We present the first measurement of the fluctuations in the number of muons in extensive air showers produced by ultra-high energy cosmic rays. We find that the measured fluctuations are in good agreement with predictions from air shower simulations.
This observation provides new insights into the origin of the previously reported deficit of muons in air shower simulations and constrains models of hadronic interactions at ultra-high energies. Our measurement is compatible with the muon deficit originating from small deviations in the predictions from hadronic interaction models of particle production that accumulate as the showers develop.
Ultra High Energy Cosmic Rays (UHECRs) are particles coming from outer space, with energies exceeding 10^18 eV. They provide the only experimental opportunity to explore particle physics beyond energies reachable by Earth-based accelerators, which go up to cosmic ray energies of 9 × 10^16 eV.The Pierre Auger Observatory detects extensive air showers that are initiated by the UHECRs colliding with the nuclei in the atmosphere. Information about UHECRs is extracted using simulations based on hadronic interaction models which rely on extrapolations of accelerator measurements to unexplored regions of phase space, most notably the forward and highest-energy region. In addition, accelerator experiments at the highest energies either probe the interactions between protons or of protons with heavy nuclei, while most interactions within air showers are between pions and light nuclei.A further challenge is that the UHECR mass has to be measured despite not being yet completely decoupled from the hadronic uncertainties. The observable with the least dependence on hadronic interactions is the atmospheric depth at which the longitudinal development of the electromagnetic (EM) component of the shower reaches the maximum number of particles, namely Xmax.In hadronic cascades the energy of each interacting particle is distributed among the secondaries, mostly pions. Neutral pions rapidly decay into two photons feeding a practically decoupled electromagnetic cascade (other resonances decaying into πº’s, electrons and or photons also contribute). Charged pions (and other long lived mesons like kaons) tend to further interact until their individual energies are below a critical value, below which they are more likely to decay.
Muons, which are products of hadronic decays, are thus predominantly produced in the final shower stages. In sufficiently inclined showers, the pure EM component is absorbed in the atmosphere and the particles that reach the ground (muons and muon decay products) directly sample the muon content, reflecting the hadronic component of the shower.Air showers are mainly detected at the Pierre Auger Observatory by the Surface Detector (SD), an array of water-Cherenkov detector stations, and the Fluorescence Detector (FD) consisting of 24 fluorescence telescopes. By selecting the sub-sample of events reconstructed with both the SD and the FD and with zenith angles exceeding 62º, both the muon content and the energy of the shower are simultaneously measured.The results obtained indicate that all the simulations underestimate the number of muons in the showers.
These analyses come with the caveat that they cannot distinguish a muon rescaling from a shift in the absolute energy scale of the FD measurement. However, muon content and energy scale were disentangled in a complementary technique based on showers with zenith angles below 60º. Using the longitudinal profile of the shower in the atmosphere obtained with the FD and the signals at the ground measured with the SD, it was shown that the muonic component still has to be scaled up to match observed data, while no rescaling of the EM component and the FD energy is required. The measurements with the FD also show that both the position of the shower maximum in the atmosphere (Xmax) and the entire shape of the EM shower are well described by the simulations.
At lower energies, down to ∼ 10^17.3 eV, in a measurement using the sub-array of buried scintillators of the Pierre Auger Observatory, a direct count of the muons independent of EM contamination was obtained, which also shows that simulations produce too few muons.
There is much evidence that all the simulations underpredict the average number of muons in the showers: a comprehensive study of muon number measurements made with different experiments has shown that the muon deficit in simulations starts around ∼ 10^16 eV and steadily increases with energy. Depending on model and experiment, the deficit at ∼ 10^20 eV ranges between tens of percent up to a factor of two.The increased statistics obtained at the Pierre Auger Observatory allows us to now take a further step and explore fluctuations in the number of muons between showers, hereinafter referred to as physical fluctuations. The ratio of the physical fluctuations to the average number of muons (relative fluctuations) has been shown to be mostly dominated by the first interaction, rather than the lower energy interactions deeper in the shower development. Here, we exploit the sensitivity of fluctuations to the first-interaction to explore hadronic interactions well above the energies achievable in accelerator experiments.
The paper concludes with the following summary of the study's results:
We have presented for the first time a measurement of the fluctuations in the number of muons in inclined air showers, as a function of the UHECR primary energy. Within the current uncertainties, the relative fluctuations show no discrepancy with respect to the expectation from current high-energy hadronic interaction models and the composition taken from Xmax measurements.
This agreement between models and data for the fluctuations, combined with the significant deficit in the predicted total number of muons, points to the origin of the models’ muon deficit being a small deficit at every stage of the shower which accumulates along the shower development, rather than a discrepancy in the first interaction. Adjustments to models to address the current muon deficit, must therefore not alter the predicted relative fluctuations.