Direct Measurement of the $^{39}$Ar Half-life from 3.4 Years of Data with the DEAP-3600 Detector

The half-life of $^{39}$Ar is measured using the DEAP-3600 detector located 2 km underground at SNOLAB. Between 2016 and 2020, DEAP-3600 used a target mass of (3269 $\pm$ 24) kg of liquid argon distilled from the atmosphere in a direct-detection dark matter search. Such an argon mass also enables direct measurements of argon isotope properties. The decay of $^{39}$Ar in DEAP-3600 is the dominant source of triggers by two orders of magnitude, ensuring high statistics and making DEAP-3600 well-suited for measuring this isotope's half-life. Use of the pulse-shape discrimination technique in DEAP-3600 allows powerful discrimination between nuclear recoils and electron recoils, resulting in the selection of a clean sample of $^{39}$Ar decays. Observing over a period of 3.4 years, the $^{39}$Ar half-life is measured to be $(302 \pm 8_{\rm stat} \pm 6_{\rm sys})$ years. This new direct measurement suggests that the half-life of $^{39}$Ar is significantly longer than the accepted value, with potential implications for measurements using this isotope's half-life as input.