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The neutrinoless double beta decay (0νββ) is a commonly proposed and experimentally pursued theoretical
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
process that would prove a Majorana nature of the
neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
particle In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from ...
. To this day, it has not been found. The discovery of the neutrinoless
double beta decay In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move clos ...
could shed light on the absolute neutrino masses and on their mass hierarchy (
Neutrino mass A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
). It would mean the first ever signal of the violation of total
lepton number In particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. Lepton number ...
conservation. A Majorana nature of neutrinos would confirm that the neutrino is its own
antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
. 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.


Historical development of the theoretical discussion

Back in 1939,
Wendell H. Furry Wendell Hinkle Furry (February 18, 1907 – December 17, 1984) was a professor of physics at Harvard University who made contributions to theoretical and particle physics. The Furry theorem is named after him. Early life Furry was born in Pra ...
proposed the idea of the Majorana nature of the neutrino, which was associated with beta decays. Furry stated the transition probability to even be higher for the neutrino''less'' double beta decay. It was the first idea proposed to search for the violation of lepton number conservation. It has, since then, drawn attention to it for being useful to study the nature of neutrinos (see quote). The Italian physicist
Ettore Majorana Ettore Majorana (,, uploaded 19 April 2013, retrieved 14 December 2019 ; born on 5 August 1906 – possibly dying after 1959) was an Italian theoretical physicist who worked on neutrino masses. On 25 March 1938, he disappeared under mysteri ...
first introduced the concept of a particle being its own antiparticle. Particles' nature was subsequently named after him as Majorana particles. The neutrinoless double beta decay is one method to search for the possible Majorana nature of neutrinos.


Physical relevance


Conventional double beta decay

Neutrinos are conventionally produced in weak decays. Weak beta decays normally produce one
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
(or
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collide ...
), emit an antineutrino (or neutrino) and increase the
nucleus Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: * Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucl ...
' proton number Z by one. The nucleus' mass (i.e.
binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
) is then lower and thus more favorable. There exists a number of elements that can decay into a nucleus of lower mass, but they cannot emit ''one'' electron only because the resulting nucleus is kinematically (that is, in terms of energy) not favorable (its energy would be higher). These nuclei can only decay by emitting ''two'' electrons (that is, via ''double beta decay''). There are about a dozen confirmed cases of nuclei that can only decay via double beta decay. The corresponding decay equation is: :(A,Z)\rightarrow (A,Z+2)+2e^-+2\bar_e. It is a weak process of second order. A simultaneous decay of two
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...
s in the same nucleus is extremely unlikely. Thus, the experimentally observed lifetimes of such decay processes are in the range of 10^-10^ years. A number of
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass num ...
s have been observed already to show this two-neutrino double beta decay. This conventional double beta decay is allowed in the
Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
of
particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
. It has thus both a theoretical and an experimental foundation.


Overview

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. As Dirac particles, both the neutrinos produced by the decay of the W bosons would be emitted, and not absorbed after. The neutrinoless double beta decay can only occur if * the neutrino particle is Majorana, ''and'' * there exists a right-handed component of the weak leptonic current ''or'' the neutrino can change its
handedness In human biology, handedness is an individual's preferential use of one hand, known as the dominant hand, due to it being stronger, faster or more dextrous. The other hand, comparatively often the weaker, less dextrous or simply less subject ...
between emission and absorption (between the two W vertices), which is possible for a non-zero neutrino mass (for at least one of the neutrino species). The simplest decay process is known as the light neutrino exchange. It features one neutrino emitted by one nucleon and absorbed by another nucleon (see figure to the right). In the final state, the only remaining parts are the nucleus (with its changed proton number Z) and two electrons: :(A,Z)\rightarrow (A,Z+2)+2e^- The two electrons are emitted quasi-simultaneously. 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. The electrons will be emitted back-to-back due to momentum conservation. In that case, the
decay rate Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consid ...
can be calculated with : \Gamma_^=\frac = G^\cdot\left, M^\^2\cdot\langle m_\rangle^2 , where G^ denotes the
phase space In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usuall ...
factor, \left, M^\^2 the (squared) matrix element of this nuclear decay process (according to the Feynman diagram), and \langle m_\rangle^2 the square of the effective Majorana mass. First, the effective Majorana mass can be obtained by : \langle m_\rangle = \sum_i U_^2m_i, where m_i are the Majorana neutrino masses (three neutrinos \nu_i ) and U_ the elements of the neutrino mixing matrix U (see PMNS matrix). Contemporary experiments to find neutrinoless double beta decays (see section on experiments) aim at both the proof of the Majorana nature of neutrinos and the measurement of this effective Majorana mass \langle m_\rangle (can only be done if the decay is actually generated by the neutrino masses). The nuclear matrix element (NME) \left, M^\ cannot be measured independently; it must, but also can, be calculated. The calculation itself relies on sophisticated nuclear many-body theories and there exist different methods to do this. The NME \left, M^\ differs also from nucleus to nucleus (i.e.
chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
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 \left, M^\ as the theoretical uncertainty and whether this is then to be understood as a ''statistical'' uncertainty. Different approaches are being chosen here. The obtained values for \left, M^\ often vary by factors of 2 up to about 5. Typical values lie in the range of from about 0.9 to 14, depending on the decaying nucleus/element. Lastly, the phase-space factor G^ must also be calculated. It depends on the total released kinetic energy ( Q=M_\text^\text-M_\text^\text-2m_\text , i.e. "Q-value") and the atomic number Z. Methods utilize Dirac
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
s, finite nuclear sizes and electron screening. There exist high-precision results for G^ for various nuclei, ranging from about 0.23 (for \mathrm), and 0.90 (\mathrm) to about 24.14 (\mathrm). It is believed that, if neutrinoless double beta decay is found under certain conditions (decay rate compatible with predictions based on experimental knowledge about neutrino masses and mixing), this would indeed "likely" point at Majorana neutrinos as the main mediator (and not other sources of new physics). 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: \mathrm. They all have arguments for and against their use in an experiment. Factors to be included and revised are natural abundance, reasonably priced enrichment, and a well understood and controlled experimental technique. The higher the Q-value, the better are the chances of a discovery, in principle. The phase-space factor G^ , and thus the decay rate, grows with Q^5. Experimentally of interest and thus measured is the sum of the kinetic energies of the two emitted electrons. It should equal the Q-value of the respective nucleus for neutrinoless double beta emission. The table shows a summary of the currently best limits on the lifetime of 0νββ. From this, it can be deduced that neutrinoless double beta decay is an extremely rare process - if it occurs at all.


Heidelberg-Moscow collaboration

The so-called "Heidelberg-Moscow collaboration" (HDM; 1990-2003) of the German Max-Planck-Institut für Kernphysik and the Russian science center
Kurchatov Institute The Kurchatov Institute (russian: Национальный исследовательский центр «Курчатовский Институт», 'National Research Centre "Kurchatov Institute) is Russia's leading research and developmen ...
in Moscow famously claimed to have found "evidence for neutrinoless double beta decay" ( Heidelberg-Moscow controversy). Initially, in 2001 the collaboration announced a 2.2σ, or a 3.1σ (depending on the used calculation method) evidence. The decay rate was found to be around 2\cdot 10^ years. This result has been topic of discussions between many scientists and authors. To this day, no other experiment has ever confirmed or approved the result of the HDM group. Instead, recent results from the GERDA experiment for the lifetime limit clearly disfavor and reject the values of the HDM collaboration. Neutrinoless double beta decay has not yet been found.


GERDA (Germanium Detector Array) experiment

The GERDA collaboration's result of phase I of the detector was a limit of T_^>2.1\cdot 10^ years (90% C.L.). It used
Germanium Germanium is a chemical element with the symbol Ge and atomic number 32. It is lustrous, hard-brittle, grayish-white and similar in appearance to silicon. It is a metalloid in the carbon group that is chemically similar to its group neighbors ...
both as source and detector material. Liquid
argon Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice a ...
was used for
muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As w ...
vetoing and as a shielding from background radiation. The Q-value of Germanium for 0νββ 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 exposure analyzed until July 2020 was 10.8 kg yr. Again, no signal was found and thus a new limit was set to T_^>5.3\cdot 10^ years (90% C.L.). The detector has stopped working and published its final results in December 2020. No neutrinoless double beta decay was observed.


EXO (Enriched Xenon Observatory) experiment

The Enriched Xenon Observatory-200 experiment uses
xenon Xenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the ...
both as source and detector. The experiment is located in New Mexico (US) and uses a time-projection chamber (TPC) for three-dimensional spatial and temporal resolution of the electron track depositions. The EXO-200 experiment yielded a lifetime limit of T_^>3.5\cdot 10^ years (90% C.L.). When translated to effective Majorana mass, this is a limit of the same order as that obtained by GERDA I and II.


Currently data-taking experiments

* '' CUORE (Cryogenic Underground Observatory for Rare Events) experiment'': ** The CUORE experiment consists of an array of 988 ultra-cold TeO2 crystals (for a total mass of 206 kg of \mathrm) used as bolometers to detect the emitted beta particles and as the source of the decay. CUORE is located underground at the
Laboratori Nazionali del Gran Sasso Laboratori Nazionali del Gran Sasso (LNGS) is the largest underground research center in the world. Situated below Gran Sasso mountain in Italy, it is well known for particle physics research by the INFN. In addition to a surface portion of th ...
, and it began its first physics data run in 2017. CUORE published in 2020 results from the search for neutrinoless double-beta decay in \mathrm with a total exposure of 372.5 kg⋅yr, finding no evidence for 0νββ decay and setting a 90% CI Bayesian lower limit of T_^>3.2\cdot 10^ years and in April 2022 a new limit was set on T_^>2.2\cdot 10^ years at the same confidence level. The experiment is steadily taking data, and it is expected to finalize its physics program by 2024. * '' KamLAND-Zen (Kamioka Liquid Scintillator Antineutrino Detector-Zen) experiment'': ** The KamLAND-Zen experiment commenced using 13 tons of xenon as a source (enriched with about 320 kg of \mathrm), contained in a nylon balloon that is surrounded by a liquid
scintillator A scintillator is a material that exhibits scintillation, the property of luminescence, when excited by ionizing radiation. Luminescent materials, when struck by an incoming particle, absorb its energy and scintillate (i.e. re-emit the absorbe ...
outer balloon of 13 m diameter. Starting in 2011, KamLAND-Zen Phase I started taking data, eventually leading to set a limit on the lifetime for neutrinoless double beta decay of T_^>1.9\cdot 10^ years (90% C.L.). This limit could be improved by combining with Phase II data (data-taking started in December 2013) to T_^>2.6\cdot 10^ years (90% C.L.). For Phase II, the collaboration especially managed to reduce the decay of \mathrm, which disturbed the measurements in the region of interest for 0νββ decay of \mathrm. In August 2018, ''KamLAND-Zen 800'' was completed containing 800 kg of \mathrm. It is reported to be now the biggest and most sensitive experiment in the world to search for neutrinoless double beta decay.


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 0νββ experiments. The detector material is planned to weigh about 5 t, serving a 1% energy resolution at the Q-value. The experiment is planned to deliver a lifetime sensitivity of about T_^>1.35\cdot 10^ years after 10 years of data-taking. *'' LEGEND (experiment)'' * '' SuperNEMO''


See also

*
Double beta decay In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move clos ...
* Heidelberg-Moscow controversy * Neutrinoless double electron capture


References

{{Neutrino detectors Nuclear physics Standard Model Physics beyond the Standard Model Radioactivity Hypothetical processes