What do the highest-energy cosmic-ray data suggest about possible new physics around 50 TeV?

The latest observations of extensive air showers (EASs) induced by ultrahigh-energy cosmic rays appear to indicate, prima facie, a transition to heavy primaries at the highest energies. However, this interpretation is based on extrapolations of the Standard Model (SM) to ultra-LHC energies. We consider the alternative that after some energy threshold, the first collision of the primary in the atmosphere results in a state, the decay of which leads to a considerably increased shower particle multiplicity, so that light-primary EASs appear heavy-like. We show that a minimal implementation of such a model yields predictions for the average EAS depth and shower-to-shower fluctuations that are consistent with each other, and an excellent fit to Auger data. If such an effect indeed takes place, we predict that (a) the center-of-momentum (c.m.) energy threshold for the effect is of order 50 TeV; (b) the probability with which the effect occurs is high, and it will be detected easily by next-generation accelerators; (c) the increase in multiplicity compared to the SM prediction grows with c.m. energy roughly as $\sim E_{\mathrm{CM}}$; and (d) the cosmic-ray composition at the highest energies is light. Remarkably, if the latter is confirmed electromagnetically, this would necessitate the existence of new physics by these energies.

Figure 1

Upper panel: Cosmic-ray spectrum between $10^{16}$ and $10^{20}\mathrm{eV}$. Filled circles: Auger 2017 ICRC spectrum [9] (error bars are statistical). Brown triangles: KASCADE-Grande 2015 all-particle spectrum [31], QGSJET II-04 reconstruction (error bars are systematic). Purple line: Galactic population model spectrum (this work). Open green circles: Auger total flux minus Galactic model. The vertical black dotted line indicates the lowest energy for which there are spectrum measurements from Auger. Lower panel: Fraction of cosmic rays of Galactic origin as a function of energy, derived from the Galactic flux model over the total observed flux.

Figure 2

Upper panel: $⟨X_{\max }⟩$ as a function of energy. Filled circles: Auger 2017 ICRC data [10] (error bars are systematic). Red/blue dashed lines: SM (Sibyll) predictions for protons/iron, from Ref. [8]. The hatched boxes indicate the systematic uncertainty of SM predictions (result of using EPOS/QGSJet instead of Sibyll). Thick lines: Our model (purple: Galactic, green: extragalactic, orange: total). Lower panel: ${\sigma }_{X_{\max }}$ as a function of energy. Filled circles: Auger ICRC 2017 data [10] (error bars are statistical). Orange line: $\delta =0$. Cyan line: $\delta =2.9$. Other lines as above. For clarity, the extragalactic model is only shown for $\delta =0$.