# Development of Cryogenic Detectors for Neutrinoless Double Beta Decay Searches with CUORE and CUPID
## 4 Beyond the CUORE Sensitivity
### The CUPID Challenge  
The CUORE upgrade to achieve CUPID objectives passes through three fundamental steps:  
* Increase the 0\(\
u\beta\beta\) emitters via isotopic enrichment;
* Active rejection of alphas and surface backgrounds in detector materials;
* Further reduction (compared to CUORE) in the \(\gamma\) backgrounds by careful material and isotope selection and an active veto for muon-induced events. In the last ten years, different isotopes (see Figure 2) and approaches were investigated for CUPID. Background rejection with scintillation, Cherenkov radiation, ionization, and pulse-shape discrimination were evaluated, and novel materials and sensor technologies were tested [58; 59]. The activities carried out over the last years to design a next-generation 0\(\
u\beta\beta\) bolometric experiment are briefly summarized here, divided according to the isotope under investigation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment** & **Exposure\({}_{\text{Iso}}\) [kg yr]** & **Resolution [keV]** & **Background [cnts/(kev kg yr)]** & **Efficiency [\%]** & **Reference** \\ \hline MiBETA & 0.66 & \(8\pm 1\) & \(0.5^{+0.4}_{-0.3}\) & 84.5 & [29] \\ CUORICINO & 19.75 & \(6\pm 0.5\) & 0.2 & 82.8 \(\pm\) 1.1 & [36] \\ CUORE-0 & 9.8 & \(5.1\pm 0.3\) & (\(5.8\pm 0.4_{\text{stat}}\pm 0.2_{\text{syst}}\))\(\times 10^{-2}\) & 81.3 \(\pm\) 0.6 & [39] \\ CUORE & 103.6 & \(7.0\pm 0.4\) & (\(1.38\pm 0.07\))\(\times 10^{-2}\) & 77.3 \(\pm\) 0.1 & [5] \\ \hline CUPID-0 & 5.09 & 20.0 \(\pm\) 0.3 & \(3.5^{+1}_{-0.9}\cdot 10^{-3}\) & 70 \(\pm\) 1 & [52] \\ CUPID-Mo & 0.48 & \(7.7\pm 0.7\) & \(3^{+7}_{-3}\cdot 10^{-3}\) & 68 \(\pm\) 1 & [57] \\ \hline CUPID & 1000 & 5 & \(10^{-4}\) & 64 & [42] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance of different 0\(\
u\beta\beta\) experiments based on cryogenic calorimeters. The data are measured for all of the experiments except for CUPID, where the best prediction of performances at the end of the operation time was reported, as derived from Monte Carlo simulations. CUORE data reflect the latest published results, and therefore these performances are expected to change as its data taking progresses. Figure 2: Expected energy signature in the two-electron sum-energy spectrum for the nine most suitable double-beta emitters. These are compared with background energy markers related to the maximum \(\gamma\) energies of the \({}^{238}\)U and \({}^{232}\)Th chains and the maximum \(\beta\) energy of the \({}^{238}\)U chain. The main experiments are also mentioned in relation with their selected nucleus. For essentially technical reasons, most searches investigate the three least favorable isotopes. The isotope selected for the CUPID baseline is \({}^{100}\)Mo. We also report the natural isotropic abundance [14]. The most favorable isotopes from the point of view of the background are also those with the lowest isotopic abundance. Figure adapted from [42]. \({}^{130}\)**Te. ** Large-scale production of high-quality TeO\({}_{2}\) crystals was already demonstrated within the CUORE experience. However, the production of enriched crystal has to be validated to certify the energy resolution as well as the internal contaminations. This work has started on 2015, producing and operating two highly-enriched (92%) TeO\({}_{2}\) crystals (435 g each) [60]. This first test gave very satisfactory results, showing an energy resolution of 6.5 and 4.3 keV FWHM at 2615 keV, respectively. The only observable internal radioactive contamination came from \({}^{238}\)U (15 and 8 uBq/kg, respectively). The internal contamination of the most problematic nuclei for 0\(\
u\beta\beta\), \({}^{226}\)Ra and \({}^{228}\)Th, were both evaluated as \(<\)3.1 uBq/kg and \(<\)2.3 uBq/kg, respectively.