Relative Measurement and Extrapolation of the Scintillation Quenching Factor of $\alpha$-Particles in Liquid Argon using DEAP-3600 Data

The knowledge of scintillation quenching of $\alpha$-particles plays a paramount role in understanding $\alpha$-induced backgrounds and improving the sensitivity of liquid argon-based direct detection of dark matter experiments. We performed a relative measurement of scintillation quenching in the MeV energy region using radioactive isotopes (${}^{222}$Rn, ${}^{218}$Po and ${}^{214}$Po isotopes) present in trace amounts in the DEAP-3600 detector and quantified the uncertainty of extrapolating the quenching factor to the low-energy region.