CUORE and CUPID: Catching a Double Beta Decay as a Whisper of Heat

A few-MeV energy deposit in a piece of matter is a microscopic event — a few electron-volts of ionisation here, a few photons there, a phonon cascade through the lattice. Most detector technologies amplify some particular component of that cascade: ionisation electrons drifted through a TPC, scintillation photons collected by photomultipliers, charge collected on a semiconductor electrode. Each amplification is imperfect, and each loses some fraction of the deposited energy along the way.

A cryogenic bolometer does something more direct. It cools a chunk of crystalline material to such low temperatures — typically 10 millikelvin — that the heat capacity drops by orders of magnitude and a single MeV-scale energy deposit produces a measurable temperature rise of tens of microkelvins. A sensitive thermistor attached to the crystal records the temperature pulse, and the integrated heat is a direct measurement of the deposited energy with essentially no amplification step in between. The energy resolution is correspondingly excellent — a few electron-volts at the MeV scale.

The technique was developed in the 1980s and 1990s for X-ray astronomy and microcalorimetric measurements of single beta-decay endpoints. CUORE, the Cryogenic Underground Observatory for Rare Events, at Gran Sasso scales the same idea up to a single facility containing 988 tellurium-dioxide crystals totalling 742 kg of TeO${}_2$, all cooled to 10 mK simultaneously. Since 2017, CUORE has been pursuing the most ambitious neutrinoless double beta decay search using ${}^{130}$Te. The planned successor CUPID adds a per-event particle-identification channel and aims at the inverted-mass-ordering parameter space. This post is about how the technique works, what CUORE has measured, and what CUPID will do.

How a bolometer measures energy

The heat capacity of an insulating dielectric crystal at low temperature is dominated by phonons and follows the Debye law:

$C(T)=\frac{12{\pi }^4}{5}N{k}_B{\left(\frac{T}{T_D}\right)}^3$

where $T_D$ is the Debye temperature (about 230 K for TeO${}_2$) and $N$ is the number of atoms. At a working temperature of $T=10$ mK, this gives a heat capacity for a 750-gram TeO${}_2$ crystal of roughly $10^{-9}$ J/K — nine orders of magnitude lower than at room temperature.

A 2.5 MeV energy deposit, equivalent to $4\times 10^{-13}$ J, then produces a temperature rise of

$\Delta T=\frac{E}{C(T)}\approx \frac{4\times 10^{-13}\mathrm{J}}{10^{-9}J/K}\approx 400\mu \mathrm{K}$

This is far above the noise floor of a well-designed thermistor reading at this temperature. The temperature pulse rises over a millisecond, decays over a hundred milliseconds (set by the thermal coupling to the mixing-chamber cold sink), and is recorded as a single waveform per event.

The resulting energy resolution at the 2.527 MeV ${}^{130}$Te Q-value is about 5 keV FWHM — comparable to germanium semiconductors and far better than any other large-scale 0νββ technology. The crystal is its own target and its own detector, with no separate amplification chain.

The CUORE detector

CUORE’s design is a tower of bolometers cooled together. The active volume consists of 988 TeO${}_2$ crystals, each $5\times 5\times 5$ cm in size and weighing about 750 grams, assembled into 19 vertical towers of 13 crystals on 4 floors each. The total active mass is 742 kg of TeO${}_2$, containing about 207 kg of ${}^{130}$Te through its natural 34% abundance.

Each crystal is held by ultra-pure copper supports that minimise heat conduction to the mounting structure. A small neutron-transmutation-doped germanium thermistor (NTD) is glued to one face of each crystal — a chunk of germanium activated by neutron irradiation in a reactor to give it a precise impurity concentration, which in turn provides a steep temperature-dependent resistance at the milli-kelvin operating point. A current bias through the NTD reads out as a voltage that tracks the crystal temperature in real time.

Cooling 988 crystals plus their copper mounts and the ancillary structure to 10 mK simultaneously requires a multi-stage dilution refrigerator at the largest scale ever built. CUORE’s cryostat passes through several intermediate temperature stages — 40 K, 4 K, 1 K, 100 mK, 10 mK — using a combination of pulse-tube refrigerators and dilution mixing. The total cooling power at 10 mK is approximately 4 microwatts, just enough to maintain the operating temperature against the heat leak from cables and supports.

The entire detector sits behind thick lead and copper shielding to suppress external gamma and muon backgrounds, in the Gran Sasso underground laboratory.

What CUORE has measured

CUORE began data-taking in 2017. Its initial physics result, published in 2018 with one year of data, set the strongest limit on the ${}^{130}$Te 0νββ half-life at $T_{1/2}^{0\nu }>1.5\times 10^{25}$ years at 90% confidence. Subsequent analyses with two and three years of additional data have pushed the limit to approximately $T_{1/2}^{0\nu }>2.2\times 10^{25}$ years.

Translating to effective Majorana mass involves the ${}^{130}$Te nuclear matrix element, which carries roughly 25% uncertainty across competing nuclear models. With this caveat the corresponding mass bound is approximately $|m_{\beta \beta }|<90\text{–}305$ meV, weaker than LEGEND’s germanium bound by a factor of a few but constraining the same parameter space through a different isotope.

The dominant background in CUORE’s signal region has turned out to be surface alphas from ${}^{210}$Po contamination of the crystal and copper-mount surfaces. Alpha particles emitted at the surface lose a fraction of their energy escaping the surface layer and can deposit residual energies overlapping the 2.5 MeV signal region. CUORE has no way to distinguish these from a 0νββ candidate event by heat alone — both signatures look like single-event temperature pulses of the same magnitude.

The surface-alpha background is the limiting factor for the current generation. CUORE’s quoted background level in the signal region is about $1.5\times 10^{-2}$ counts per (keV kg yr), substantially higher than GERDA Phase II at $5\times 10^{-4}$. Pushing further requires a particle-identification capability that CUORE does not have — and that CUPID adds.

CUPID: light readout for alpha rejection

CUPID, the CUORE Upgrade with Particle Identification, replaces the TeO${}_2$ crystals with a different scintillating compound, typically lithium-100 molybdate (Li_2$$^{100}MoO${}_4$) or zinc-82 selenide. These scintillating crystals produce a small amount of visible light per energy deposit — about 1 keV of light per MeV of heat in lithium molybdate.

Critically, the light-to-heat ratio depends on the particle type. Alpha particles produce relatively less scintillation light per unit heat than electrons, because of the higher local ionisation density and the corresponding scintillation quenching. Measuring both channels for each event therefore gives an event-by-event identification: alpha events sit at low light-to-heat ratio, electron events sit at high light-to-heat ratio, with a clean separation between them.

The light readout uses a second bolometer — a thin germanium absorber with its own NTD thermistor — placed on top of each scintillator. The light bolometer detects the scintillation photons via the heat they deposit, providing a calorimetric measurement of the light yield at the same temperature as the main crystal.

The combined heat-plus-light readout suppresses the surface-alpha background by roughly a factor of 100 or more, pushing CUPID’s projected background below $10^{-4}$ counts per (keV kg yr) — comparable to LEGEND-200’s achievement in germanium.

CUPID’s reach and timeline

CUPID’s design target is approximately 250 kg of isotope mass with a five-year exposure, reaching a half-life sensitivity of $5\times 10^{27}$ years and an effective Majorana mass bound around 12-20 meV — covering most of the inverted-mass-ordering region.

The timeline envisions a CUPID demonstrator (CUPID-Mo at Modane) currently taking data with a small array of lithium-100 molybdate bolometers, validating the technique at the kilogram scale. The full CUPID experiment would reuse much of CUORE’s cryogenic infrastructure at Gran Sasso, with the new scintillating crystals replacing the TeO${}_2$ bolometers in a phased installation expected in the late 2020s.

CUPID-Mo and CUPID-0 (a similar demonstrator at LNGS using zinc-82 selenide) have both produced first-generation ${}^{100}$Mo and ${}^{82}$Se limits competitive with their respective historical bests, demonstrating that the scintillating-bolometer approach scales to the larger detector.

Why a bolometer in the 0νββ portfolio matters

The four major next-generation $0\nu \beta \beta$ experiments — LEGEND-1000, KamLAND-Zen 8000, nEXO, and CUPID — pursue the same goal with four different isotopes and four different detector technologies. The diversity is essential for two reasons.

First, the conversion from measured half-life to effective Majorana mass depends on the nuclear matrix element for the specific isotope, and different nuclear-physics calculations give significantly different matrix elements for the same isotope, with shell-model, QRPA, and IBM-2 results disagreeing by factors of 2-3. Measuring the same Majorana mass through multiple isotopes constrains the underlying nuclear physics and reduces the matrix-element ambiguity.

Second, the systematic uncertainties differ between technologies. Surface alphas dominate CUORE; nuclear matrix element uncertainty dominates KamLAND-Zen at the largest masses; energy-resolution limitations and fiducialisation systematics affect different detectors differently. A coherent signal in multiple technologies would be far more compelling than a result from any single experiment, and a null in two or three would constrain the underlying physics from independent angles.

CUPID brings particle-identification capability to a cryogenic-bolometer approach with exceptional energy resolution, attacking the inverted-mass-ordering region through an isotope and technique that complement the germanium and xenon approaches. The combined portfolio is what will determine whether neutrinos are Majorana fermions in the coming decade.

Summary

CUORE is the first ton-scale cryogenic bolometer experiment, using 988 TeO${}_2$ crystals cooled to 10 mK to search for neutrinoless double beta decay in ${}^{130}$Te. Each crystal records the 2.5 MeV deposited energy as a temperature rise of about 400 microkelvins through a sensitive germanium thermistor, delivering 5 keV FWHM energy resolution. The current limit on the ${}^{130}$Te 0νββ half-life is approximately $2.2\times 10^{25}$ years, with surface alpha contamination as the dominant systematic. The planned CUPID upgrade replaces TeO${}_2$ with a scintillating crystal such as lithium-100 molybdate or zinc-82 selenide, adding a light-readout bolometer to each module for event-by-event alpha-versus-electron discrimination. CUPID will reach approximately 12-20 meV effective Majorana mass sensitivity, comparable to LEGEND-1000 and nEXO, and complements those experiments through a different isotope and technology. Together with LEGEND, KamLAND-Zen, and nEXO, the cryogenic-bolometer approach defines one of the four parallel paths into the inverted-mass-ordering parameter space — and the answer to whether neutrinos are their own antiparticles.