$\langle{}{\mathit m}_{\mathrm {ee}}\rangle{}$ = $\vert \Sigma \mathit U{}^{ 2}_{ ei}{\mathit m}_{{{\mathit \nu}_{{i}}}}\vert $, $\mathit i$ = 1,2,3. It is assumed that ${{\mathit \nu}_{{i}}}$ are Majorana particles and that the transition is dominated by the known (light) neutrinos. Note that $\mathit U{}^{ 2}_{ ei}$ and not $\vert \mathit U_{ei}\vert ^2$ occur in the sum, and that consequently cancellations are possible. The experiments obtain the limits on $\langle{}{\mathit m}_{{{\mathit \nu}}}\rangle{}$ from the measured ones on ${{\mathit T}_{{1/2}}}$ using a range of nuclear matrix elements (NME), which is reflected in the spread of $\langle{}{\mathit m}_{{{\mathit \nu}}}\rangle{}$. Different experiments may choose different NME. All assume ${{\mathit g}_{{A}}}$ = 1.27. In the following Listings, only the best or comparable limits for each isotope are reported. When not mentioned explicitly the transition is between ground states, but transitions between excited states are also reported.

$\mathit VALUE$ (eV) ISOTOPE METHOD DOCUMENT ID • • We do not use the following data for averages, fits, limits, etc. • • $ \text{<0.31 - 0.54} $ ${}^{100}\mathrm {Mo}$ CUPID-Mo 1 ARMENGAUD 2021 $ \text{<0.075 - 0.35} $ ${}^{130}\mathrm {Te}$ CUORE 2 ADAMS 2020 A $ \text{<0.079 - 0.180} $ ${}^{76}\mathrm {Ge}$ GERDA 3 AGOSTINI 2020 B $ \text{< 0.07 - 0.16} $ ${}^{76}\mathrm {Ge}$ GERDA 4 AGOSTINI 2019 $ \text{< 1.2 - 2.1} $ ${}^{100}\mathrm {Mo}$ AMoRE 5 ALENKOV 2019 $ \text{<0.200 - 0.433} $ ${}^{76}\mathrm {Ge}$ MAJORANA 6 ALVIS 2019 $ \text{<0.093 - 0.286} $ ${}^{136}\mathrm {Xe}$ EXO-200 7 ANTON 2019 $ \text{<0.311 - 0.638} $ ${}^{82}\mathrm {Se}$ CUPID-0 8 AZZOLINI 2019 $ \text{<1.3 - 3.5} $ ${}^{136}\mathrm {Xe}$ PANDAX-II 9 NI 2019 $ \text{<0.24 - 0.52} $ ${}^{76}\mathrm {Ge}$ MAJORANA Dem 10 AALSETH 2018 $ \text{<0.12 - 0.26} $ ${}^{76}\mathrm {Ge}$ GERDA 11 AGOSTINI 2018 $ \text{<0.15 - 0.40} $ ${}^{136}\mathrm {Xe}$ EXO-200 12 ALBERT 2018 $ \text{<0.11 - 0.52} $ ${}^{130}\mathrm {Te}$ CUORE 13 ALDUINO 2018 $ \text{< 1.2 - 3.0} $ ${}^{82}\mathrm {Se}$ NEMO-3 14 ARNOLD 2018 $ \text{<0.376 - 0.770} $ ${}^{82}\mathrm {Se}$ CUPID-0 15 AZZOLINI 2018 $ \text{<1.0 - 1.7} $ ${}^{116}\mathrm {Cd}$ AURORA 16 BARABASH 2018 $ \text{<0.15 - 0.33} $ ${}^{76}\mathrm {Ge}$ GERDA 17 AGOSTINI 2017 $ \text{<1.4 - 2.5} $ ${}^{116}\mathrm {Cd}$ NEMO-3 18 ARNOLD 2017 $ \text{<0.27 - 0.76} $ ${}^{130}\mathrm {Te}$ CUORE(CINO) 19 ALDUINO 2016 $ \text{< 1.6 - 5.3} $ ${}^{150}\mathrm {Nd}$ NEMO-3 20 ARNOLD 2016 A $ \text{<0.061 - 0.165} $ ${}^{136}\mathrm {Xe}$ KamLAND-Zen 21 GANDO 2016 $ \text{<0.33 - 0.62} $ ${}^{100}\mathrm {Mo}$ NEMO-3 22 ARNOLD 2015 $ \text{<0.19 - 0.45} $ ${}^{136}\mathrm {Xe}$ EXO-200 23 ALBERT 2014 B $ \text{<0.89 - 2.43} $ ${}^{82}\mathrm {Se}$ NEMO-3 24 BARABASH 2011 A $ \text{< 7.2 - 19.5} $ ${}^{96}\mathrm {Zr}$ NEMO-3 25 ARGYRIADES 2010 $ \text{<3.5 - 22} $ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint. 26 UMEHARA 2008 $ \text{<0.2 - 1.1} $ ${}^{130}\mathrm {Te}$ Cryog. det. 27 ARNABOLDI 2005 $ \text{<0.37 - 1.9} $ ${}^{130}\mathrm {Te}$ Cryog. det. 28 ARNABOLDI 2004 $ \text{<1.5 - 1.7} $ ${}^{116}\mathrm {Cd}$ ${}^{116}\mathrm {Cd}WO_{4}$ scint. 29 DANEVICH 2003 $ \text{<0.350} $ ${}^{76}\mathrm {Ge}$ Enriched HPGe 30 KLAPDOR-KLEIN.. 2001 $ <8.3 $ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint. YOU 1991 1  ARMENGAUD 2021 use the CUPID-Mo demonstrator, with 1.17 kg$\cdot{}$yr exposure of ${}^{100}\mathrm {Mo}$, to set this limit. The range reflects the estimated uncertainty of the calculated nuclear matrix elements. 2  ADAMS 2020A use the data of CUORE (372.5 kg$\cdot{}$yr exposure of TeO$_{2}$) to obtain this limit. 3  AGOSTINI 2020B use the final data set of the GERDA experiment, representing an exposure of 127.2 kg$\cdot{}$yr to derive an upper limit for $\langle {\mathit m}_{\mathrm { {{\mathit \beta}} {{\mathit \beta}} }}\rangle $. Isotopically enriched ${}^{}\mathrm {Ge}$ detectors were used. The range reflects the variability of the theoretically calculated nuclear matrix elements. Supersedes AGOSTINI 2019 . 4  AGOSTINI 2019 use 82.4 kg$\cdot{}$yr of data collected by the isotopically enriched ${}^{76}\mathrm {Ge}$ detectors of the GERDA experiment to derive an upper limit for $\langle {\mathit m}_{\mathrm { {{\mathit \beta}} {{\mathit \beta}} }}\rangle $. The range reflects the variability of the theoretically calculated nuclear matrix elements. Supersedes AGOSTINI 2018 . 5  ALENKOV 2019 report the range of the effective masses $\langle {\mathit m}_{\mathrm { {{\mathit \beta}} {{\mathit \beta}} }}\rangle $ corresponding to the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay half-life limit. It is based on the 52.1 kg$\cdot{}$d exposure of ${}^{100}\mathrm {Mo}$, in the Yangyang underground laboratory. The median sensitivity is $1.1 \times 10^{23}$ years. The range of $\langle {\mathit m}_{\mathrm { {{\mathit \beta}} {{\mathit \beta}} }}\rangle $ reflects the uncertainty of nuclear matrix elements. 6  ALVIS 2019 use the MAJORANA Demonstrator with enriched in ${}^{76}\mathrm {Ge}$ detectors to set this limit. The exposure is 26.0 kg yr. The sensitivity is $4.8 \times 10^{25}$ yr. 7  ANTON 2019 uses the complete dataset of the EXO-200 experiment to obtain these limits. The spread reflect the uncertainty in the nuclear matrix elements. Supersedes ALBERT 2018 and ALBERT 2014B. 8  AZZOLINI 2019 use the CPID-0 scintillating cryogenic bolometer to set this limit. The exposure is 5.29 kg yr. The sensitivity is $5 \times 10^{24}$ yr. 9  NI 2019 use the PandaX-II dual phase TPC at CJPL to search for the 0${{\mathit \nu}}$ ${{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{136}\mathrm {Xe}$ with 22.2 kg yr exposure. The range in the ${{\mathit m}}$ $_{ {{\mathit \beta}} {{\mathit \beta}} }$ limit of $1.3 - 3.5$ eV reflects the range of the calculated nuclear matrix elements. The sensitivity is $1.9 \times 10^{23}$ yr. 10  AALSETH 2018 uses the MAJORANA Demonstrator detector to establish this limit. 11  AGOSTINI 2018 uses the GERDA detector to establish this limit. 12  ALBERT 2018 uses the EXO-200 experiment to obtain this limit. 13  ALDUINO 2018 use the combined data of CUORE, CUORE0, and Cuoricino to obtain this limit. 14  ARNOLD 2018 use the NEMO-3 tracking detector to constrain the 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay of $^{82}$Se. The limit on $\langle {\mathit m}_{\mathrm { {{\mathit \beta}} {{\mathit \beta}} }}\rangle $ is obtained assuming light neutrino exchange; the range reflects different calculations of the nuclear matrix elements. This is a somewhat weaker limit than in BARABASH 2011A using the same detector. 15  AZZOLINI 2018 uses data collected by the CUPID-0 scintillating cryogenic calorimeter, operated in the LNGS, to derive a range of limits on $\langle {\mathit m}_{{{\mathit \nu}}}\rangle $. The reported range reflects the spread of the nuclear matrix element calculations considered in this work. Use ${{\mathit g}_{{A}}}$ = 1.269. 16  BARABASH 2018 use 1.162 kg of ${}^{116}\mathrm {Cd}WO_{4}$ scintillating crystals to obtain these limits. The spread reflects the estimated uncertainty in the nuclear matrix element. Supersedes DANEVICH 2003 . 17  AGOSTINI 2017 is based on 343 mol yr of data from GERDA phase 1 and phase 2 first part and the corresponding limit on T$_{1/2}$ using the different nuclear matrix elements mentioned by the authors. Supersedes AGOSTINI 2013A. 18  ARNOLD 2017 utilize NEMO-3 data, taken with enriched ${}^{116}\mathrm {Cd}$ to limit the effective Majorana neutrino mass. The reported range results from the use of different nuclear matrix elements. Supersedes BARABASH 2011A. 19  ALDUINO 2016 place a limit on the effective Majorana neutrino mass using the combined data of the CUORE-0 and CUORICINO experiments. The range reflects the authors' evaluation of the variability of the nuclear matrix elements. Supersededs ALFONSO 2015 . 20  ARNOLD 2016A limit is derived from data taken with the NEMO-3 detector and ${}^{150}\mathrm {Nd}$. A range of nuclear matrix elements that include the effect of nuclear deformation have been used. Supersedes ARGYRIADES 2009 . 21  GANDO 2016 result is based on the 2016 KamLAND-Zen half-life limit. The stated range reflects different nuclear matrix elements, an unquenched ${{\mathit g}_{{A}}}$ = 1.27 is used. Supersedes GANDO 2013A. 22  ARNOLD 2015 use the NEMO-3 tracking calorimeter with 34.3 kg yr exposure to determine the neutrino mass limit based on the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ -half life of ${}^{100}\mathrm {Mo}$. The spread range reflects different nuclear matrix elements. Supersedes ARNOLD 2014 and BARABASH 2011A. 23  ALBERT 2014B is based on 100 kg yr of exposure of the EXO-200 tracking calorimeter. The mass range reflects the nuclear matrix element calculations. Supersedes AUGER 2012 . 24  BARABASH 2011A limit is based on NEMO-3 data for ${}^{82}\mathrm {Se}$. The reported range reflects different nuclear matrix elements. Supersedes ARNOLD 2005A and ARNOLD 2004 . 25  ARGYRIADES 2010 use ${}^{96}\mathrm {Zr}$ and the NEMO-3 tracking detector to obtain the reported mass limit. The range reflects the fluctuation of the nuclear matrix elements considered. 26  Limit was obtained using CaF$_{2}$ scintillation calorimeter to search for double beta decay of ${}^{48}\mathrm {Ca}$. Reported range of limits reflects spread of QRPA and SM matrix element calculations used. Supersedes OGAWA 2004 . 27  Supersedes ARNABOLDI 2004 . Reported range of limits due to use of different nuclear matrix element calculations. 28  Supersedes ARNABOLDI 2003 . Reported range of limits due to use of different nuclear matrix element calculations. 29  Limit for $\langle {\mathit m}_{{{\mathit \nu}}}\rangle $ is based on the nuclear matrix elements of STAUDT 1990 and ARNOLD 1996 . Supersedes DANEVICH 2000 . 30  KLAPDOR-KLEINGROTHAUS 2001 uses the calculation by STAUDT 1990 . Using several other models in the literature could worsen the limit up to $1.2~$eV. This is the most stringent experimental bound on ${\mathit m}_{{{\mathit \nu}}}$. It supersedes BAUDIS 1999B.

References:

ARMENGAUD 2021 PRL 126 181802 New Limit for Neutrinoless Double-Beta Decay of $^{100}$Mo from the CUPID-Mo Experiment ADAMS 2020A PRL 124 122501 Improved Limit on Neutrinoless Double-Beta Decay in $^{130}$Te with CUORE AGOSTINI 2020B PRL 125 252502 Final Results of GERDA on the Search for Neutrinoless Double-$\beta$ Decay AGOSTINI 2019 SCI 365 1445 Probing Majorana neutrinos with double-$\beta$ decay ALENKOV 2019 EPJ C79 791 First Results from the AMoRE-Pilot neutrinoless double beta decay experiment ALVIS 2019 PR C100 025501 A Search for Neutrinoless Double-Beta Decay in $^{76}$Ge with 26 kg-yr of Exposure from the MAJORANA DEMONSTRATOR ANTON 2019 PRL 123 161802 Search for Neutrinoless Double-$\beta$ Decay with the Complete EXO-200 Dataset AZZOLINI 2019 PRL 123 032501 Final result of CUPID-0 phase-I in the search for the $^{82}$Se Neutrinoless Double-$\beta$ Decay NI 2019 CP C43 113001 Searching for neutrino-less double beta decay of $^{136}$Xe with PandaX-II liquid xenon detector AALSETH 2018 PRL 120 132502 Search for Zero-Neutrino Double Beta Decay in $^{76}$Ge with the Majorana Demonstrator AGOSTINI 2018 PRL 120 132503 Improved Limit on Neutrinoless Double- ? Decay of Ge76 from GERDA Phase II ALBERT 2018 PRL 120 072701 Search for Neutrinoless Double-Beta Decay with the Upgraded EXO-200 Detector ALDUINO 2018 PRL 120 132501 First Results from CUORE: A Search for Lepton Number Violation via $0\nu\beta\beta$ Decay of $^{130}$Te ARNOLD 2018 EPJ C78 821 Final results on ${}^\mathbf 82 \hbox {Se}$ double beta decay to the ground state of ${}^\mathbf 82 \hbox {Kr}$ from the NEMO-3 experiment AZZOLINI 2018 PRL 120 232502 First Result on the Neutrinoless Double-$\beta$ Decay of $^{82}Se$ with CUPID-0 BARABASH 2018 PR D98 092007 Final results of the Aurora experiment to study $2\beta$ decay of $^{116}\mathrm{Cd}$ with enriched $^{116}\mathrm{Cd}{\mathrm{WO}}_{4}$ crystal scintillators AGOSTINI 2017 NAT 544 47 Background Free Search for Neutrinoless Double beta Decay with GERDA Phase II ARNOLD 2017 PR D95 012007 Measurement of the 2${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ Decay Half-Life and Search for the 0${{\mathit \nu}}$ $\beta \beta $ Decay of ${}^{116}\mathrm {Cd}$ with the NEMO-3 Detector ALDUINO 2016 PR C93 045503 Analysis Techniques for the Evaluation of the Neutrinoless Double-${{\mathit \beta}}$ Decay Lifetime in ${}^{130}\mathrm {Te}$ with the CUORE-0 Detector ARNOLD 2016A PR D94 072003 Measurement of the 2${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ Decay Half-Life of ${}^{150}\mathrm {Nd}$ and a Search for 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ Decay Processes with the Full Exposure from the NEMO-3 Detector GANDO 2016 PRL 117 082503 Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen ARNOLD 2015 PR D92 072011 Results of the Search for Neutrinoless Double-${{\mathit \beta}}$ Decay in ${}^{100}\mathrm {Mo}$ with the NEMO-3 Experiment ALBERT 2014B NAT 510 229 Search for Majorana Neutrinos with the First Two Years of EXO-200 Data BARABASH 2011A PAN 74 312 Investigation of Double-beta Decay with the NEMO-3 Detector ARGYRIADES 2010 NP A847 168 Measurement of the Two Neutrino Double $\beta $ Decay Half-Life of ${}^{96}\mathrm {Zr}$ with the NEMO-3 Detector UMEHARA 2008 PR C78 058501 Neutrino-less Double-$\beta $ Decay of ${}^{48}\mathrm {Ca}$ Studied by CaF$_{2}$(Eu) Scintillators ARNABOLDI 2005 PRL 95 142501 New Limit on the Neutrinoless $\beta \beta $ Decay of ${}^{130}\mathrm {Te}$ ARNABOLDI 2004 PL B584 260 First Results on Neutrinoless Double Beta Decay of ${}^{130}\mathrm {Te}$ with the Calorimetric Cuoricino Experiment DANEVICH 2003 PR C68 035501 Search for 2$\beta $ Decay of Cadmium and Tungsten Isotopes: Final Results of the Solotvina Experiment KLAPDOR-KLEINGROTHAUS 2001 EPJ A12 147 Latest Results from the Heidelberg-Moscow Double $\beta $ Decay Experiment YOU 1991 PL B265 53 A Search for Neutrinoless Double $\beta $ Decay of ${}^{48}\mathrm {Ca}$