Expected sensitivity to 128Te neutrinoless double beta decay with the CUORE TeO2 cryogenic bolometers

The CUORE experiment is a ton-scale array of TeO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {TeO}_2$$\end{document} cryogenic bolometers located at the underground Laboratori Nazionali del Gran Sasso of Istituto Nazionale di Fisica Nucleare (INFN), in Italy. The CUORE detector consists of 988 crystals operated as source and detector at a base temperature of ∼10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 10$$\end{document} mK. Such cryogenic temperature is reached and maintained by means of a custom built cryogen-free dilution cryostat, designed with the aim of minimizing the vibrational noise and the environmental radioactivity. The primary goal of CUORE is the search for neutrinoless double beta decay of 130Te\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{130}\hbox {Te}$$\end{document}, but thanks to its large target mass and ultra-low background it is suitable for the study of other rare processes as well, such as the neutrinoless double beta decay of 128Te\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{128}\hbox {Te}$$\end{document}. This tellurium isotope is an attractive candidate for the search of this process, due to its high natural isotopic abundance of 31.75%. The transition energy at (866.7 ± 0.7) keV lies in a highly populated region of the energy spectrum, dominated by the contribution of the two-neutrino double beta decay of 130Te\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{130}\hbox {Te}$$\end{document}. As the first ton-scale infrastructure operating cryogenic TeO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {TeO}_2$$\end{document} bolometers in stable conditions, CUORE is able to achieve a factor >10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>10$$\end{document} higher sensitivity to the neutrinoless double beta decay of this isotope with respect to past direct experiments.

Journal of Low Temperature Physics (2022) 209:788-795 single decay is energetically forbidden. Two distinct decay modes are usually accounted for when this transition is discussed. The Standard Model-allowed one is the two-neutrino double beta decay ( 2 ): this process is characterized by the emission of two electrons and two anti-neutrinos in the final state, ensuring that the Lepton Number is conserved. The 2 decay has been directly measured in 11 nuclei ( 48 Ca , 76 Ge , 82 Se , 96 Zr , 100 Mo , 100 Ru , 116 Cd , 130 Te , 136 Xe , 150 Nd , 150 Sm ) [1]. On the contrary, the hypothesized neutrinoless double beta decay ( 0 ) has not yet been observed. If 0 decay is possible, then Lepton Number symmetry would be violated by two units, making this an important Beyond the Standard Model process. The double beta decay can be observed by measuring the summed energy of the two electrons: in the 2 case, this forms a continuous spectrum from 0 to the Q-value of the reaction, due to the presence of the two neutrinos in the final state carrying part of the momentum. The expected signature for 0 decay is instead a monochromatic peak at the Q-value, since the two electrons carry the total amount of energy. A large international effort is currently put in the experimental search of 0 decay, as its observation would shed light on several important open questions in Particle Physics [2]: it would demonstrate that the Lepton Number is not a conserved physical quantity; it would prove that neutrinos have a Majorana component ( =̄ ), giving rise to a new possible description of the mass production via the see-saw mechanism; it would provide a possible explanation of the matter-antimatter asymmetry origin via Leptogenesis.

CUORE: Cryogenic Underground Observatory for Rare Events
The CUORE experiment is a 1 ton-scale array of TeO 2 cryogenic bolometers whose main Physics goal is to search for the 0 decay of 130 Te . This element is characterized by a high natural isotopic abundance of 34.167%, and a Q-value of 2527.518 keV [3]. The CUORE detector is located at the underground Laboratori Nazionali del Gran Sasso of Istituto Nazionale di Fisica Nucleare (INFN), in Italy, and is comprised of 988 natural TeO 2 crystals for a total mass of 742 kg, including 206 kg of 130 Te , operated as thermal detectors at ∼ 10 mK. Such cryogenic temperature is reached and maintained thanks to a custom built cryogen-free structure: the cooling power is provided by the simultaneous operation of five pulse tubes until the 4 K cold stage, and by a 3 He/ 4 He Dilution Refrigerator down to the base temperature [4]. The CUORE cryostat was designed with the aim of an ultra-low background level, which was measured to be (1.49 ± 0.04) × 10 −2 cts∕(keV ⋅ kg ⋅ y) in the region of interest of (2490 -2575) keV, i.e. in the vicinity of the 130 Te 0 decay Q-value. At this energy, the FWHM resolution in physics data resulted to be ( 7.8 ± 0.5 ) keV [5].
CUORE started its operation at the beginning of 2017, and its data taking is currently proceeding; the milestone of 1 ton ⋅ y acquired data was recently achieved, and from the analysis of this exposure a new 90% C.I. Bayesian limit on 130 Te 0 decay half life of T 0 1∕2 > 2.2 × 10 25 y was obtained [5].

128 Te Neutrinoless Double Beta Decay Search with CUORE
The ton-scale mass and low background level of CUORE make it suitable for the investigation of other rare events, among which is the search for 0 decay of 128 Te [6]. With its natural isotopic abundance of 31.75% [7], this tellurium isotope is characterized by one of the highest natural abundances among the nuclei that can undergo 0 decay, together with 130 Te : this feature makes it an attractive candidate for the 0 decay search. A particular interest for the study of such a process also comes from the theoretical point of view: indeed, information on this decay can provide a discriminator among the different models that try to describe the mechanism underlying 0 decay [8]. The Q-value of (866.7 ± 0.7) keV [9] of this transition lies in a highly populated region of the spectrum, where the dominant source of background is due to the 2 decay of 130 Te . Its half-life was recently measured by CUORE and resulted to be 7.71 +0.08 −0.06 (stat.) +0.12 −0.15 (syst.) × 10 20 y [10]. Additionally, several lines due to natural radioactivity also contribute to this region of energy. For this reason, past direct search experiments that operated tens of kg of TeO 2 were characterized by a poor sensitivity to this decay. The latest lower limit on the half life of 128 Te 0 decay from direct experiments was published in 2003 by MiDBD, that set a limit of T 0 1∕2 > 1.1 × 10 23 y with 6.8 kg of TeO 2 and two crystals enriched in 128 Te at 82.3% [11]. More stringent limits were instead extracted from geochemical experiments, which measured the ratio between 130 Te and 128 Te half lives 1 [12]. The latest published value of T 128 Te 1∕2 was calculated by exploiting this ratio and an average of the 130 Te half lives from CUORE-0 [13] and CUORE [3], and resulted to be T 128 Te 1∕2 = (2.0 ± 0.3) × 10 24 y [1]. The 742 kg TeO 2 detectors of CUORE include 188.5 kg of the 128 Te isotope, corresponding to 9.51 × 10 26 128 Te nuclei. Since the sensitivity to the 0 decay half life scales proportionally to the square root of the experimental mass -in the nonzero background condition -, a factor ∼ 10 higher sensitivity with respect to MiDBD is expected in CUORE, which might be able to set a limit competitive with the geochemical results. In this work, we calculate the expected CUORE sensitivity to 128 Te 0 decay from the Background Model knowledge.

Analysis Strategy
The statistical approach for the investigation of 128 Te 0 decay in CUORE consists of a Bayesian binned fit based on the BAT (Bayesian Analysis Toolkit) software, which samples from the posterior distribution of all the model parameters with a Markov Chain Monte Carlo [14]. The goal of the analysis is to make a statistical inference on the parameter of interest, i.e. the 0 decay signal rate Γ 0 . As a first step towards the event selection, the fraction of 0 events corresponding to the two electrons fully absorbed by the same single CUORE crystal was evaluated. This efficiency can be extracted from Monte Carlo simulations of the 128 Te 0 decay in CUORE: from the ratio between the number of events reconstructed at the Q-value peak and the number of simulated decays, this efficiency resulted to be 97.6%. The choice of a region of interest (ROI), and thus the contributions to be included in the Bayesian fit model, followed the identification of the background structures in the proximity of the Q-value. This information was obtained from the CUORE Background Model (BM) simulated spectrum. The energy region under investigation is shown in Fig. 1, where two structures are well visible: the left peak corresponds to a line at 834.8 keV from 54 Mn , whose presence is attributed to the cosmogenic activation of the copper structures near the detectors, while the right peak is due to a 860.6 keV emission from 208 Tl , a nucleus belonging to the 232 Th chain. The Bayesian fit model includes, besides these two lines, a continuum contribution modelled with a linear function and the posited 128 Te 0 signal peak. The Bayesian fit method was tested and validated on toy Monte Carlo simulations (toyMC) of the ROI spectrum components. The parameters according to which such components were generated are the 54 Mn rate Γ toy Mn , the 208 Tl rate Γ toy Tl , the continuous background rate BI toy , and the background slope slope toy , all extracted from a binned maximum likelihood fit on the BM simulations (Fig. 1). These values are summarized in Table 1. These toyMC were used to test the Bayesian fit, and to calculate the expected CUORE Limit Setting Sensitivity to the 0 decay of 128 Te.

Expected CUORE Limit Setting Sensitivity from Background Model knowledge
If no evidence of 0 decay is found, an upper limit on the decay rate can be set. This is taken as the rate corresponding to the 90% of the marginalized posterior (i.e. the posterior distribution integrated over all the parameters of the fit but the signal rate); this corresponds to a lower limit on the decay half life. To extract the expected CUORE Limit Setting (or Exclusion) Sensitivity, 10 4 toyMC were simulated with background components only, according to the parameters listed in Table 1; the Bayesian fit with signal plus background contributions was independently run on each toyMC. The Limit Setting Sensitivity is defined as the median of the distribution of the 90% C.I. limits on T 0 1∕2 ; thus, all the extracted 90% C.I. half life limits were used to construct the distribution in Fig. 2. The corresponding median is the CUORE expected Exclusion Sensitivity to 128 Te 0 decay, and is equal to T 1∕2 = 2.2 × 10 24 y. This value provides a reliable indication of the actual CUORE Exclusion Sensitivity, and demonstrates that over a factor 10 improvement on the 128 Te 0 decay half life limit with respect to past direct experiments can be obtained with the CUORE data, and that this can possibly overcome the geochemical results for the first time. CUORE has already collected enough statistics to achieve this sensitivity, and the analysis on real data is currently being finalized; therefore, new results on 128 Te 0 decay search with CUORE are expected to be released soon.