The CROSS experiment: detector construction, background projection, and sensitivity to $^{100}$Mo $0\nu2\beta$ decay
The CROSS experiment to search for neutrinoless double-beta ($0\nu2\beta$) decay in $^{100}$Mo with the help of an array of scintillating cryogenic calorimeters, containing 4.9 kg of $^{100}$Mo, has been ongoing in a low-background setup at the Canfranc underground laboratory (Spain) since mid-November 2025. In this paper, we present the construction of the CROSS detector and the description of Geant4-based Monte Carlo simulations of expected background in the region of interest. The simulations predict the background index in a 100-keV-wide interval centered at the $Q$-value of $^{100}$Mo (3034 keV) on the level of 3.2(5) $\times$ 10$^{-3}$ cnts/keV/kg/yr. Taking into account an 18% deadtime induced by the muon veto cut and a typical 90% duty cycle of the facility, such background level would allow to reach the world-leading sensitivity to $^{100}$Mo $0\nu2\beta$ decay (lim $T_{1/2} \sim 4 \times 10^{24}$ yr) in 1 year of data taking. Considering conservatively a factor 3 (10) worse background index due to unpredictable radioactive contamination of construction materials and/or detector performance, a 2-yr-long operation of the CROSS array would be still compatible with the best (competitive) sensitivity to $0\nu2\beta$ decay in $^{100}$Mo.