Supplementary material

Figure 1

Detector rendering
   
Rendering of the 6-stage cryostat with the array of TeO2 crystals.


The Detector after installation
   
The detector right after the installation.


Real CUORE crystal
   
One of the CUORE calorimeters.

Figure 2

Cryostat performance
   
Cryogenic performance. Top: The exposure accumulated by CUORE (left, teal), along with the exposure used for this analysis (left, orange). Middle: Examples of common temperature instabilities induced by external causes, e.g. blackouts and earthquakes, or human intervention, such as regular maintenance or the insertion of calibration sources.
Bottom: The temperature stability of CUORE over ~1 yr of continuous operation.
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Figure 3

PT phase optimization
   
PT phase optimization. Top: frequency spectrum of the noise for a random combination of the PT phases (orange) and after the active phase tuning (teal). The frequency spectrum of physical signals is also reported for reference. Bottom: integral of the power spectrum at the PT frequency (1.4 Hz) and its harmonics before and after active noise cancellation.

Figure 4

Physics spectrum for 1038 kg yr exposure
   
Physics spectrum for 1038.4 kg · yr of TeO2 exposure in counts/(keV kg yr). We separately show the effects of the base cuts, the anti-coincidence (AC) cut, and the pulse shape discrimination (PSD). The most prominent background peaks in the spectrum are highlighted. Top right inset: the ROI after all selection cuts, with the best-fit curve (solid red), the best-fit curve with the 0νββ rate fixed to the 90% CI limit (blue), and background-only fit (black) superimposed.

Extended Data Figure 1

Schematic of a bolometer
   
Simplified calorimeter thermal model. The detector is modeled as a single object with heat capacity C coupled to the heat bath (with constant temperature T0) through the thermal conductance G. The NTD thermistor for signal readout is glued to the absorber.


Typical CUORE pulse
   
Example of a CUORE pulse from the 2615 keV calibration line: T0 corresponds to the baseline height, the pulse amplitude is proportional to the deposited energy, and the decay time depends on the C/G ratio.

Extended Data Figure 2

Roman lead under the sea
   
The lead bricks recovery from the Sardinian sea.


Roman lead cutting
   
The ingot inscriptions were cut and preserved, while the ingot bodies were used for the CUORE internal lead shield.


Roman lead shielding
   
Lateral view of the internal lead shield.

Extended Data Figure 3

Pulse Shape Discrimination
   
Effect of the PSD cut on calibration data around the 2615 keV line (left) and on physics data near Qββ (right). In calibration data, the AC is not applied in order to maximize the statistics on the γ peaks, and the PSD mostly removes pileup events (events with more than one energy deposit in the time window). In physics data, the PSD mostly eliminates random noise events, which can correspond to either physical events with excessive noise or to noise-induced events with non-physical pulse shapes.
Such events appear randomly across the energy spectrum, so the cut mostly acts on the continuum.

Extended Data Figure 4

Trigger and High Level Analysis
   
Optimum trigger and statistical analysis. Top left: Distribution of energy thresholds at 90% trigger efficiency for the OT algorithm in a single dataset. The 40 keV analysis threshold is indicated by the vertical line. Top right: 90% C.I. exclusion limits on T1/2 from an ensemble of 104 toy experiments generated with the background-only model, with background rates obtained from the background-only fit to the data. The median exclusion sensitivity is indicated by the orange line. Bottom left: Posterior probability distribution for Γ obtained from the Bayesian fit, with the 90% C.I. highlighted. Bottom right: ΔΧ2 values obtained from the profile likelihood of Γ, with ΔΧ2 = 0 being the most-favored value.
The frequentist limit at 90% confidence level (C.L.) is indicated.

Extended Data Figure 5

Principal Component Analysis
   
PCA performance. Left: example of a normalization fit of the PCA reconstruction error vs energy for a single calorimeter and dataset. The distribution contains only events that passed the other base cuts. The second order polynomial fit is shown in orange. Right: two example pulses from this calorimeter. %, along with their locations in the left scatter plot. The actual pulse is drawn in teal, and the corresponding reconstruction obtained by the PCA is drawn in orange.
The top pulse deviates from the expected shape of a good pulse and is rejected, while the bottom one conforms to the expected response and is accepted.