$\langle{}{\mathit m}_{\mathrm {ee}}\rangle{}$ = $\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{<0.036 - 0.156} $ ${}^{136}\mathrm {Xe}$ KamLAND-Zen 1 ABE 2023 $ \text{<0.113 - 0.269} $ ${}^{76}\mathrm {Ge}$ MAJORANA 2 ARNQUIST 2023 $ \text{<0.09 - 0.305} $ ${}^{130}\mathrm {Te}$ CUORE 3 ADAMS 2022 A $ \text{<0.8 - 2.5} $ ${}^{136}\mathrm {Xe}$ XENON1T 4 APRILE 2022 A $ \text{<0.28 - 0.49} $ ${}^{100}\mathrm {Mo}$ CUPID-Mo 5 AUGIER 2022 $ \text{<0.263 - 0.545} $ ${}^{82}\mathrm {Se}$ CUPID-0 6 AZZOLINI 2022 $ \text{<0.31 - 0.54} $ ${}^{100}\mathrm {Mo}$ CUPID-Mo 7 ARMENGAUD 2021 $ \text{<0.075 - 0.35} $ ${}^{130}\mathrm {Te}$ CUORE 8 ADAMS 2020 A $ \text{<0.079 - 0.180} $ ${}^{76}\mathrm {Ge}$ GERDA 9 AGOSTINI 2020 B $ \text{< 1.2 - 2.1} $ ${}^{100}\mathrm {Mo}$ AMoRE 10 ALENKOV 2019 $ \text{<0.093 - 0.286} $ ${}^{136}\mathrm {Xe}$ EXO-200 11 ANTON 2019 $ \text{<1.3 - 3.5} $ ${}^{136}\mathrm {Xe}$ PANDAX-II 12 NI 2019 $ \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{<1.0 - 1.7} $ ${}^{116}\mathrm {Cd}$ AURORA 15 BARABASH 2018 $ \text{<1.4 - 2.5} $ ${}^{116}\mathrm {Cd}$ NEMO-3 16 ARNOLD 2017 $ \text{<0.27 - 0.76} $ ${}^{130}\mathrm {Te}$ CUORICINO 17 ALDUINO 2016 $ \text{< 1.6 - 5.3} $ ${}^{150}\mathrm {Nd}$ NEMO-3 18 ARNOLD 2016 A $ \text{<0.33 - 0.62} $ ${}^{100}\mathrm {Mo}$ NEMO-3 19 ARNOLD 2015 $ \text{< 7.2 - 19.5} $ ${}^{96}\mathrm {Zr}$ NEMO-3 20 ARGYRIADES 2010 $ \text{<3.5 - 22} $ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint. 21 UMEHARA 2008 $ \text{<1.5 - 1.7} $ ${}^{116}\mathrm {Cd}$ ${}^{116}\mathrm {Cd}WO_{4}$ scint. 22 DANEVICH 2003 1  ABE 2023 utilize 745 kg of ${}^{136}\mathrm {Xe}$ isotope exposure from the combined data set of the KamLAND-Zen 400 and 800 to derive a limit on $\langle {\mathit m}_{\mathrm { {{\mathit \beta}} {{\mathit \beta}} }}\rangle $. The range reflects the author's assessment of the variability of the theoretically calculated nuclear matrix elements. 2  ARNQUIST 2023 use the final data set of the MAJORANA DEMONSTRATOR experiment, with 64.5 kg$\cdot{}$yr of isotop exposure, to derive an upper limit for $\langle {\mathit m}_{\mathrm { {{\mathit \beta}} {{\mathit \beta}} }}\rangle $. The range reflects the author's assessment of the variability of the theoretically calculated nuclear matrix elements. 3  ADAMS 2022A use 1038.4 kg$\cdot{}$yr of TeO$_{2}$ exposure collected by the CUORE experiment to determine this range of limits. The range reflects the uncertainty of nuclear matrix element calculations needed for the conversion of half-life to neutrino mass. 4  APRILE 2022A use data taken with the XENON1T detector to limit the Majorana neutrino mass. 36.16 kg$\cdot{}$yr of ${}^{136}\mathrm {Xe}$ exposure were utilized. The reported range of limits is due to uncertainties in the nuclear matrix elements. 5  AUGIER 2022 use the final data set of the CUPID-Mo cryogenic calorimeter with an isotop exposure of 1.47 kg$\cdot{}$y to derive a range of neutrino mass limits. The range reflects the authors' estimate of the spread of nuclear matrix element calculations. 6  AZZOLINI 2022 use 8.82 kg$\cdot{}$yr of isotopic exposure of the CPID-0 scintillating cryogenic bolometer to set this range of neutrino mass limits. The range reflects the authors' estimate of the spread of nuclear matrix element calculations. 7  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. 8  ADAMS 2020A use the data of CUORE (372.5 kg$\cdot{}$yr exposure of TeO$_{2}$) to obtain this limit. 9  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 . 10  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. 11  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. 12  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. 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  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 . 16  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. 17  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 . 18  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 . 19  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. 20  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. 21  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 . 22  Limit for $\langle {\mathit m}_{{{\mathit \nu}}}\rangle $ is based on the nuclear matrix elements of STAUDT 1990 and ARNOLD 1996 . Supersedes DANEVICH 2000 .

References:

ABE 2023 PRL 130 051801 Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND-Zen ARNQUIST 2023 PRL 130 062501 Final Result of the Majorana Demonstrator?s Search for Neutrinoless Double-$?$ Decay in ${}^{76}\mathrm{Ge}$ ADAMS 2022A NAT 604 53 Search for Majorana neutrinos exploiting millikelvin cryogenics with CUORE APRILE 2022A PR C106 024328 Double-Weak Decays of $^{124}$Xe and $^{136}$Xe in the XENON1T and XENONnT Experiments AUGIER 2022 EPJ C82 1033 Final results on the $0\nu \beta \beta $ decay half-life limit of $^{100}$Mo from the CUPID-Mo experiment AZZOLINI 2022 PRL 129 111801 Final Result on the Neutrinoless Double Beta Decay of $^{82}$Se with CUPID-0 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 ALENKOV 2019 EPJ C79 791 First Results from the AMoRE-Pilot neutrinoless double beta decay experiment ANTON 2019 PRL 123 161802 Search for Neutrinoless Double-$\beta$ Decay with the Complete EXO-200 Dataset NI 2019 CP C43 113001 Searching for neutrino-less double beta decay of $^{136}$Xe with PandaX-II liquid xenon 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 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 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 ARNOLD 2015 PR D92 072011 Results of the Search for Neutrinoless Double-${{\mathit \beta}}$ Decay in ${}^{100}\mathrm {Mo}$ with the NEMO-3 Experiment 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 DANEVICH 2003 PR C68 035501 Search for 2$\beta $ Decay of Cadmium and Tungsten Isotopes: Final Results of the Solotvina Experiment