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The shape of the cosmic ray proton spectrum

Recent observations of cosmic ray protons in the energy range $10^2$--$10^5$~GeV have revealed that the spectrum cannot be described by a simple power law. A hardening of the spectrum around an energy of order few hundred~GeV, first observed by the magnetic spectrometers PAMELA and AMS02, has now been confirmed by several calorimeter detectors (ATIC, CREAM, CALET, NUCLEON and DAMPE). These new measurements reach higher energy and indicate that the hardening corresponds to a larger step in spectral index than what estimated by the magnetic spectrometers. Data at still higher energy (by CREAM, NUCLEON and DAMPE) show that the proton spectrum undergoes a marked softening at $E \approx 10^4$~GeV. Understanding the origin of these unexpected spectral features is a significant challenge for models of the Galactic cosmic rays. An important open question is whether additional features are present in the proton spectrum between the softening and the "Knee". Extensive Air Shower detectors, using unfolding procedures that require the modeling of cosmic ray showers in the atmosphere, estimated the proton flux below and around the Knee (at $E \simeq 3$~PeV). These results however have large systematic uncertainties and are in poor agreement with each other. The measurement in the PeV energy range, recently presented by IceTop/IceCube, indicates a proton flux higher than extrapolations of the direct measurements calculated assuming a constant slope, and therefore requires the existence of an additional spectral hardening below the Knee. A clarification of this point is very important for an understanding of the origin of the Galactic cosmic rays, and is also essential for a precise calculation of the spectra of atmospheric neutrinos in the energy range ($E \gtrsim 10$~TeV) where they constitute the foreground for the emerging astrophysical $ν$ signal.