# Development of Cryogenic Detectors for Neutrinoless Double Beta Decay Searches with CUORE and CUPID
## 4 Beyond the CUORE Sensitivity
### The CUPID Challenge
Thanks to the readout of the weak Cherenkov light emitted by \(\beta/\gamma\) particles by means of Germanium Neganov-Luke [61] bolometric light detectors, it was possible to perform an event-by-event identification of \(\beta/\gamma\) events with a 95% acceptance level, while establishing a rejection factor of 99.99% for \(\alpha\) particles. Alongside this study, silicon Neganov-Luke amplified light detectors were also successfully tested on a 1\(\times\)1\(\times\)1 cm\({}^{3}\) TeO\({}_{2}\) crystal, obtaining a full rejection (4.6\(\sigma\)) of the \(\alpha\)-particles [62]. Other previous results can be found in references [63; 64; 65; 66; 67; 68; 69; 70; 71]. Despite the excellent results obtained, there are still two critical factors to be dealt with:  
* The emitted Cherenkov light at the \({}^{130}\)Te \(Q_{\beta\beta}\) is very small (\(\sim\)100 eV), and therefore the energy RMS resolution of the light detectors must be less than 20 eV, and this cannot currently be guaranteed;
* The \(\gamma\)-background at the \({}^{130}\)Te \(Q_{\beta\beta}\) is one order of magnitude higher with respect to the CUPID goal. Such limitations prevent the use of \({}^{130}\)Te for a next-generation experiment at the current state of the art. On the other hand, the unambiguous advantage due to the high natural isotopic abundance of \({}^{130}\)Te provides a good reason for keeping the optimization going on this route too. * \({}^{82}\)**Se. ** This isotope was thoroughly investigated within the Low Background Installation For Elusive Rates (LUCIFER) program, establishing from scratch the ZnSe powder synthesis and purification protocols [72]. The crystals' growth was refined, studying the properties of dozens of ZnSe samples by means of cryogenic tests [49; 73; 74; 75]. Finally 24 ZnSe crystals, 95%-enriched in \({}^{82}\)Se, were produced and mounted in CUPID-0 [6]. The CUPID-0 demonstrator has taken data from 2017 to 2019, demonstrating a complete rejection for \(\alpha\) particles by exploiting a light-assisted particle discrimination. With this tagging capability, the delayed coincidences between \({}^{212}\)Bi \(\alpha\)-decays and \({}^{208}\)Tl \(\beta\)-decays could be identified, thus removing from the measured spectrum the \({}^{208}\)Tl \(\beta\) events falling in the \({}^{82}\)Se ROI. Combining the excellent particle identification with the delayed coincidence analysis, CUPID-0 has archived a background index of 3.5\({}^{+1}_{-0.9}\times 10^{-3}\) counts/(keV\(\cdot\)kg\(\cdot\) yr), the lowest value ever measured in a cryogenic calorimeter [52]. This important result established the potential of bolometers for a next-generation experiment, setting also the most stringent limit on \({}^{82}\)Se 0\(\
u\beta\beta\) half-life [52]. Finally, a full modelization of the measured spectrum has also been performed, demonstrating that the main residual background in the ROI is due to muon-induced events [76]. The deep understanding of the data also allowed a high-precision measurement of \({}^{82}\)Se 2\(\
u\beta\beta\)[77] and the extraction of limits for other rare processes [78; 79; 80]. The critical point of this technique is the mass production of high-quality ultra-pure crystals, which still demands an extensive R&D effort. * \({}^{100}\)**Mo. ** Large-mass (\(\sim\)1 kg), high optical quality, radiopure \({}^{100}\)Mo-containing molybdenum crystals have been produced and used to develop high-performance single-detector modules based on 0.2-0.4 kg scintillating calorimeters. Even if the production of such crystals was not established as TeO\({}_{2}\) ones, in a relatively short amount of time impressive performances were achieved both in term of energy resolution (4-6 keV at 3 MeV) and radiopurity (10 uBq/kg of \({}^{232}\)Th and \({}^{226}\)Ra). Moreover, the rejection of the \(\alpha\)-induced dominant background above 2.6 MeV is better than 8\(\sigma\)[81; 82].