# Development of Cryogenic Detectors for Neutrinoless Double Beta Decay Searches with CUORE and CUPID
## 4 Beyond the CUORE Sensitivity
### The CUPID Challenge
An extensive R&D has been carried out to select the best candidate crystal for a next-generation experiment in the framework of the LUMINEU project and by the AMoRE collaboration [8], converging on Li\({}_{2}\)MoO\({}_{4}\) as best candidate [83; 84]. The most advanced example of this technology is the CUPID-Mo experiment. It consists of a 2.6 kg array of 20 enriched Li\({}_{2}\)MoO\({}_{4}\) crystals, arranged in four towers, operated as cryogenic calorimeters for more than one year. Bolometric Ge light detectors are interleaved between the crystals, resulting in all but the top elements of the towers facing an LD both at the top and the bottom [7]. In addition, the CROSS project (Cryogenic Rare-event Observatory with Surface Sensitivity) [85] is intended to develop a cryogenic detector for investigating the double beta decay of \({}^{100}\)Mo and \({}^{130}\)Te. The basic concept of CROSS consists in rejecting the background from the crystal surface by pulse-shape discrimination, assisted by a proper coating of the faces of the crystal containing the isotope of interest and serving as an energy absorber of the bolometric detector [86]. These techniques will have a major impact on background reduction in next generation experiments. The experiences and information acquired carrying out the aforementioned activities allowed to identify enriched Li\({}_{2}\)MoO\({}_{4}\) crystals as the best candidates for the next-generation CUPID experiment, given their excellent performances in terms of energy resolution, radiopurity and particle identification. Based on the available information, a design for the CUPID detector has been defined [42]. The different specifications are listed in Table 2. The predicted performances of the experiment have been conservatively estimated taking into account all of the information acquired during the investigation of different approaches and mainly by the CUORE, CUPID-0 and CUPID-Mo experiments. One of the main constraint of this design is the requirement for CUPID to be fully compatible with the existing CUORE infrastructure in terms of mechanical coupling, cryogenics, readout, and DAQ features. This characteristic is mandatory to boost the time schedule and to have the experiment running before 2030. In the current design, the background index reduction is limited by the non-resolved fraction of the two-neutrino double-beta decay pile-up on the rising edge of the bolometric signal. Such an effect is due to the relatively short \({}^{100}\)Mo \(2\
u\beta\beta\) half-life, combined with its high isotopic abundance, and the slow response time of the bolometric detectors. New methods are being developed in order to study and tackle this issue [87], and a further improvement of the pile-up rejection is expected to be achieved by combining a faster sensor (100 \(\upmu\)s) with new analysis techniques based on Principal Component Analysis and Single Value Decomposition [58; 88; 89]. The exact evaluation of the expected pile-up rejection efficiency is underway and will be presented in future works of the CUPID collaboration. \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Baseline** \\ \hline Crystal & Li\({}_{2}^{100}\)MoO\({}_{4}\) \\ Crystal size & 4.5 \(\times\) 4.5 \(\times\) 4.5 cm\({}^{3}\) \\ Crystal mass (g) & 241 \\ Number of crystals & 1500 \\ Number of light detectors & 1500 \\ Detector mass (kg) & 362 \\ \({}^{100}\)Mo mass (kg) & 200 \\ Energy resolution FWHM (keV) & 5 \\ Background index (counts/(keV\(\times\)kg\(\times\) year)) & \(10^{-4}\) \\ Containment efficiency & 79\% \\ Selection efficiency & 90\% \\ Lifetime & 10 years \\ Half-life limit sensitivity (90\%) C.L. & \(1.5\times 10^{27}\) years \\ Half-life discovery sensitivity (3\(\sigma\)) & \(1.1\times 10^{27}\) years \\ \(m_{\beta\beta}\) limit sensitivity (90\%) C.L. & 10–17 meV \\ \(m_{\beta\beta}\) discovery sensitivity (3\(\sigma\)) & 12–20 meV \\ \hline \end{tabular}
\end{table} 
Table 2: Main parameters of the conservative baseline CUPID detector design. The values are taken from [42].