# Double beta decay

Double beta decay is a radioactive decay process where a nucleus releases two beta rays as a single process.

## History

The idea of double beta decay was first proposed by Maria Goeppert-Mayer in 1935.[1] In 1937 Ettore Majorana theoretically demonstrated that all results of beta decay theory remain unchanged if the neutrino is its own anti-particle, i.e. if it is a Majorana particle. In 1939 Wendell H. Furry for the first time proposed that, if neutrino is a Majorana particle, double beta decay can proceed without emission of any neutrino at all; the process which is now called the neutrinoless beta decay.[2]

In 1930–40s parity violation in weak interactions was not known and consequently calculations showed that neutrinoless double beta decay should be much more likely to occur than ordinary double beta decay (if neutrinos are Majorana particles). The predicted half-lives were on the order of 1015–16 years. Efforts to observe the process in laboratory date back to at least 1948 when Edward L. Fireman made the first attempt to measure the half-life of the 124Sn isotope. Radiometric experiments through about 1960 produced either negative results or false positives, which were not confirmed by later experiments. In 1950 for the first time the half-life of the 130Te isotope was measured by geochemical methods. The result, 1.4×1021 years, was reasonably close to the modern value.[2]

In 1956 after the V-A nature of weak interactions was established it became clear that the half-life of neutrinoless double beta decay would significantly exceed that of ordinary double beta decay. Despite significant progress in the experimental techniques in 1960–70s, double beta decay was not observed until the 1980s in a laboratory setting. The experiments had only been able to establish the lower bound for the half-life—about 1021 years. On the other hand in the geochemical experiments double beta decay of 82Se and 128Te isotopes was detected.[2]

Double beta decay was first observed in a laboratory counter experiment in 1987 by a group led by Michael Moe at the UC Irvine on isotope 82Se. Since then many experiments have been conducted, which observed ordinary double beta decay in a number of other isotopes. However none of those experiments has produced positive results for the neutrinoless process, pushing the lower bound for its half-life up to 1025 years. The geochemical experiments continued until the end of 1990s and produced positive results for a few more isotopes.[2] Double beta decay is the rarest known kind of radioactive decay; as of 2012 it has been observed for only 12 isotopes (including double electron capture in 130Ba observed in 2001), and all of them have a mean lifetime of more than 1018 yr (see table below).[2]

## Ordinary double beta decay

In double beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted. The process can be thought as a sum of two beta minus decays. In order for (double) beta decay to be possible, the final nucleus must have a larger binding energy than the original nucleus. For some nuclei, such as germanium-76, the nucleus with atomic number one higher has a smaller binding energy, preventing a singular beta decay from occurring. However, the nucleus with atomic number two higher, selenium-76, has a larger binding energy, so the double beta decay process is allowed.

For some nuclei, the process occurs as conversion of two protons to neutrons, with emission of two electron neutrinos and absorption of two orbital electrons (double electron capture). If the mass difference between the parent and daughter atoms is more than 1.022 MeV/c2 (two electron masses), another decay branch is accessible, with capture of one orbital electron and emission of one positron. When the mass difference is more than 2.044 MeV/c2 (four electron masses), the emission of two positrons is possible. These theoretically possible double beta decay branches have not yet been observed.

### List of known double beta decay isotopes

There are 35 naturally occurring isotopes that are capable of undergoing double beta decay. The decay can be observed in practice if the single beta-decay is forbidden by energy conservation. This happens for even-Z, even-N isotopes, which are more stable due to spin-coupling, expressed by the pairing term in the semi-empirical mass formula.

Many isotopes are, in theory, capable both of double beta decay and other decays. In most cases, the double beta decay is so rare as to be nearly impossible to observe against the background of other radiation. However, the double beta decay rate of 238U (also an alpha emitter) has been measured radiochemically; 238Pu is produced by this type of radioactivity. Two of the nuclides (48Ca and 96Zr) from the table below can decay also via single beta decay but this decay is extremely suppressed and has never been observed.

Eleven isotopes have been experimentally observed undergoing two-neutrino double beta decay.[3] The table below contains information about nuclides with experimentally measured half-lives. The results are as of December 2012. Only the latest direct measurements are reported if available.[3]

Nuclide Half-life, 1021 years Transition Method Experiment
48Ca 0.044+0.005
−0.004
± 0.004
direct NEMO-3
76Ge 1.84 +0.09
−0.08
+0.11
−0.06
direct GERDA (2013)
82Se 0.096 ± 0.003 ± 0.010 direct NEMO-3
96Zr 0.0235 ± 0.0014 ± 0.0016 direct NEMO-3
100Mo 0.00711 ± 0.00002 ± 0.00054 direct NEMO-3
0.69+0.10
−0.08
± 0.07
0+→ 0+1 direct Ge coincidence
116Cd 0.028 ± 0.001 ± 0.003 direct NEMO-3
128Te 7200 ± 400 geochemical
130Te 0.7 ± 0.09 ± 0.11 direct NEMO-3
136Xe 2.165 ± 0.016 ± 0.059 direct EXO-200
150Nd 0.00911+0.00025
−0.00022
± 0.00063
direct NEMO-3
238U 2.0 ± 0.6 geochemical

Note:In the table above where two errors are specified the first one is statistical error and the second is systematic.[3]

Note:The GERDA-2013 results from [4]

## Neutrinoless double beta decay

Feynman diagram of neutrinoless double beta decay, with two neutrons decaying to two protons. The only emitted products in this process are two electrons, which can occur if the neutrino and antineutrino are the same particle (i.e. Majorana neutrinos) so the same neutrino can be emitted and absorbed within the nucleus. In conventional double beta decay, two antineutrinos — one arising from each W vertex — are emitted from the nucleus, in addition to the two electrons. The detection of neutrinoless double beta decay is thus a sensitive test of whether neutrinos are Majorana particles.

The processes described in the previous section are also known as two-neutrino double beta decay, as two neutrinos (or antineutrinos) are emitted. If the neutrino is a Majorana particle (meaning that the antineutrino and the neutrino are actually the same particle), and at least one type of neutrino has non-zero mass (which has been established by the neutrino oscillation experiments), then it is possible for neutrinoless double beta decay to occur. In the simplest theoretical treatment of neutrinoless double beta decay (light neutrino exchange), in essence the two neutrinos annihilate each other, or equivalently, one nucleon absorbs the neutrino emitted by another nucleon of the nucleus.

The neutrinos in the above diagram are virtual particles. With only the two electrons in the final state, the total kinetic energy of the two electrons would be approximately the difference in binding energy between the initial and final state nuclei (with the recoil of the nucleus accounting for the rest of the available energy). To a very good approximation, the two electrons are emitted back-to-back to conserve momentum.

The decay rate for this process is given (approximately) by

$\Gamma = ~~~~{G |M|^2 |m_{\beta \beta}|^2},$

where $G$ is the two-body phase-space factor, $M$ is the nuclear matrix element, and mββ is the so-called effective Majorana neutrino mass given by

$m_{\beta \beta} = \sum_{i=1}^3 m_i U^2_{ei}.$

In this latter expression, the mi are the neutrino masses (of the ith mass eigenstate), and the Uei are elements of the lepton mixing matrix or Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix. Hence the observation of neutrinoless double beta decay, in addition to confirming the Majorana nature of the neutrino, would give information on the absolute neutrino mass scale, and potentially also on the neutrino mass hierarchy and the Majorana phases appearing in the PMNS matrix.[5][6]

The deep significance of the process stems from the "black-box theorem" which establishes that observing neutrinoless double beta decay implies that at least one neutrino is a Majorana particle in complete generality, irrespective of whether the process is engendered by neutrino exchange.[7]

### Neutrinoless double beta decay experiments

Numerous experiments have been carried out to search for neutrinoless double beta decay. Some recent and proposed future experiments include:

### Controversy with Heidelberg-Moscow collaboration

In 2001 Heidelberg-Moscow collaboration released their data, which set limits on the neutrinoless beta decay in Germanium-76.[1] The low limit for the half-life was 1.9×1025 years, while the upper limit on the neutrino mass was estimated at 0.3–0.6 eV. However in the same year a part of the collaboration claimed that they actually observed the neutrinoless beta decay with the half-life of about 1.5×1025 years corresponding to the neutrino mass of about 0.4 eV.[8] This claim was criticized by outside physicists[1][9][10] as well as by other members of the collaboration.[11] The analysis of the Heidelberg-Moscow data of the complete period 1990-2003 resulted in a half-life of 1.19×1025  years. In 2006 a refined estimate was published by the same authors stating that the half-life was 2.3×1025 years.[12] As of 2012 the situation is unclear but future more sensitive experiments are expected to eventually resolve this controversy.[1] A recent review compares previous and recent experiment and points out that the selection efficiency of the 2006 analysis is not evaluated and hence not included in the published T1/2 value.[13]

As of 2014 GERDA has reached much lower background and obtained a half-life limit of 2.1×1025 years with 21.6 kgyr exposure.[14] Including the data from the IGEX and HDM experiments the limit increases to 3×1025 years. Furthermore, two experiments with 136Xe, Kamland and EXO, have given limits in the order of 1.6×1025 years. Using the latest nuclear matrix elements also the 136Xe results disfavour the claim.

## References

1. ^ a b c d Giuliani, A.; Poves, A. (2012). "Neutrinoless Double-Beta Decay". Advances in High Energy Physics 2012: 1. doi:10.1155/2012/857016. edit
2. Barabash, A. S. (2011). "Experiment double beta decay: Historical review of 75 years of research". Physics of Atomic Nuclei 74 (4): 603–613. arXiv:1104.2714. Bibcode:2011PAN....74..603B. doi:10.1134/S1063778811030070. edit
3. ^ a b c Beringer, J.; Arguin, J.; Barnett, R.; Copic, K.; Dahl, O.; Groom, D.; Lin, C.; Lys, J.; Murayama, H.; Wohl, C. G.; Yao, W. -M.; Zyla, P. A.; Amsler, C.; Antonelli, M.; Asner, D. M.; Baer, H.; Band, H. R.; Basaglia, T.; Bauer, C. W.; Beatty, J. J.; Belousov, V. I.; Bergren, E.; Bernardi, G.; Bertl, W.; Bethke, S.; Bichsel, H.; Biebel, O.; Blucher, E.; Blusk, S.; Brooijmans, G. (2012). "Review of Particle Physics". Physical Review D 86. Bibcode:2012PhRvD..86a0001B. doi:10.1103/PhysRevD.86.010001. edit
4. ^ Agostini, M.; Allardt, M.; Andreotti, E.; Bakalyarov, A. M.; Balata, M.; Barabanov, I.; Heider, M. B.; Barros, N.; Baudis, L.; Bauer, C.; Becerici-Schmidt, N.; Bellotti, E.; Belogurov, S.; Belyaev, S. T.; Benato, G.; Bettini, A.; Bezrukov, L.; Bode, T.; Brudanin, V.; Brugnera, R.; Budjáš, D.; Caldwell, A.; Cattadori, C.; Chernogorov, A.; Cossavella, F.; Demidova, E. V.; Denisov, A.; Domula, A.; Egorov, V. et al. (2013). "Measurement of the half-life of the two-neutrino double beta decay of76Ge with the GERDA experiment". Journal of Physics G: Nuclear and Particle Physics 40 (3): 035110. doi:10.1088/0954-3899/40/3/035110. edit
5. ^ K. Grotz and H.V. Klapdor, „The Weak Interaction in Nuclear, Particle and Astrophysics“, Adam Hilger, Bristol, 1990, 461 ps.
6. ^ H.V. Klapdor, A. Staudt „Non-accelerator Particle Physics“, 2.edition, Institute of Physics Publishing, Bristol, Philadelphia, 1998, 535 ps.
7. ^ Schechter, J.; J. W. F. Valle (1982-06-01). "Neutrinoless Double beta Decay in SU(2) ⊗ U(1) theories". Physical Review D 25 : 2951. Bibcode:1982PhRvD..25.2951S.doi:10.1103/PhysRevD.25.2951
8. ^ Klapdor-Kleingrothaus, H. V.; Dietz, A.; Harney, H. L.; Krivosheina, I. V. (2001). "Evidence for Neutrinoless Double Beta Decay". Modern Physics Letters A 16 (37): 2409. doi:10.1142/S0217732301005825. edit
9. ^ Aalseth, C. E.; Avignone, F. T.; Barabash, A.; Boehm, F.; Brodzinski, R. L.; Collar, J. I.; Doe, P. J.; Ejiri, H.; Elliott, S. R.; Fiorini, E.; Gaitskell, R. J.; Gratta, G.; Hazama, R.; Kazkaz, K.; King, G. S.; Kouzes, R. T.; Miley, H. S.; Moe, M. K.; Morales, A.; Morales, J.; Piepke, A.; Robertson, R. G. H.; Tornow, W.; Vogel, P.; Warner, R. A.; Wilkerson, J. F. (2002). "Comment on "evidence for Neutrinoless Double Beta Decay"". Modern Physics Letters A 17 (22): 1475. doi:10.1142/S0217732302007715. edit
10. ^ Zdesenko, Y. G.; Danevich, F. A.; Tretyak, V. I. (2002). "Has neutrinoless double β decay of 76Ge been really observed?". Physics Letters B 546 (3–4): 206. doi:10.1016/S0370-2693(02)02705-3. edit
11. ^ A. M. Bakalyarov, A. Y. Balysh, S. T. Belyaev, V. I. Lebedev, and S. V. Zhukov, (2003). "Results of the experiment on investigation of Germanium-76 double beta decay". Proceedings of the NANP, Dubna, Russia.
12. ^ Klapdor-Kleingrothaus, H. V.; Krivosheina, I. V. (2006). "THE EVIDENCE FOR THE OBSERVATION OF 0νββ DECAY: THE IDENTIFICATION OF 0νββ EVENTS FROM THE FULL SPECTRA". Modern Physics Letters A 21 (20): 1547. doi:10.1142/S0217732306020937. edit
13. ^ Schwingenheuer, B. (2013). "Status and prospects of searches for neutrinoless double beta decay". Annalen der Physik 525 (4): 269. doi:10.1002/andp.201200222. edit
14. ^ Agostini, M.; Allardt, M.; Andreotti, E.; Bakalyarov, A. M.; Balata, M.; Barabanov, I.; Barnabé Heider, M.; Barros, N.; Baudis, L.; Bauer, C.; Becerici-Schmidt, N.; Bellotti, E.; Belogurov, S.; Belyaev, S. T.; Benato, G.; Bettini, A.; Bezrukov, L.; Bode, T.; Brudanin, V.; Brugnera, R.; Budjáš, D.; Caldwell, A.; Cattadori, C.; Chernogorov, A.; Cossavella, F.; Demidova, E. V.; Domula, A.; Egorov, V.; Falkenstein, R. et al. (2013). "Results on Neutrinoless Double-β Decay of ^{76}Ge from Phase I of the GERDA Experiment". Physical Review Letters 111 (12). doi:10.1103/PhysRevLett.111.122503. edit