TeO$_2$ bolometers with Cherenkov signal tagging: towards next-generation neutrinoless double beta decay experiments

CUORE, an array of 988 TeO$_2$ bolometers, is about to be one of the most sensitive experiments searching for neutrinoless double-beta decay. Its sensitivity could be further improved by removing the background from $\alpha$ radioactivity. A few years ago it has been pointed out that the signal from $\beta$s can be tagged by detecting the emitted Cherenkov light, which is not produced by $\alpha$s. In this paper we confirm this possibility. For the first time we measured the Cherenkov light emitted by a CUORE crystal, and found it to be 100 eV at the $Q$-value of the decay. To completely reject the $\alpha$ background, we compute that one needs light detectors with baseline noise below 20 eV RMS, a value which is 3-4 times smaller than the average noise of the bolometric light detectors we are using. We point out that an improved light detector technology must be developed to obtain TeO$_2$ bolometric experiments able to probe the inverted hierarchy of neutrino masses.


Introduction
Neutrinoless double beta decay (0νββ) is a process that violates the lepton number conservation law by two units, in which a parent nucleus decays into a daughter nucleus and emits two β particles. Unlike the process accompanied by the emission of two neutrinos, allowed by the Standard Model and observed in several nuclei, 0νββ has not been observed yet. Its discovery would reveal physics beyond the Standard Model: it would tell us that neutrinos, unlike all other elementary fermions, are Majorana particles, and would point to the Leptogenesis, the origin of the matterantimatter asymmetry after the Big Bang (for a recent review see for example [1] and references therein). The experimental signature is very clear, a peak in the sum energy spectrum of the βs at the Q-value of the decay.
Bolometers proved to be good detectors to search for 0νββ, thanks to the high variety of isotopes that can be studied, the excellent energy resolution, and the low background they can achieve. The CUORE experiment [2,3] will search for the 0νββ of 130 Te with an array of 988 TeO 2 bolometers, cryogenic calorimeters working at a temperature around 10 mK. Each bolometer weighs 750 g, for a total active mass of 741 kg, 206 kg of which are 130 Te (34.2% natural abundance [4] in tellurium). The energy resolution at the Q-value of the decay, 2528 keV [5], is expected to be 5 keV FWHM. CUORE is in construction at Laboratory Nazionali del Gran Sasso (LNGS) in Italy, and will start to take data in 2015.
The technology of TeO 2 bolometers has been proved by Cuoricino, a 40 kg tower of 62 bolometers that, with 19.75 kg y of 130 Te data, set a lower limit to the decay half-life of 2.8 · 10 24 y at 90% C.L. [6]. The analysis of the data pointed out that the main source of background in the energy region of interest (ROI) for the 0νββ consisted in α particles generated by natural radioactivity of the copper structure holding the crystals. To reduce it, the CUORE collaboration developed techniques to clean the copper and to assemble the detector in ultra radiopure environments. The success of this effort has been recently demonstrated by the CUORE-0 experiment, an array of 52 bolometers that reached an α background index of 0.019 ± 0.002 counts/(keV kg y), a factor 6 less than Cuoricino [7]. The background in CUORE, however, is still foreseen to be dominated by α particles, limiting the sensitivity to the 0νββ half-life to around 10 26 years in 5 years of data taking. This corresponds to an effective neutrino Majorana mass that ranges, depending on the choice of the nuclear matrix element, from 40 to 100 meV, values that are quite far from covering the entire interval of masses corresponding to the inverted hierarchy scenario, that ranges from 10 to 50 meV [1].
The background can be reduced by detecting the small amount of Cherenkov light that is emitted by interacting particles in TeO 2 crystals. In fact, at the energy scale of interest for 0νββ, the βs (signal) are above threshold for Cherenkov emission, while α particles (background) are not [8]. In a previous paper [9] we operated a 117 g TeO 2 bolometer surrounded by a 3M VM2002 reflecting foil, monitoring a crystal face with a germanium bolometer acting as light detector. In coincidence with the heat released in the TeO 2 we were able to detect the light emitted by β/γ particles, which amounted to 173 eV at 2528 keV. The crystal was doped with natural samarium, which contains 147 Sm, an α-unstable isotope with Q = 2310 keV. The light detected from these decays was compatible with zero, confirming that at the 0νββ energy scale no light is emitted by αs. Finally, room temperature tests confirmed that the light emitted by particles interacting in TeO 2 can be ascribed to the sole Cherenkov emission, excluding a contribution from the scintillation [10].
In this paper we present the results of a test conducted on a CUORE bolometer, i.e. a 750 g crystal, 6 times larger than that used in our previous work and without samarium doping. The results confirm that the α discrimination in CUORE is possible, but the light signal is small and requires light detectors with higher sensitivity than that provided by bolometers.

Experimental setup
The TeO 2 crystal comes from samples of the CUORE batches used to check the radiopurity and the bolometric performances during the production [11], and therefore is identical to the crystals that are currently being mounted in CUORE. The crystal is a cube of 5 × 5 × 5 cm 3 with translucent faces, two opposite of which have a better polishing quality, close to optical polishing grade. All faces are surrounded by the VM2002 light reflector except for an optical one that is monitored by a 5 cm in diameter, 300 µm thick germanium light detector (LD) [12] (Fig. 1). Both the TeO 2 crystal and the germanium are operated as bolometers, using a neutron transmutation doped germanium (NTD-Ge) thermistor as temperature sensor [13]. The detectors are held in a copper structure by means of teflon (PTFE) supports, anchored to the mixing chamber of a dilution refrigerator. The setup is operated in the CUORE/LUCIFER R&D cryostat, in the Hall C of LNGS [14].
As in Ref. [9], the read-out of the thermistor is performed using the Cuoricino electronics [15]. The analog signals are filtered by 6-pole active Bessel filters [16] and then fed into an 18-bit National Instrument PXI analogto-digital converter (ADC), the same system being used in CUORE-0. The filter cutoff and the ADC sampling frequency are set to 12 Hz and 125 Hz for the TeO 2 , respectively, and to 120 Hz and 2000 Hz for the LD, respectively. The trigger is software generated on each bolometer. When it fires, waveforms 5 s long on the TeO 2 and 250 ms long on the LD are saved on disk. Additionally, when the trigger fires on the TeO 2 , the waveform on the LD is acquired irrespective of its own trigger.
To maximize the signal to noise ratio, the waveforms are processed offline with the optimum filter algorithm [17,18]. On the TeO 2 the pulse is identified with a peak finder algorithm, and the amplitude is evaluated as the maximum of the peak. On the LD, to eliminate noise artifacts at the threshold, the pulse amplitude is evaluated at the characteristic time delay of the LD response with respect to the pulse on the TeO 2 , which is estimated in calibration runs using events generated by particles interacting in both detectors (for more details see Ref. [19]).
The light detector is exposed to a permanent 55 Fe source, providing 5.9 and 6.5 keV calibration X-rays. The typical rise and decay times of the pulses are 2.6 and 6 ms, respectively, while the energy resolution at the iron peaks and at the baseline is 135 and 72 eV RMS, respectively. To calibrate the TeO 2 and to generate events in the 0νββ region, the setup is illuminated by a 232 Th source placed outside the cryostat. The rise and decay times of the TeO 2 pulses are 40 and 532 ms, respectively, values that are similar to the CUORE-0 ones [7]. The energy resolution at the 2615 keV 208 Tl peak from the thorium source is 11.5 keV FWHM, worse than the 5.7 keV FWHM obtained averaging all the CUORE-0 bolometers. This might be due to the slightly higher temperature of this test or to the different assembly, but it does not affect our results since the attention is focused on the light signal.

Results
The energy spectrum acquired from the TeO 2 bolometer in 6.86 days of data taking is shown in Fig. 2. The peak around 5400 keV is due to the α-decay of 210 Po, a natural contamination of the TeO 2 crystal observed also in the 117 g detector and in CUORE-0. The remaining peaks are γs from the 232 Th source, except for the peak at 1461 keV, which is a γ from 40 K contamination of the cryostat. Both the single (SE) and double escape (DE) peaks of the 2615 keV γ from 208 Tl are visible. The presence of the DE peak is of particular interest because it is a single site production of a β and of a β + , a process similar to the 0νββ.
The light detected versus calibrated heat in the TeO 2 crystal is shown in Fig. 3. The distribution of the light corresponding to each peak in Fig. 2 (blue dots in the figure) is fitted with a Gaussian, the mean of which is overlaid onto the figure. The mean light from the α-decay of 210 Po is found to be < L α >= −3.9±14.5 eV, i.e. compatible with zero. The mean light from the γ peaks is fitted with a line < L β/γ >= LY · (Energy − E th ), with E th = 280 ± 60 keV and LY = 45 ± 2 eV/MeV. The standard deviations of the light distributions are found compatible with the baseline noise of the LD, which therefore appears as the dominant source of fluctuation, hiding any possible dependence on the position of the interaction in the TeO 2 crystal or statistical fluctuations of the number of photons. As in our previous work, the light from the DE peak is compatible with the light from γs, indicating that the fitted line can be used to predict the amount of light detectable from 0νββ events. We compute 101.4±3.4 eV of light for a β/γ event with 0νββ energy, 72 eV less than the light detected at the same energy in the 117 g detector.
The detected light at the 0νββ is few, at the same level of the LD noise, and does not allow one to perform an event  by event rejection of the α background. As indicated in Ref. [8], the emitted Cherenkov light amounts to several hundreds of eV, a much higher value than what we detect.
To increase the light collection efficiency, we applied different modifications to the setup: 1) we changed the VM 2002 light reflector to aluminum foils. Aluminum is expected to have higher reflectivity in the UV band, the region where the Cherenkov emission is more intense. Nevertheless, the amount of light detected is 25% less than in the case of VM 2002; 2) we removed the VM 2002, which is a specular light reflector, and wrapped the crystal with teflon tape, which is a light diffusor. The amount of light detected is compatible with the VM 2002 measurement; 3) we changed the LD to an identical one, but we coated the side faced to the TeO 2 with 60 nm of SiO 2 . It has been demonstrated, in fact, that in the red/infrared band this layer enhances the light absorption by up to 20% [20,21]. In our application, however, the amount of light detected does not change significantly; 4) we added a second LD, monitoring opposite faces with two different light detectors. The amount of light detected from each LD is found to be the 50% of the amount detected with a single LD. This causes an overall decrease of the signal to noise ratio, because each LD adds its own noise; 5) we replaced the crystal with a cylindrical one, 4 cm in diameter and in height. Again the amount of light detected does not change.
Summarizing, none of the above trials succeeded in providing a significant increase of the light collection efficiency, indicating that most of the light is absorbed by the TeO 2 crystal. The setup providing the highest light signal, around 100 eV at the 0νββ, consists in a single LD with the crystal surrounded by the VM 2002 reflector or wrapped with teflon tape.

Perspectives
The recent CUORE-0 result restricted the prediction of the amount of α background in CUORE from B α = 0.01− 0.04 to B α = 0.01 counts/(keV kg y) [7], while the ultimate source of background, due to β/γ radioactivity from the setup, still amounts to B β/γ = 0.001 counts/(keV kg y). From these numbers and from the specs of CUORE we perform toy Monte Carlo simulations to estimate the 90% C.L. sensitivity of CUORE equipped with light detectors.
The outcome of a toy experiment is fitted in energy with a flat probability density function (pdf) for the background and a Gaussian pdf for the signal, and is simultaneously fitted in light with Gaussians pdfs for the α and β/γ light distributions. The posterior pdf of the signal events is obtained integrating over the nuisance parameters and assuming a flat prior. The sensitivity of a single experiment (N 90 ) is computed as the number of signal events corresponding to the 90% of the posterior cumulative distribution. Several (∼ 3000) experiments are generated, and the median of N 90 is used as estimator of the sensitivity. The entire procedure is reiterated by varying the signal to noise ratio in the light detector (Fig. 4).
From the figure one sees that the application of light detectors to CUORE would increase its 90% C.L. sensitivity to the half-life of 130 Te to 2.7 · 10 26 y, a factor 3 higher than CUORE without light detectors. To achieve this goal one needs a signal to noise ratio in the light detector greater than 5, a value that is far from that featured by the setup in this work, equal to 101/72 = 1.4 eV/eV.
From the results presented the increase of the light signal seems not possible, and therefore to upgrade CUORE light detectors able to provide a noise level below 20 eV RMS are needed. Other than trying to improve the NTD technology, there are at least two possible alternatives. The use of phonon-mediated transition edge sensors (TES), as in the CRESST dark matter experiment [22], or the use of phonon-mediated kinetic inductance detectors (KID), as recently proposed by some of us [23]. The TES technology has already proved to reach very good noise levels, but the implementation of 988 light detectors implies a complicated readout, mainly because of the cryogenic SQUID amplifiers that are employed. KIDs already proved to be a highly multiplexable technology in astrophysical applications (up to 400 channels on the same readout line [24]) but the required energy resolution in our application still needs to be demonstrated.

Conclusions
We tested the possibility to discriminate the α background in CUORE by tagging the signal from β particles through the detection of Cherenkov light. The detected light at the 130 Te Q-value is around 100 eV for β/γ particles and no light is detected from α interactions, confirming the validity of this technology. The signal is however small, at the same level of the noise of the bolometric light detectors we are using, and does not allow us to perform an event by event discrimination of the background. We tested modifications of the setup, by using different light reflectors or multiple light detectors, but the light yield did not increase.
We are working on simulations to estimate the fraction of emitted light that escapes the crystal and is eventually absorbed by the light detector. Critical parameters are the index of refraction and the absorbance of TeO 2 , which unfortunately are not available in the literature for low temperatures. To this end we are setting up a dedicated measurement.
Given the results obtained so far, we conclude that, to remove completely the α background in CUORE, light detectors with a noise of 20 eV RMS are needed, a factor 3-4 times better than the bolometric light detectors we used in this work. Changing the technology to TES or KID devices could be an alternative, provided that the present readout and sensitivity limits get overcome.
CUORE without α background would reach a 90% C.L. sensitivity to the 0νββ half-life of more than 3 · 10 26 y, a factor 3 better than the upcoming experiment. Combining the light readout with an enrichment in 130 Te from the natural 34% to ∼ 90% would push the half-life sensitivity by another factor ∼ 3. Depending on the choice of the nuclear matrix elements, this corresponds to an effective neutrino mass sensitivity in the range 14 − 35 meV, down into the inverted hierarchy of neutrino masses.