  Muon-induced neutrons can lead to potentially irreducible backgrounds in rare
event search experiments. We have investigated the implication of laboratory
depth on the muon-induced background in a future dark matter experiment capable
of reaching the so-called neutrino floor. Our simulation study focused on a
xenon-based detector with 70 tonnes of active mass, surrounded by additional
veto systems plus a water shield. Two locations at the Boulby Underground
Laboratory (UK) were analysed as examples: an experimental cavern in salt at a
depth of 2850 m w. e. (similar to the location of the existing laboratory), and
a deeper laboratory located in polyhalite rock at a depth of 3575 m w. e. Our
results show that no cosmogenic background events are likely to survive
standard analysis cuts for 10 years of operation at either location. The
largest background component we identified comes from beta-delayed neutron
emission from $^{17}$N which is produced from $^{19}$F in the fluoropolymer
components of the experiment. Our results confirm that a dark matter search
with sensitivity to the neutrino floor is viable (from the point of view of
cosmogenic backgrounds) in underground laboratories at these levels of rock
overburden. This work was conducted in 2019-21 in the context of a feasibility
study to investigate the possibility of developing the Boulby Underground
Laboratory to host a next-generation dark matter experiment; however, our
findings are also relevant for other underground laboratories.
