Neutrinoless double beta decay

Neutrinoless double beta decay (0νββ) is a commonly proposed and experimentally pursued theoretical radioactive decay process that would prove a Majorana nature of the neutrino particle.

The discovery of neutrinoless double beta decay could shed light on the absolute neutrino masses and on their mass hierarchy (Neutrino mass). It would mean the first ever signal of the violation of total lepton number conservation. A Majorana nature of neutrinos would confirm that the neutrino is its own antiparticle.

To search for neutrinoless double beta decay, there are currently a number of experiments underway, with several future experiments for increased sensitivity proposed as well. Two years later, in 1937, the Italian physicist Ettore Majorana first introduced the concept of a particle being its own antiparticle, explicitly mentioning his theory's possible application to neutrinos. Particles of this nature were subsequently named after him as Majorana particles.

In 1939, Wendell H. Furry realized that Majorana's theory allowed a new decay channel. The privative label "neutrino-less" appeared in 1953 and largely replaced the original terminology.

This theoretical decay was the first idea proposed which could be used to search for the violation of lepton number conservation. It has, since then, drawn attention for being useful to study the nature of neutrinos (see quote).

Physical relevance

Conventional double beta decay

Neutrinos are conventionally produced in weak decays. These nuclei can only decay by emitting two electrons (that is, via double beta decay). There are about a dozen nuclei that have been confirmed to decay only via a double beta decay.]]

If the nature of the neutrinos is Majorana, then they can be emitted and absorbed in the same process without showing up in the corresponding final state.

The simplest decay process is known as the light neutrino exchange.

The two resulting electrons are then the only emitted particles in the final state and must carry approximately the difference of the sums of the binding energies of the two nuclei before and after the process as their kinetic energy. The heavy nuclei do not carry significant kinetic energy.

In that case, the decay rate can be calculated with

:<math>\ \Gamma_{\beta\beta}^{0\nu}\ =\ \frac{1}{T_{\beta\beta}^{0\nu\ =\ G^{0\nu}\ \left| M^{0\nu} \right|^2\ \langle m_{\beta\beta} \rangle^2\ ,</math>

where <math>\ G^{0\nu}\ </math> denotes the phase space factor, <math>\ \left| M^{0\nu}\right|^2\ </math> the (squared) matrix element of this nuclear decay process (according to the Feynman diagram), and <math>\ \langle m_{\beta\beta}\rangle^2\ </math> the square of the effective Majorana mass. The calculation itself relies on sophisticated nuclear many-body theories and there exist different methods to do this. The NME, <math>\ \left| M^{0\nu}\right|\ ,</math> differs also from nucleus to nucleus (i.e. chemical element to chemical element). Today, the calculation of the NME is a significant problem and it has been treated by different authors in different ways. One question is whether to treat the range of obtained values for <math>\ \left| M^{0\nu}\right|\ </math> as the theoretical uncertainty and whether this is then to be understood as a statistical uncertainty. There are 35 nuclei that can undergo neutrinoless double beta decay (according to the aforementioned decay conditions).

Experiments and results

Nine different candidates of nuclei are being considered in experiments to confirm neutrinoless double beta-decay: <math >\mathrm{ {}^{48}Ca, {}^{76}Ge, {}^{82}Se, {}^{96}Zr, {}^{100}Mo, {}^{116}Cd, {}^{130}Te, {}^{136}Xe, {}^{150}Nd } ~.</math>

|align="right"| <math>\mathrm{ {}^{76}Ge}~</math> || Heidelberg-Moscow || ||

|align="right"| <math>\mathrm{ {}^{76}Ge}~</math> || GERDA || ||

|align="right"| <math>\mathrm{ {}^{76}Ge}~</math> || MAJORANA

| ||

|align="right"| <math>\mathrm{ {}^{76}Ge}~</math> || LEGEND || ||

|align="right"| <math>\mathrm{ {}^{82}Se}~</math> || NEMO-3 || ||

|align="right"| <math>\mathrm{ {}^{82}Se}~</math> || CUPID-0 || ||

|align="right"| <math>\mathrm{ {}^{96}Zr}~</math> || NEMO-3 || ||

|align="right"| <math>\mathrm{ {}^{100}Mo}~</math> || NEMO-3 || ||

|align="right"| <math>\mathrm{ {}^{116}Cd}~</math> || Aurora || ||

|align="right"| <math>\mathrm{ {}^{116}Cd}~</math> || Solotvina || ||

|align="right"| <math>\mathrm{ {}^{128}Te}~</math> || CUORE

| ||

|align="right"| <math>\mathrm{ {}^{130}Te}~</math> || CUORE || ||

|align="right"| <math>\mathrm{ {}^{136}Xe}~</math> || EXO || ||

|align="right"| <math>\mathrm{ {}^{136}Xe}~</math> || KamLAND-Zen || ||

|align="right"| <math>\mathrm{ {}^{150}Nd}~</math> || NEMO-3 || ||

|colspan="4" align="center"| Experimental limits (at least 90% C.L.) Initially, in 2001 the collaboration announced a or a evidence (depending on the used calculation method). The <math>Q</math>-value of for 0ββ decay is 2039 keV, but no excess of events in this region was found. Phase II of the experiment started data-taking in 2015, and it used around 36 kg of germanium for the detectors. The detector has been decommissioned and published its final results in December 2020. No neutrinoless double beta decay was observed.

Majorana Demonstrator

The Majorana collaboration published their first result from data taken during construction, commissioning, and the beginning of operations in 2018. With a total of 9.95 kg yr of enriched exposure, the collaboration set a lower limit on the half-life of 0ββ in of <math>\ 1.9 \cdot 10^{25}\ \mathrm{years} ~.</math> In 2019, a new result was published with of enriched exposure. The Majorana Demonstrator observed one event in the region of interests, where only 0.65 events were expected from the estimated background. This resulted in a lower limit on the neutrinoless double-𝛽 decay half-life of <math>\ 2.7\cdot 10^{25}\ \mathrm{years}\ </math> (90% C.L.). The final result of the 0ββ search of the experiment was published in 2023, with a total enriched active exposure of 64.5 kg yr. This result set a half-life limit of 0ββ in at <math>T_{\beta\beta}^{0\nu}>8.3\cdot 10^{25}</math>yr (90% C.L.). Additionally, the Majorana Demonstrator had a world-leading energy resolution of 2.52 keV FWHM at the 2039 keV <math>Q_{\beta\beta}</math>. CUORE published in 2020 results from the search for neutrinoless double-beta decay in <math>\mathrm{ {}^{130}Te}</math> with a total exposure of 372.5 kg⋅yr, finding no evidence for 0ββ decay and setting a 90% CI Bayesian lower limit of <math>\ T_{\beta\beta}^{0\nu}>3.2\cdot 10^{25}\ \mathrm{years}\ </math> and in April 2022 a new limit was set on <math>\ T_{\beta\beta}^{0\nu}>2.2\cdot 10^{25}\ \mathrm{years}\ </math> at the same confidence level. Further results published in January 2026 increased the limit to <math>\ T_{\beta\beta}^{0\nu}>3.5\cdot 10^{25}\ \mathrm{years}\ </math>. reporting a limit of <math>T_{\beta\beta}^{0\nu}>1.07\cdot 10^{26}\ \mathrm{years}\ </math> (90% C.L.). In 2023 the limit was improved to <math>T_{\beta\beta}^{0\nu}>2.3\cdot 10^{26}\ \mathrm{years}\ </math> (90% C.L.), and in 2025 it was improved to <math>T_{\beta\beta}^{0\nu}>3.8\cdot 10^{26}\ \mathrm{years}\ </math> (90% C.L.).

JUNO (Jiangmen Underground Neutrino Observatory)

Proposed/future experiments

nEXO experiment:
As EXO-200's successor, nEXO is planned to be a ton-scale experiment and part of the next generation of 0ββ experiments. The detector material is planned to weigh about 5 t, serving a 1% energy resolution at the <math>Q</math>-value.
SuperNEMO
NuDoubt<sup>++</sup>:
The NuDoubt⁺⁺ experiment aims at the measurement of two-neutrino and neutrinoless positive double weak decays (2β⁺/ECβ⁺). It is based on a new detector concept combining hybrid and opaque scintillators paired with a novel light read-out technique. The technology is particularly suitable detecting positrons (β⁺) signatures. In its first phase, NuDoubt⁺⁺ is going to operate under high-pressure loading of enriched Kr gas. It expects to discover two-neutrino positive double weak decay modes of Kr within 1 tonne-week exposure