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Evaluation of cosmogenic production of $^{39}Ar$ and $^{42}Ar$ for rare-event physics using underground argon

Underground argon (UAr) with lower cosmogenic activities of $^{39}Ar$ and $^{42}Ar$ has been planned as a detector in detecting scintillation light and charge collection using time projection chambers for dark matter searches and as a veto detector in suppressing backgrounds for neutrinoless double beta decay (0$νββ$) experiments. Long-lived radioactive isotopes, $^{39}Ar$ and $^{42}Ar$, can also be produced on the surface when UAr is pumped out from a deep well. Understanding the production of long-lived isotopes in Ar is important for utilizing UAr for dark matter and 0$νββ$ experiments in terms of its production, transportation, and storage. Ar exposure to cosmic rays at sea-level is simulated using Geant4 for a given cosmic ray muon, neutron, and proton energy spectrum. We report the simulated cosmogenic production rates of $^{39}Ar$, $^{42}Ar$, and other long-lived isotopes at sea-level from fast neutrons, high energy muons, and high energy protons. Total production rates of 938.53/kg$_{Ar}\cdot$day and 5.81$\times$10$^{-3}$/kg$_{Ar}\cdot$day for $^{39}$Ar and $^{42}$Ar are found from our simulation. Utilizing these production rates, we set a time limit of 954 days constrained by the production of $^{39}$Ar for UAr to be on the surface before it compromises the sensitivity for a dark matter experiment. Similarly, a time limit of 1702 days constrained by the production of $^{42}$Ar is found for a 0$νββ$ experiment.