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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 (Tibet-AS) and the underground muon detector (MD) 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 two-dimensional 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$10\% even when using different hadronic interaction models in the dataset and the response matrix. On the other hand, the unfolded spectra of individual mass groups have a clear dependence on the hadronic interaction model. The model dependence of the proton and helium spectra amounts to \pm25% below 10$^{6.5}$ GeV. The dependence in the carbon group is at a \pm25% 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.