Energy sensitivity of the GRAPES-3 EAS array for primary cosmic ray protons

Low energy ground-based cosmic ray air shower experiments generally have energy threshold in the range of a few tens to a few hundreds of TeV. The shower observables are measured indirectly with an array of detectors. The atmospheric absorption of low energy secondaries limits their detection frequencies at the Earth's surface. However, due to selection effects, a tiny fraction of low energy showers, which are produced in the lower atmosphere can reach the observational level. But, due to less information of shower observables, the reconstruction of these showers are arduous. Hence, it is believed that direct measurements by experiments aboard on satellites and balloon flights are more reliable at low energies. Despite having very small efficiency ($\sim$0.1%) at low energies, the large acceptance ($\sim$5 m$^2$sr) of GRAPES-3 experiment allows observing primary cosmic rays down below to $\sim$1 TeV and opens up the possibility to measure primary energy spectrum spanning from a few TeV to beyond cosmic ray knee (up to 10$^{16}$ eV), covering five orders of magnitude. The GRAPES-3 energy threshold for primary protons through Monte Carlo simulations are calculated, which gives reasonably good agreement with data. Furthermore, the total efficiencies and acceptance are also calculated for protons primaries. The ability of GRAPES-3 experiment to cover such a broader energy range may provide a unique handle to bridge the energy spectrum between direct measurements at low energies and indirect measurements at ultra-high energies.