Proton spectrum shape varies with interaction models.

A spectral break at 10-15 TeV improves muon flux reproduction.

Existing data are insufficient to confirm the spectral break.

Abstract

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.