Cosmogenic production of $^{37}$Ar in the context of the LUX-ZEPLIN experiment

We estimate the amount of $^{37}$Ar produced in natural xenon via cosmic ray-induced spallation, an inevitable consequence of the transportation and storage of xenon on the Earth's surface. We then calculate the resulting $^{37}$Ar concentration in a 10-tonne payload~(similar to that of the LUX-ZEPLIN experiment) assuming a representative schedule of xenon purification, storage and delivery to the underground facility. Using the spallation model by Silberberg and Tsao, the sea level production rate of $^{37}$Ar in natural xenon is estimated to be 0.024~atoms/kg/day. Assuming the xenon is successively purified to remove radioactive contaminants in 1-tonne batches at a rate of 1~tonne/month, the average $^{37}$Ar activity after 10~tonnes are purified and transported underground is 0.058--0.090~$\mu$Bq/kg, depending on the degree of argon removal during above-ground purification. Such cosmogenic $^{37}$Ar will appear as a noticeable background in the early science data, while decaying with a 35~day half-life. This newly-noticed production mechanism of $^{37}$Ar should be considered when planning for future liquid xenon-based experiments.