A Simulation Study on the Cosmic-Ray Energy Spectra of Elemental Mass Groups using the Tibet Air-Shower and Muon Detector Arrays through the Bayesian Unfolding Method

Abstract We study the analysis method to determine the cosmic-ray energy spectra of different mass groups assuming the use of the Tibet AS$\gamma$ experiment, which consists of the high-density Tibet air-shower array and the underground muon detector array. These arrays measure the sampling air-shower size $\Sigma \rho$ and the total muon number $\Sigma N_{\mu }$ of each air-shower event. These parameters are known to contain information on the energy and mass of the primary particle. To reconstruct the energy spectra of individual cosmic-ray mass groups, we apply a multidimensional unfolding method based on Bayes’ theorem to the 2D distribution of $\Sigma \rho$ and $\Sigma N_{\mu }$ produced by Monte Carlo simulation. Simulated datasets with combinations of the EPOS-LHC, SIBYLL-2.3c, and QGSJET II-04 high-energy hadronic interaction models and a helium-dominant composition model are analyzed while using a response matrix produced by EPOS-LHC. The unfolded spectra of the EPOS + helium-dominant composition model dataset show a deviation from the input flux within $\pm$10% except for a few bins, meaning that the uncertainty of the technique itself and the composition model dependence is at that level. It is also shown that the deviation in the all-particle spectrum is within $\pm$10% even when using different hadronic interaction models in the dataset and the response matrix. On the other hand, the unfolded spectra of individual mass groups have a clear dependence on the hadronic interaction model. The model dependence of the proton and helium spectra amounts to $\pm 25$% below 10$^{6.5}$ GeV. The dependence in the carbon group is at a $\pm 25\rm{\%}$ level below 10$^{6}$ GeV, and for the iron spectrum, it amounts to $+55\%$ and $-30\%$ in the energy range of 10$^{5.1}$ GeV to 10$^{6.7}$ GeV. We are now able to measure individual energy spectra in the knee region—including those of heavy nuclei, which remain poorly understood. Thanks to the recent extension of direct measurements beyond 10$^{4}$ GeV, a comparison between our analysis and the direct measurements will provide a good test of the hadronic interaction models.