Neutrino-free double beta decay

The neutrino-free double beta decay is a hypothetical radioactive decay process . As a short symbol it is referred to as 0νββ. He would prove that neutrinos are Majorana fermions and therefore their own antiparticles . It would violate the lepton number conservation. His observation could provide information about the absolute neutrino masses and their mass hierarchy.

A number of experiments are in progress to demonstrate neutrino-free double beta decay. To date (2020) the process has not been observed.

Historical development of the theoretical discussion

Ettore Majorana, who was the first to introduce the idea that particles and antiparticles can be identical.

The Italian physicist Ettore Majorana introduced the concept in 1937 that a type of particle could be its own antiparticle. Such particles were later named after him as Majorana particles.

As early as 1939, Wendell Hinkle Furry expressed the idea of ​​the Majorana nature of the neutrino with beta decays. Since then, this possibility of studying the nature of neutrinos has been considered:

"[T] he 0ν mode [...] which violates the lepton number and has been recognized since a long time as a powerful tool to test neutrino properties."

- Oliviero Cremonesi

Physical description

Double beta decay in general

→ Main article : Double beta decay

The double beta decay is to be expected for certain nuclides with an even number of protons and an even number of neutrons ("gg nuclei"), for which a single beta decay is energetically impossible. 35 such nuclides are known. The double beta decay has been demonstrated in around 12 of these nuclides - with half-lives between 10 ¹⁹ and 10 ²⁵ years - and is compatible with the standard model . The changing atomic nucleus emits two electrons (in the case of beta-plus decay, positrons) and two electron antineutrinos or neutrinos. The energy spectrum of the electrons / positrons is continuous as in simple beta decay. The process is called two neutrino double beta decay, or 2νββ for short.

Neutrino-free double beta decay

The neutrino-free double beta decay , abbreviated to 0νββ, would be another decay channel for the above-mentioned nuclides. It differs significantly from the 2νββ decay, because here only the two electrons / positrons would be emitted. The sum of their kinetic energies, determined by the difference in mass between the mother and daughter nucleus, would have to be constant, i.e. instead of a continuum it would have to result in a "spectral line". Such a line superimposed on the continuum has not been shown in the previous evidence of double beta decays. Therefore, if this process exists, it must take place with the same nuclides as the 2νββ decay, but it must be orders of magnitude rarer.

The neutrino-free double beta decay can only occur if

• the neutrino is a Majorana particle, and
• there is a right-handed component of the weak lepton current or the neutrino can change its handedness between emission and absorption (between the two W-vertices), which is possible with non-zero neutrino masses (with at least one of the neutrino species).

The simplest form of this decay is known as light neutrino exchange. A neutrino is emitted by one nucleon and absorbed by another nucleon (see figure). In the final state, only the daughter nucleus and two electrons are left:

${\displaystyle (A,Z)\rightarrow (A,Z+2)+2e^{-}}$

The two electrons are emitted quasi-simultaneously.

The two resulting electrons are then the only emitted particles in the final state and together have to carry almost the entire energy gain of the decay as kinetic energy, since the relatively heavy nuclei do not absorb any kinetic energy worth mentioning. Due to the conservation of momentum, the electrons are emitted anti-parallel (in opposite directions).

The rate of decay is

${\displaystyle \Gamma _{\beta \beta }^{0\nu }={\frac {1}{T_{\beta \beta }^{0\nu }}}=G^{0\nu }\left|{\mathcal {M}}^{0\nu }\right|^{2}\langle m_{\beta \beta }\rangle ^{2}}$,

where denotes the phase space factor, the squared matrix element of this nuclear decay process (according to the Feynman diagram) and the square of the effective Majorana mass. ${\displaystyle G^{0\nu }}$ ${\displaystyle \left|{\mathcal {M}}^{0\nu }\right|^{2}}$ ${\displaystyle \langle m_{\beta \beta }\rangle ^{2}}$

The effective Majorana mass can be calculated by

${\displaystyle \langle m_{\beta \beta }\rangle =\sum _{i}U_{ei}^{2}m_{i}}$,

where are the Majorana neutrino masses (three types of neutrinos ) and the entries are the neutrino mixing matrix (see PMNS matrix ). Modern experiments looking for neutrinoless double beta decays (see section on experiments) aim at both demonstrating the Majorana nature of neutrinos and measuring this effective Majorana mass (this can only be inferred if the decay is actually due to the neutrino masses is produced). ${\displaystyle m_{i}}$ ${\displaystyle \nu _{i}}$ ${\displaystyle U_{ei}}$ ${\displaystyle U}$ ${\displaystyle \langle m_{\beta \beta }\rangle }$

The core matrix element cannot be measured independently, but it can be calculated. The calculation itself is based on various methods of sophisticated nuclear many-body theories. The core matrix element differs from core to core. The range of values ​​for obtained with different methods represents an uncertainty; the values ​​obtained vary by a factor of 2 to about 5. Typical values ​​are in the range from about 0.9 to 14, depending on the decaying nuclide. ${\displaystyle \left|M^{0\nu }\right|}$ ${\displaystyle \left|M^{0\nu }\right|}$

The phase space factor depends on the total kinetic energy released and the atomic number . The calculation methods for this are based on Dirac wave functions , finite nucleus sizes and electron screening. There are high-precision results for for different kernels in the range of about 0.23 (for ) and 0.90 (for ) to about 24.14 (for ). ${\displaystyle G^{0\nu }}$ ${\displaystyle Q=M_{\text{Kern}}^{\text{vor}}-M_{\text{Kern}}^{\text{nach}}-2m_{\text{Elektron}}}$ ${\displaystyle Z}$ ${\displaystyle G^{0\nu }}$ ${\displaystyle \mathrm {^{128}_{52}Te\rightarrow _{54}^{128}Xe} }$ ${\displaystyle \mathrm {^{76}_{32}Ge\rightarrow _{34}^{76}Se} }$ ${\displaystyle \mathrm {^{150}_{60}Nd\rightarrow _{62}^{150}Sm} }$

A neutrinoless double beta decay (decay rate compatible with predictions based on experimental evidence of neutrino mass and mixing) discovered under certain conditions would "likely" indicate Majorana neutrinos as the main mediator (rather than other sources of new physics).

Experiments and results

Nine different nuclides are considered for experiments to confirm the neutrino-less double beta decay into account: . The criteria for selection are: isotope frequency, if necessary, enrichment at reasonable costs and a well-understood and controlled experimental technique. In principle, the higher the Q value (energy gain from decay), the better the chances of detection. The phase space factor and thus the rate of decay grows with it . ${\displaystyle \mathrm {^{48}Ca,^{76}Ge,^{82}Se,^{96}Zr,^{100}Mo,^{116}Cd,^{130}Te,^{136}Xe,^{150}Nd} }$ ${\displaystyle G^{0\nu }}$ ${\displaystyle Q^{5}}$

As explained above, the measured quantity is the sum of the kinetic energies of the two emitted electrons.

The table shows a summary of the currently best lower limits for the partial half-lives compared to 0νββ decay.

Experimental lower limits (at least 90% confidence interval ) for the 0νββ decay process

nuclide	experiment	Part. Half-life [years] ${\displaystyle T_{\beta \beta }^{0\nu }}$
${\displaystyle \mathrm {^{48}Ca} }$	ELEGANT VI	${\displaystyle >1{,}4\cdot 10^{22}}$
${\displaystyle \mathrm {^{76}Ge} }$	Heidelberg-Moscow experiment	${\displaystyle >1{,}9\cdot 10^{25}}$
${\displaystyle \mathrm {^{76}Ge} }$	GERDA	${\displaystyle >2{,}1\cdot 10^{25}}$
${\displaystyle \mathrm {^{82}Se} }$	NEMO -3	${\displaystyle >1{,}0\cdot 10^{23}}$
${\displaystyle \mathrm {^{96}Zr} }$	NEMO-3	${\displaystyle >9{,}2\cdot 10^{21}}$
${\displaystyle \mathrm {^{100}Mo} }$	NEMO-3	${\displaystyle >2{,}1\cdot 10^{25}}$
${\displaystyle \mathrm {^{116}Cd} }$	Solotvina	${\displaystyle >1{,}7\cdot 10^{23}}$
${\displaystyle \mathrm {^{130}Te} }$	CUORICINO	${\displaystyle >2{,}8\cdot 10^{24}}$
${\displaystyle \mathrm {^{136}Xe} }$	EXO	${\displaystyle >1{,}1\cdot 10^{25}}$
${\displaystyle \mathrm {^{136}Xe} }$	KamLAND Zen	${\displaystyle >2{,}6\cdot 10^{25}}$
${\displaystyle \mathrm {^{150}Nd} }$	NEMO-3	${\displaystyle >2{,}1\cdot 10^{25}}$

Heidelberg-Moscow experiment

The researchers of the Heidelberg-Moscow experiment at the German Max Planck Institute for Nuclear Physics and the Russian Science Center Kurchatov Institute in Moscow claimed to have found evidence of neutrino-free double beta decay. In 2001, the group initially announced evidence with 2.2σ or 3.1σ evidence (depending on the calculation method used). The partial half-life is close to years. This result has been the subject of much discussion. To date, no other experiment has confirmed the result of the HDM group. In contrast, the latest results of the GERDA experiment for the minimum half-life clearly contradict the figures of the HDM group. So a neutrino-free double beta decay has not yet been found. ${\displaystyle 2\cdot 10^{25}}$

Currently running experiments

• GERDA (Germanium Detector Array):
  • The result of the GERDA working group with phase I of the detector is a partial half-life of years (90% CI). The decay events that take place in germanium single crystal detectors (see semiconductor detector ) are observed ; So germanium is both source and detector at the same time. An anticoincidence detector made of liquid argon is used as a scintillator to exclude muons from cosmic rays and other background radiation . The Q value of germanium-76 for the double beta decay is 2039 keV, but no excess of events was found in this region. ${\displaystyle T_{\beta \beta }^{0\nu }>2{,}1\cdot 10^{25}}$
  • In phase II of the experiment, with around 36 kg of germanium, data collection began in 2015. Until July 2020, no excess was found at 2039 keV and thus years (90% CI) were determined as the new lower limit. ${\displaystyle T_{\beta \beta }^{0\nu }>5{,}3\cdot 10^{25}}$

• EXO (Enriched Xenon Observatory):
  • The Enriched Xenon Observatory 200 experiment uses xenon as both a source and a detector. The experiment is located in New Mexico (USA) and uses a time projection chamber (TPC) for the three-dimensional spatial and temporal resolution of the electron tracks. EXO-200 gave less accurate results than GERDA I and II with a partial half-life of years (90% CI). ${\displaystyle T_{\beta \beta }^{0\nu }>1{,}1\cdot 10^{25}}$

• KamLAND -Zen (Kamioka Liquid Scintillator Antineutrino Detector-Zen):
  • The KamLAND Zen experiment began with 13 tons of xenon as a source (enriched with about 320 kg ), contained in a nylon balloon, which is surrounded by an outer balloon with liquid scintillator material 13 m in diameter. From 2011 the KamLAND-Zen-Phase I began with the data acquisition, which resulted in a partial half-life for this neutrino-free double beta decay of years (90% CI). This value could be improved over years (90% CI) by combining it with phase II data (data collection started in December 2013) . ${\displaystyle \mathrm {^{136}Xe} }$ ${\displaystyle T_{\beta \beta }^{0\nu }>1{,}9\cdot 10^{25}}$ ${\displaystyle T_{\beta \beta }^{0\nu }>2{,}6\cdot 10^{25}}$
  • In August 2018, the KamLAND-Zen - 800 apparatus with 800 kg was completed. It is described as the currently (2020) largest and most sensitive experiment in the search for neutrino-free double beta decay. ${\displaystyle \mathrm {^{136}Xe} }$

Proposed and Future Experiments

• nEXO experiment:
  • As the successor to EXO-200, nEXO is to be an experiment on the scale of several tons of enriched xenon, thus part of the next generation of 0νββ experiments. The detector should have an energy resolution of 1% in the range of the Q value. The experiment should provide a half-life sensitivity of about years after 10 years of data acquisition . ${\displaystyle T_{\beta \beta }^{0\nu }>9{,}5\cdot 10^{27}}$

Individual evidence

1. ↑ ^{a b} Ettore Majorana: Teoria simmetrica dell'elettrone e del positrone . In: Il Nuovo Cimento (1924-1942) . 14, No. 4, 1937. doi : 10.1007 / BF02961314 .
2. ↑ ^{a b c d e} K. Grotz, HV Klapdor: The weak interaction in nuclear, particle, and astrophysics . Hilger, 1990, ISBN 978-0-85274-313-3 .
3. ↑ ^{a b c} Lothar Oberauer, Aldo Ianni, Aldo Serenelli: Solar neutrino physics: the interplay between particle physics and astronomy . Wiley-VCH, 2020, ISBN 978-3-527-41274-7 , pp. 120-127.
4. ↑ ^{a b} C. Patrignani et al. (Particle Data Group): Review of Particle Physics . In: Chinese Physics C . 40, No. 10, October 2016. doi : 10.1088 / 1674-1137 / 40/10/100001 .
5. ↑ ^{a b c d e f g h i j k} S. M. Bilenky, C. Giunti: Neutrinoless double-beta decay: A probe of physics beyond the Standard Model . In: International Journal of Modern Physics A . 30, No. 04n05, February 11, 2015, p. 1530001. doi : 10.1142 / S0217751X1530001X .
6. ↑ ^{a b c d e f g h} Werner Rodejohann: Neutrino-less double beta decay and particle physics . In: International Journal of Modern Physics E. 20, No. 09, May 2012, pp. 1833-1930. doi: 10.1142 / S0218301311020186.
7. ↑ ^{a b} Frank F. Deppisch: A modern introduction to neutrino physics . Morgan & Claypool Publishers, 2019, ISBN 978-1-64327-679-3 .
8. ^ WH Furry: On Transition Probabilities in Double Beta Disintegration . In: Physical Review . 56, No. 12, December 15, 1939, pp. 1184-1193. doi : 10.1103 / PhysRev.56.1184 .
9. ↑ Oliviero Cremonesi: Neutrinoless double beta decay: Present and future . In: Nuclear Physics B - Proceedings Supplements . 118, April 2003, pp. 287-296. doi : 10.1016 / S0920-5632 (03) 01331-8 .
10. ↑ J. Schechter, JWF Valle: Neutrinoless double-beta decay in SU (2) x U (1) theories . In: Physical Review D. 25, No. 11, June 1, 1982, pp. 2951-2954. doi: 10.1103 / PhysRevD.25.2951
11. ^ DR Artusa, FT Avignone, O. Azzolini, M. Balata, TI Banks, G. Bari, J. Beeman, F. Bellini, A. Bersani, M. Biassoni: Exploring the neutrinoless double beta decay in the inverted neutrino hierarchy with bolometric detectors . In: The European Physical Journal C . 74, No. 10, October 15, 2014. doi : 10.1140 / epjc / s10052-014-3096-8 .
12. ↑ SM Bilenky, JA Grifols: The possible test of the calculations of nuclear matrix elements of the (ββ) 0ν-decay . In: Physics Letters B . 550, No. 3-4, December 2002, pp. 154-159. doi : 10.1016 / S0370-2693 (02) 02978-7 .
13. ↑ The Heidelberg-Moscow Experiment with enriched 76 Ge . HVKlapdor small house. Retrieved July 16, 2020.
14. ↑ ^{a b c d e f g h i j} Werner Tornow: Search for Neutrinoless Double-Beta Decay . 1st December 2014.
15. ↑ ^{a b} H. V. Klapdor-Kleingrothaus, A. Dietz, HL Harney, IV Krivosheina: Evidence for neutrinoless double beta decay . In: Modern Physics Letters A . 16, No. 37, November 21, 2011, pp. 2409-2420. doi : 10.1142 / S0217732301005825 .
16. ↑ ^{a b} M. Agostini, M. Allardt, E. Andreotti, AM Bakalyarov, M. Balata, I. Barabanov, M. Barnabé Heider, N. Barros, L. Baudis, C. Bauer: Results on Neutrinoless Double-Beta Decay of 76Ge from Phase I of the GERDA Experiment . In: Physical Review Letters . 111, No. 12, September 19, 2013. doi : 10.1103 / PhysRevLett.111.122503 .
17. ↑ M Agostini, M Allardt, AM Bakalyarov, M Balata, I Barabanov, L Baudis, C Bauer, E Bellotti, S Belogurov, ST Belyaev, G Benato: First results from GERDA Phase II . In: Journal of Physics: Conference Series . 888, September 2017, p. 012030. doi : 10.1088 / 1742-6596 / 888/1/012030 .
18. ↑ ^{a b} KamLAND-ZEN ( en ) May 16, 2014. Accessed July 17, 2020.
19. ↑ Investigating the Neutrino Mass Scale with the ultra-low background KamLAND-Zen detector (en) . In: phys.org . Retrieved July 17, 2020. 
20. ^ ^{A b} C. Licciardi * on behalf of the EXO-200 and nEXO collaborations: Recent Results and Status of EXO-200 and the nEXO Experiment . In: 38th International Conference on High Energy Physics (ICHEP2016) - Neutrino Physics . 282, September. doi : 10.22323 / 1.282.0494 .