Hadronic Interaction Model Dependence in Cosmic Gamma-ray Flux Estimation Using an Extensive Air Shower Array with a Muon Detector

Observation techniques of high-energy gamma rays using air showers have remarkably progressed via the Tibet AS$\gamma$, HAWC, and LHAASO experiments. These observations have significantly contributed to gamma-ray astronomy in the northern sky's sub-Peta electron volts (PeV) region. Moreover, in the southern sky, the ALPACA experiment is underway at 4,740\,m altitude on the Chacaltaya plateau in Bolivia. This experiment estimates the gamma-ray flux from the difference between the number of on-source and off-source events by real data, utilizing the gamma-ray detection efficiency calculated through Monte Carlo simulations, which in turn depends on the hadronic interaction models. Even though the number of cosmic-ray background events can be experimentally estimated, this model dependence affects the estimation of gamma-ray detection efficiency. However, previous reports have assumed that the model dependence is negligible and have not included it in the error of gamma-ray flux estimation. Using ALPAQUITA, the prototype experiment of ALPACA, we quantitatively evaluated the model dependence on hadronic interaction models for the first time. We evaluate the model dependence on hadronic interactions as less than 3.6\,\% in the typical gamma-ray flux estimation performed by ALPAQUITA; this is negligible compared with other uncertainties such as energy scale uncertainty in the energy range from 6 to 300 TeV, which is dominated by the Monte Carlo statistics. This upper limit of 3.6\,\% model dependence is expected to apply to ALPACA.