The detector itself is a striking piece of engineering. CUORE consists of 19 towers, each holding 13 floors of 2-by-2 calorimeter arrays, for an active detector mass of 742 kilograms of TeO2. The crystals serve simultaneously as the source of tellurium-130 decays and the means of detecting them. When a particle deposits energy in a crystal held at roughly 10 millikelvin, the energy is converted into thermal phonons and measured as a temperature variation of about 100 microkelvin per megaelectronvolt by a neutron-transmutation-doped germanium thermistor. The mean relative energy resolution of the calorimeters is approximately 0.3 percent at the decay’s Q-value of 2527.5 kiloelectronvolts, where a hypothetical neutrinoless signal would appear as a monoenergetic peak.

Operating close to a thousand detectors at once creates challenges that predecessor experiments, which used at most tens of detectors on the kilogram scale, never faced. Each calorimeter has slightly different intrinsic properties, so the collaboration treats every channel independently, optimizing its data acquisition and analysis separately. CUORE’s cryogen-free cryostat enables a high duty cycle, but its mechanical cryocoolers introduce significant vibrational noise. Four pulse tube cryocoolers maintain the 40-kelvin and 4-kelvin stages of the cryostat, and their rotating motors inject vibrational noise between 0.1 and 1.5 hertz, with a prominent 1.4-hertz frequency and its harmonics. A system that controls individual pulse tube pressure oscillations was developed to reduce this impact, and the relative phases of the cryocoolers are tuned between datasets to the configuration that minimizes induced noise.

Software denoising provides a second line of defense. The algorithm correlates the noise measured by each calorimeter with that measured by auxiliary devices, including accelerometers, seismometers and microphones installed around the cryostat in the CUORE Faraday room. From these correlations, a transfer function from auxiliary device output to calorimeter noise is constructed at each frequency, convolved with the auxiliary waveforms, and the predicted noise is subtracted from the continuous data stream in the time domain. The method acts as a time-dependent filter, removing steady-state cryocooler noise as well as transient noise from anthropogenic activity near the detector. It is applied to each calorimeter independently for every physics run, capturing daily fluctuations in the noise environment.

Triggering the data is a layered affair. Three trigger types run in parallel during acquisition: signal triggers for particle-induced pulses, noise triggers flagging segments for noise studies, and pulser triggers identifying pulses injected by silicon heaters used for thermal gain correction. An online derivative trigger enables low-latency monitoring, while the official data production relies on an offline Optimum Trigger based on the matched filter technique. This algorithm filters the continuous data in the frequency domain to maximize the signal-to-noise ratio, allowing significantly lower thresholds than the online trigger. By injecting simulated pulses of various energies into the data stream and measuring how often the trigger fires, the collaboration determines trigger efficiency curves; a threshold below 10 kiloelectronvolts has been achieved for up to 59 percent of channel-dataset pairs, and 0.9 percent of them reach below 3 kiloelectronvolts.

Converting raw pulses into energies requires several careful steps. Each event is first characterized by basic parameters such as baseline, baseline slope and baseline root-mean-square, which flag pileup and noisy events. An Optimum Filter, built from a calorimeter-specific averaged pulse template and an averaged noise power spectrum, then yields a precise amplitude estimate. Because small temperature drifts change the intrinsic detector gain, two thermal gain stabilization techniques correct the amplitudes: one relies on fixed-energy pulses injected by the silicon heaters, the other uses the 2615-kiloelectronvolt gamma peak from thorium-232 and cobalt-60 calibration sources as a monoenergetic reference. A statistical figure of merit compared at the 2615-kiloelectronvolt peak selects between the two resulting energy estimators for each calorimeter, and for a typical dataset the calibration-based estimator is chosen for roughly 100 to 150 calorimeters, about 20 percent of which have malfunctioning heaters.

Reconstructing multi-site events adds another dimension. From Monte Carlo simulations, the probability that a hypothetical neutrinoless double-beta decay is fully absorbed in its crystal of origin is about 88 percent, so the collaboration exploits the single-site nature of the decay with an anticoincidence cut that removes events coincident in other crystals. To make this work, all calorimeters must be synchronized in time, since each detector’s intrinsic pulse rise time shifts the apparent timing of events. The collaboration characterizes these delays using true physical coincidences, double events whose energies sum to the 2615-kiloelectronvolt thorium-208 gamma line, supplemented by simultaneously induced pulser events when statistics are low. After synchronization, a coincidence window of 10 milliseconds is used for the neutrinoless decay analysis, while a wider 60-millisecond window serves the background model, which must accurately track coincidences from the gamma region below 3 megaelectronvolts down to the alpha region.

Pulse shape discrimination provides further background rejection. The Reconstruction Error method compares each event with an average pulse representative of particle-induced signals in the range between roughly 100 and 2615 kiloelectronvolts, quantifying how atypical a pulse shape is. The normalized reconstruction error is thresholded at a value of 10 for all calorimeters, chosen by optimizing a figure of merit that balances signal acceptance against background rejection in predefined energy regions. Separately, a blinding procedure protects the decay search from unconscious bias: an artificial peak is inserted at the Q-value by randomly exchanging 10 to 12.5 percent of events between the 2615-kiloelectronvolt peak and the region of interest, ensuring any fake peak would camouflage a potential true signal.

Quantifying exposure and efficiency is central to the search’s credibility. Data quality selections and the analysis chain reduce the collected exposure by about 9 percent, with pulser crosstalk adding roughly 1 percent more, so that from a total collected exposure of 2264.32 kilogram-years the final analyzed exposure is 2039.0 kilogram-years of TeO2, corresponding to 567.0 kilogram-years in tellurium-130. Base cut efficiencies, measured with heater pulses of known amplitude, cover detection, pileup rejection and energy reconstruction; detection and energy reconstruction efficiencies in the decay region of interest are nearly 100 percent, while pileup rejection sits at about 96 percent. The exposure-weighted anticoincidence efficiency is 99.80 percent with an uncertainty of 0.05 percent, the pulse shape discrimination efficiency is 97.9 percent with an uncertainty of 1.8 percent, and the total analysis efficiency is 93.4 percent with an uncertainty of 1.8 percent.

The payoff extends beyond the flagship decay search. The same analysis framework underpins a detailed background model of radioactive contamination, a precise measurement of the two-neutrino double-beta decay half-life of tellurium-130, spectral shape studies for cross-validating nuclear models, searches for fractionally charged particles, muon track reconstruction, and low-energy studies enabled by the keV-scale thresholds, including potential dark matter signals. The collaboration notes that the dataset represents the first high-statistics report on the performance of a tonne-scale cryogenic calorimeter system operated in a modern cryogen-free cryostat, an important benchmark for next-generation experiments applying this technology to dark matter, neutrinoless double-beta decay or coherent elastic neutrino-nucleus scattering. The current data-taking plan aims to reach 3 tonne-years of analyzed TeO2 exposure, about 1 tonne-year in tellurium-130, for the ongoing neutrinoless double-beta decay search.

Subject of Research: End-to-end data analysis methods for the CUORE cryogenic calorimeter experiment

Article Title: End-to-end data analysis methods for the CUORE experiment

Article References: Adams, D. Q., Alduino, C., Alfonso, K., Armatol, A., Avignone, F. T., III, Azzolini, O., Bari, G., Bellini, F., Benato, G., Beretta, M., Biassoni, M., Branca, A., Brofferio, C., Bucci, C., Camilleri, J., Caminata, A., Campani, A., Cao, J., Capelli, C., … Zucchelli, S. (2026). End-to-end data analysis methods for the CUORE experiment. The European Physical Journal C, 86(10), Article 1237. https://doi.org/10.1140/epjc/s10052-026-16350-3

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16350-3

Keywords: CUORE, neutrinoless double-beta decay, tellurium-130, cryogenic calorimeters, TeO2, Gran Sasso, detector response, signal efficiency, background rejection, optimum filter, pulse shape discrimination, exposure