In most cases the transitions (Z,A)$~\rightarrow~$(Z+2,A) $+~2{{\mathit e}^{-}}$ to the 0${}^{+}$ ground state of the final nucleus are listed. We also list transitions that decrease the nuclear charge (2${{\mathit e}^{+}}$ , ${{\mathit e}^{+}}$ CC and double EC) and transitions to an excited state of the final nucleus (0${}^{+}_{i}$, 2${}^{+}$, and 2${}^{+}_{i}$). In the following Listings only the best or comparable limits for the half-lives of each transition are reported and only those with about T$_{1/2}>10^{23}$ years that are relevant for particle physics.

${\mathrm {\mathit t_{1/2}}}$ ($ 10^{23} $ yr) CL$\%$ ISOTOPE TRANSITION METHOD DOCUMENT ID • • We do not use the following data for averages, fits, limits, etc. • • $ >59 $ $90$ ${}^{130}\mathrm {Te}$ $g.s. \rightarrow 0{}^{+}_{1}$ CUORE 1 ADAMS 2021 A $ >15 $ $90$ ${}^{100}\mathrm {Mo}$ CUPID-Mo 2 ARMENGAUD 2021 $ >39.9 $ $90$ ${}^{76}\mathrm {Ge}$ $g.s. \rightarrow 0{}^{+}_{1}$ MAJORANA-Dem 3 ARNQUIST 2021 $ >21.2 $ $90$ ${}^{76}\mathrm {Ge}$ $g.s. \rightarrow 2{}^{+}_{1}$ MAJORANA-Dem 4 ARNQUIST 2021 $ >9.7 $ $90$ ${}^{76}\mathrm {Ge}$ $g.s. \rightarrow 2{}^{+}_{2}$ MAJORANA-Dem 5 ARNQUIST 2021 $ >320 $ $90$ ${}^{130}\mathrm {Te}$ CUORE 6 ADAMS 2020 A $ >1800 $ $90$ ${}^{76}\mathrm {Ge}$ GERDA 7 AGOSTINI 2020 B $ >900 $ $90$ ${}^{76}\mathrm {Ge}$ GERDA 8 AGOSTINI 2019 $ >14 $ $90$ ${}^{130}\mathrm {Te}$ $g.s. \rightarrow 0{}^{+}_{1}$ CUORE-0 9 ALDUINO 2019 $ >0.95 $ $90$ ${}^{100}\mathrm {Mo}$ AMoRE 10 ALENKOV 2019 $ >270 $ $90$ ${}^{76}\mathrm {Ge}$ MAJORANA 11 ALVIS 2019 $ >350 $ $90$ ${}^{136}\mathrm {Xe}$ EXO-200 12 ANTON 2019 $ >35 $ $90$ ${}^{82}\mathrm {Se}$ CUPID-0 13 AZZOLINI 2019 $ >2.4 $ $90$ ${}^{136}\mathrm {Xe}$ PANDAX-II 14 NI 2019 $ >190 $ $90$ ${}^{76}\mathrm {Ge}$ MAJORANA 15 AALSETH 2018 $ >800 $ $90$ ${}^{76}\mathrm {Ge}$ GERDA 16 AGOSTINI 2018 $ >180 $ $90$ ${}^{136}\mathrm {Xe}$ EXO-200 17 ALBERT 2018 $ >150 $ $90$ ${}^{130}\mathrm {Te}$ CUORE 18 ALDUINO 2018 $ >2.5 $ $90$ ${}^{82}\mathrm {Se}$ NEMO-3 19 ARNOLD 2018 $ >24 $ $90$ ${}^{82}\mathrm {Se}$ CUPID-0 20 AZZOLINI 2018 $ >0.81 $ $90$ ${}^{82}\mathrm {Se}$ $g.s. \rightarrow 0{}^{+}_{1}$ CUPID-0 21 AZZOLINI 2018 A $ >2.2 $ $90$ ${}^{116}\mathrm {Cd}$ AURORA 22 BARABASH 2018 $ >530 $ $90$ ${}^{76}\mathrm {Ge}$ GERDA 23 AGOSTINI 2017 $ >1.1 $ $90$ ${}^{134}\mathrm {Xe}$ EXO-200 24 ALBERT 2017 C $ >1 $ $90$ ${}^{116}\mathrm {Cd}$ NEMO-3 25 ARNOLD 2017 $ >40 $ $90$ ${}^{130}\mathrm {Te}$ CUORE(CINO) 26 ALDUINO 2016 $ >260 $ $90$ ${}^{136}\mathrm {Xe}$ $g.s. \rightarrow 2{}^{+}_{1}$ KamLAND-Zen 27 ASAKURA 2016 $ >260 $ $90$ ${}^{136}\mathrm {Xe}$ $g.s. \rightarrow 2{}^{+}_{2}$ KamLAND-Zen 28 ASAKURA 2016 $ >240 $ $90$ ${}^{136}\mathrm {Xe}$ $g.s. \rightarrow 0{}^{+}_{1}$ KamLAND-Zen 29 ASAKURA 2016 $ >1070 $ $90$ ${}^{136}\mathrm {Xe}$ KamLAND-Zen 30 GANDO 2016 $ >11 $ $90$ ${}^{100}\mathrm {Mo}$ NEMO-3 31 ARNOLD 2015 $ >110 $ $90$ ${}^{136}\mathrm {Xe}$ EXO-200 32 ALBERT 2014 B $ >9.4 $ $90$ ${}^{130}\mathrm {Te}$ $g.s. \rightarrow 0{}^{+}_{1}$ CUORICINO 33 ANDREOTTI 2012 $ >3.6 $ $90$ ${}^{82}\mathrm {Se}$ NEMO-3 34 BARABASH 2011 A $ >30 $ $90$ ${}^{130}\mathrm {Te}$ CUORICINO 35 ARNABOLDI 2008 $ >0.58 $ $90$ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint. 36 UMEHARA 2008 $ >0.89 $ $90$ ${}^{100}\mathrm {Mo}$ $g.s. \rightarrow 0{}^{+}_{1}$ NEMO-3 37 ARNOLD 2007 $ >1.6 $ $90$ ${}^{100}\mathrm {Mo}$ $g.s. \rightarrow 2{}^{+}$ NEMO-3 38 ARNOLD 2007 $ >1 $ $90$ ${}^{82}\mathrm {Se}$ NEMO-3 39 ARNOLD 2005 A $ >1.1 $ $90$ ${}^{128}\mathrm {Te}$ Cryog. det. 40 ARNABOLDI 2003 $ >1.7 $ $90$ ${}^{116}\mathrm {Cd}$ ${}^{116}\mathrm {Cd}WO_{4}$ scint. 41 DANEVICH 2003 $ >157 $ $90$ ${}^{76}\mathrm {Ge}$ Enriched HPGe 42 AALSETH 2002 B $ >190 $ $90$ ${}^{76}\mathrm {Ge}$ Enriched HPGe 43 KLAPDOR-KLEIN.. 2001 1  ADAMS 2021A et al. used 101.76 kg yr of ${}^{130}\mathrm {Te}$ exposure of the CUORE (LNGS) bolometric detector to place a limit on the decay to the first excited state of ${}^{130}\mathrm {Xe}$, superseding ALDUINO 2019 as the most restrictive bound on this particular decay. 2  ARMENGAUD 2021 use the CUPID-Mo 4.2 kg array of enriched Li$_{2}{}^{100}\mathrm {Mo}O_{4}$ scintillating bolometers, with 1.17 kg$\cdot{}$yr exposure, to set this limit. 3  ARNQUIST 2021 use the MAJORANA demonstrator to set this limit for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay to the first excited 0${}^{+}$ state, with a 41.9 kg yr isotopic exposure. The median sensitivity is $39.9 \times 10^{23}$ yr. 4  ARNQUIST 2021 use the MAJORANA demonstrator to set this limit for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay to the first excited 2${}^{+}$ state, with a 41.9 kg yr isotopic exposure. The median sensitivity is $21.2 \times 10^{23}$ yr. 5  ARNQUIST 2021 use the MAJORANA demonstrator to set this limit for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay to the second excited 2${}^{+}$ state, with a 41.9 kg yr isotopic exposure. The median sensitivity is $18.6 \times 10^{23}$ yr. 6  ADAMS 2020A use the CUORE detector to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{130}\mathrm {Te}$. The exposure was 372.5 kg$\cdot{}$yr of TeO$_{2}$ corresponding to 103.6 kg$\cdot{}$yr of ${}^{130}\mathrm {Te}$. The exclusion sensitivity is $1.7 \times 10^{25}$yr. Supersedes ALDUINO 2018 . 7  AGOSTINI 2020B present the final data set of the GERDA experiment, searching for 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{76}\mathrm {Ge}$ with isotopically enriched, high resolution ${}^{}\mathrm {Ge}$ detectors. A final exposure of 127.2 kg$\cdot{}$yr is reported. The experiment reports the lowest background and longest half life limit ever achieved by any double beta decay experiment. The reported experiment sensitivity equals the limit. Supersedes AGOSTINI 2019 . 8  AGOSTINI 2019 use 82.4 kg$\cdot{}$yr of data, collected by the GERDA experiment, to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{76}\mathrm {Ge}$. High resolution ${}^{}\mathrm {Ge}$-calorimeters, made from isotopically enriched ${}^{}\mathrm {Ge}$, are used. A median sensitivity of $1.1 \times 10^{26}$ yr is reported. Supersedes AGOSTINI 2018 . 9  ALDUINO 2019 use the combined data of the CUORICINO and CUORE-0 experiments to place a lower limit on the half life of the 0 ${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{130}\mathrm {Te}$ to the first excited 0${}^{+}$ state of ${}^{130}\mathrm {Xe}$. Supersedes ANDREOTTI 2012 . 10  ALENKOV 2019 report the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay half-life limit based on the 52.1 kg$\cdot{}$d exposure of ${}^{100}\mathrm {Mo}$, of a a cryogenic dual heat and light detector in the Yangyang underground laboratory. The median sensitivity is $1.1 \times 10^{23}$ years. 11  ALVIS 2019 use the MAJORANA Demonstrator with enriched in ${}^{76}\mathrm {Ge}$ detectors to set this limit on 0 ${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ half-life of ${}^{76}\mathrm {Ge}$. The exposure is 26.0 kg yr. The sensitivity is $4.8 \times 10^{25}$ yr. 12  ANTON 2019 uses he complete dataset of the EXO-200 detector to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay. The exposure is 234.1 kg yr. The median sensitivity is $5.0 \times 10^{25}$ yr. Supersedes ALBERT 2018 and ALBERT 2014B. 13  AZZOLINI 2019 use the CPID-0 scintillating cryogenic bolometer to set this limit on 0 ${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ half-life of ${}^{82}\mathrm {Se}$. The exposure is 5.29 kg yr. The sensitivity is $5 \times 10^{24}$ yr. 14  NI 2019 use the PandaX-II dual phase TPC at CJPL to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{136}\mathrm {Xe}$. The half-life limit $2.4 \times 10^{23}$ yr is obtained from 22.2 kg yr exposure with a sensitivity of $1.9 \times 10^{23}$ yr. 15  AALSETH 2018 uses the MAJORANA Demonstrator to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay. The exposure is 9.95 kg$\cdot{}$year. The median sensitivity is $2.1 \times 10^{25}$ yr. 16  AGOSTINI 2018 uses the GERDA detector to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay. The exposure is 46.7 kg$\cdot{}$year. The median sensitivity is $5.8 \times 10^{25}$ yr. Supersedes AGOSTINI 2017 . 17  ALBERT 2018 uses the EXO-200 detector to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay. The exposure is 177.6 kg$\cdot{}$year. The median sensitivity is $3.7 \times 10^{25}$ years. 18  ALDUINO 2018 uses the CUORE detector to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{130}\mathrm {Te}$. The exposure is 86.3 kg$\cdot{}$year of natural TeO$_{2}$ corresponding to 24.0 kg$\cdot{}$year for ${}^{130}\mathrm {Te}$. The median sensitivity is $0.7 \times 10^{25}$ yr. The limit is obtained combining the new data from CUORE with those of CUORE0 (9.8 kg$\cdot{}$year of ${}^{130}\mathrm {Te}$) and Cuoricino (19.8 kg$\cdot{}$year of ${}^{130}\mathrm {Te}$). 19  ARNOLD 2018 use the NEMO-3 tracking detector to place a limit on the 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{82}\mathrm {Se}$. This is a slightly weaker limit than in BARABASH 2011A, using the same detector. Supersedes ARNOLD 2005A. 20  AZZOLINI 2018 uses CUPID-0 detector, a novel scintillating cryogenic calorimeter, operated in the LNGS. This results replaces BARABASH 2011A (NEMO-3) as the most stringent limit on the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ -decay of ${}^{82}\mathrm {Se}$. 21  AZZOLINI 2018A data collected by CUPID-0 based on scintillating bolometers is used to derive a new most stringent limit on the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ -decay of ${}^{82}\mathrm {Se}$ to the 0${}^{+}_{1}$ state of ${}^{82}\mathrm {Kr}$. 22  BARABASH 2018 use 1.162 kg of ${}^{116}\mathrm {Cd}WO_{4}$ scintillating crystals to obtain this limit. Supersedes DANEVICH 2003 with analogous source and is more sensitive than ARNOLD 2017 . 23  AGOSTINI 2017 result corresponds to data collected with GERDA phase 1 and first release of phase 2 for a total of 343 mol-yr exposure. Supersedes AGOSTINI 2013A. The median sensitivity is 4.0 10${}^{25}$ yr. 24  ALBERT 2017C uses the EXO-200 detector that contains $19.098$ $\pm0.014\%$ admixture of ${}^{134}\mathrm {Xe}$ to search for the 0${{\mathit \nu}}$ and 2${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay modes. The exposure is 29.6 kg$\cdot{}$year. The median sensitivity is $1.9 \times 10^{21}$ years. 25  ARNOLD 2017 use the NEMO-3 tracking calorimeter, containing 410 g of enriched ${}^{116}\mathrm {Cd}$ exposed for 5.26 yr, to determine the half-life limit. Supersedes BARABASH 2011A. 26  ALDUINO 2016 report result obtained with 9.8 kg y of data collected with the CUORE-0 bolometer, combined with data from the CUORICINO. Supersedes ALFONSO 2015 . 27  ASAKURA 2016 use the KamLAND-Zen liquid scintillator calorimeter (${}^{136}\mathrm {Xe}$ 89.5 kg yr) to place a limit on the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ -decay into the first excited state of the daughter nuclide. 28  ASAKURA 2016 use the KamLAND-Zen liquid scintillator calorimeter (${}^{136}\mathrm {Xe}$ 89.5 kg yr) to place a limit on the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ -decay into the second excited state of the daughter nuclide. 29  ASAKURA 2016 use the KamLAND-Zen liquid scintillator calorimeter (${}^{136}\mathrm {Xe}$ 89.5 kg yr) to place a limit on the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ -decay into the third excited state of the daughter nuclide. 30  GANDO 2016 use the the KamLAND detector to search for the 0${{\mathit \nu}}$ decay of ${}^{136}\mathrm {Xe}$. With a significant background reduction, the combination of results of the first (270.7 days) and the second phase (263.8 days) of the experiment leads to about six fold improvement over the previous limit. Supersedes GANDO 2013A. The sensitivity is 5.6 10${}^{25}$ yr. 31  ARNOLD 2015 use the NEMO-3 tracking calorimeter with 34.3 kg yr exposure to determine the limit of 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ -half life of ${}^{100}\mathrm {Mo}$. Supersedes {ARNOLD 2005A} and BARABASH 2011A. 32  ALBERT 2014B use 100 kg yr of exposure of the EXO-200 tracking calorimeter to place a lower limit on the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ -half life of ${}^{136}\mathrm {Xe}$. Supersedes AUGER 2012 . 33  ANDREOTTI 2012 use high resolution TeO$_{2}$ bolometric calorimeter to search for the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{130}\mathrm {Te}$ leading to the excited 0${}^{1}_{+}$ state at 1793.5 keV. 34  BARABASH 2011A use the NEMO-3 detector to measure 2${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ rates and place limits on 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ half lives for various nuclides. Supersedes ARNOLD 2005A, ARNOLD 2004 , ARNOLD 1998 , and ELLIOTT 1992 . 35  Supersedes ARNABOLDI 2004 . Bolometric TeO$_{2}$ detector array CUORICINO is used for high resolution search for 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay. The half-life limit is derived from 3.09 kg yr ${}^{130}\mathrm {Te}$ exposure. 36  UMEHARA 2008 use CaF$_{2}$ scintillation calorimeter to search for double beta decay of ${}^{48}\mathrm {Ca}$. Limit is significantly more stringent than quoted sensitivity: $18 \times 10^{21}$ years. 37  Limit on 0${{\mathit \nu}}$ -decay to the first excited 0${}^{+}_{1}$-state of daughter nucleus using NEMO-3 tracking calorimeter. Supersedes DASSIE 1995 . 38  Limit on 0${{\mathit \nu}}$ -decay to the first excited 2${}^{+}$-state of daughter nucleus using NEMO-3 tracking calorimeter. 39  NEMO-3 tracking calorimeter is used in ARNOLD 2005A to place limit on 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ half-life of ${}^{82}\mathrm {Se}$. Detector contains 0.93 kg of enriched ${}^{82}\mathrm {Se}$. Supersedes ARNOLD 2004 . 40  Supersedes ALESSANDRELLO 2000 . Array of TeO$_{2}$ crystals in high resolution cryogenic calorimeter. Some enriched in ${}^{128}\mathrm {Te}$. Ground state to ground state decay. 41  Limit on 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{116}\mathrm {Cd}$ using enriched CdWO$_{4}$ scintillators. Supersedes DANEVICH 2000 . 42  AALSETH 2002B limit is based on 117 mol$\cdot{}$yr of data using enriched Ge detectors. Background reduction by means of pulse shape analysis is applied to part of the data set. Reported limit is slightly less restrictive than that in KLAPDOR-KLEINGROTHAUS 2001 However, it excludes part of the allowed half-life range reported in KLAPDOR-KLEINGROTHAUS 2001B for the same nuclide. The analysis has been criticized in KLAPDOR-KLEINGROTHAUS 2004B. The criticism was addressed and disputed in AALSETH 2004 . 43  KLAPDOR-KLEINGROTHAUS 2001 is a continuation of the work published in BAUDIS 1999 . Isotopically enriched Ge detectors are used in calorimetric measurement. The most stringent bound is derived from the data set in which pulse-shape analysis has been used to reduce background. Exposure time is $35.5~$kg$~$y. Supersedes BAUDIS 1999 as most stringent result.

References:

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