  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 focuses on a
xenon-based detector with 71 tonnes of active mass, surrounded by additional
veto systems including an instrumented water shield. Two locations at the
Boulby Underground Laboratory (UK) served as a case study: 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 less than one event of cosmogenic
background is likely to survive standard analysis cuts for 10 years of
operation at either location. The largest background component that we
identified comes from 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. We present details of the
performed simulations and of the obtained results.
