# $\langle{}{\boldsymbol m}_{\mathrm {ee}}\rangle{}$, The Effective Weighted Sum of Majorana Neutrino Masses Contributing to Neutrinoless Double-$\beta$ Decay INSPIRE search

$\langle{}{\mathit m}_{\mathrm {ee}}\rangle{}$ = $\vert \Sigma \mathit U{}^{ 2}_{ ei}{\mathit m}_{{{\mathit \nu}_{{i}}}}\vert$, $\mathit i$ = 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. • • •
$\text{< 0.07 - 0.16}$ ${}^{76}\mathrm {Ge}$ GERDA 1
 2019
$\text{< 1.2 - 2.1}$ ${}^{100}\mathrm {Mo}$ AMoRE 2
 2019
$\text{<0.200 - 0.433}$ ${}^{76}\mathrm {Ge}$ MAJORANA 3
 2019
$\text{<0.093 - 0.286}$ ${}^{136}\mathrm {Xe}$ EXO-200 4
 2019
$\text{<0.311 - 0.638}$ ${}^{82}\mathrm {Se}$ CUPID-0 5
 2019
$\text{<1.3 - 3.5}$ ${}^{136}\mathrm {Xe}$ PANDAX-II 6
 2019
$\text{<0.24 - 0.52}$ ${}^{76}\mathrm {Ge}$ MAJORANA Dem 7
 2018
$\text{<0.12 - 0.26}$ ${}^{76}\mathrm {Ge}$ GERDA 8
 2018
$\text{<0.15 - 0.40}$ ${}^{136}\mathrm {Xe}$ EXO-200 9
 2018
$\text{<0.11 - 0.52}$ ${}^{130}\mathrm {Te}$ CUORE 10
 2018
$\text{< 1.2 - 3.0}$ ${}^{82}\mathrm {Se}$ NEMO-3 11
 2018
$\text{<0.376 - 0.770}$ ${}^{82}\mathrm {Se}$ CUPID-0 12
 2018
$\text{<1.0 - 1.7}$ ${}^{116}\mathrm {Cd}$ AURORA 13
 2018
$\text{<0.15 - 0.33}$ ${}^{76}\mathrm {Ge}$ GERDA 14
 2017
$\text{<1.4 - 2.5}$ ${}^{116}\mathrm {Cd}$ NEMO-3 15
 2017
$\text{<0.27 - 0.76}$ ${}^{130}\mathrm {Te}$ CUORE(CINO) 16
 2016
$\text{< 1.6 - 5.3}$ ${}^{150}\mathrm {Nd}$ NEMO-3 17
 2016 A
$\text{<0.061 - 0.165}$ ${}^{136}\mathrm {Xe}$ KamLAND-Zen 18
 2016
$\text{<0.33 - 0.62}$ ${}^{100}\mathrm {Mo}$ NEMO-3 19
 2015
$\text{<0.19 - 0.45}$ ${}^{136}\mathrm {Xe}$ EXO-200 20
 2014 B
$\text{<0.89 - 2.43}$ ${}^{82}\mathrm {Se}$ NEMO-3 21
 2011 A
$\text{< 7.2 - 19.5}$ ${}^{96}\mathrm {Zr}$ NEMO-3 22
 2010
$\text{<3.5 - 22}$ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint. 23
 2008
$\text{<0.2 - 1.1}$ ${}^{130}\mathrm {Te}$ Cryog. det. 24
 2005
$\text{<0.37 - 1.9}$ ${}^{130}\mathrm {Te}$ Cryog. det. 25
 2004
$\text{<1.5 - 1.7}$ ${}^{116}\mathrm {Cd}$ ${}^{116}\mathrm {Cd}WO_{4}$ scint. 26
 2003
$\text{<0.350}$ ${}^{76}\mathrm {Ge}$ Enriched HPGe 27
 2001
$<8.3$ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint.
 1991
1  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 .
2  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.
3  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.
4  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.
5  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.
6  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.
7  AALSETH 2018 uses the MAJORANA Demonstrator detector to establish this limit.
8  AGOSTINI 2018 uses the GERDA detector to establish this limit.
9  ALBERT 2018 uses the EXO-200 experiment to obtain this limit.
10  ALDUINO 2018 use the combined data of CUORE, CUORE0, and Cuoricino to obtain this limit.
11  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.
12  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.
13  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 .
14  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.
15  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.
16  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 .
17  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 .
18  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.
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  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 .
21  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 .
22  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.
23  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 .
24  Supersedes ARNABOLDI 2004 . Reported range of limits due to use of different nuclear matrix element calculations.
25  Supersedes ARNABOLDI 2003 . Reported range of limits due to use of different nuclear matrix element calculations.
26  Limit for $\langle {\mathit m}_{{{\mathit \nu}}}\rangle$ is based on the nuclear matrix elements of STAUDT 1990 and ARNOLD 1996 . Supersedes DANEVICH 2000 .
27  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:
 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
 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
NP A847 168 Measurement of the Two Neutrino Double $\beta$ Decay Half-Life of ${}^{96}\mathrm {Zr}$ with the NEMO-3 Detector
PR C78 058501 Neutrino-less Double-$\beta$ Decay of ${}^{48}\mathrm {Ca}$ Studied by CaF$_{2}$(Eu) Scintillators
PRL 95 142501 New Limit on the Neutrinoless $\beta \beta$ Decay of ${}^{130}\mathrm {Te}$
PL B584 260 First Results on Neutrinoless Double Beta Decay of ${}^{130}\mathrm {Te}$ with the Calorimetric Cuoricino Experiment
PR C68 035501 Search for 2$\beta$ Decay of Cadmium and Tungsten Isotopes: Final Results of the Solotvina Experiment
EPJ A12 147 Latest Results from the Heidelberg-Moscow Double $\beta$ Decay Experiment
PL B265 53 A Search for Neutrinoless Double $\beta$ Decay of ${}^{48}\mathrm {Ca}$