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

$\langle{}{\mathit m}_{{{\mathit \nu}}}\rangle{}$ = $\vert \Sigma \mathit U{}^{ 2}_{ ei}{\mathit m}_{{{\mathit \nu}_{{i}}}}\vert$, $\mathit i$ = 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.

$\mathit VALUE$ ${\mathrm {(eV)}}$ ISOTOPE TRANSITION METHOD DOCUMENT ID
• • • We do not use the following data for averages, fits, limits, etc. • • •
$\text{<0.24 - 0.52}$ ${}^{76}\mathrm {Ge}$ $\text{MAJORANA Dem}$ 1
 2018
$\text{<0.12 - 0.26}$ ${}^{76}\mathrm {Ge}$ $\text{GERDA}$ 2
 2018
$\text{<0.15 - 0.40}$ ${}^{136}\mathrm {Xe}$ $\text{EXO-200}$ 3
 2018
$\text{<0.11 - 0.52}$ ${}^{130}\mathrm {Te}$ $\text{CUORE}$ 4
 2018
$\text{<0.15 - 0.33}$ ${}^{76}\mathrm {Ge}$ $\text{GERDA}$ 5
 2017
$\text{<1.4 - 2.5}$ ${}^{116}\mathrm {Cd}$ $\text{NEMO-3}$ 6
 2017
$\text{<0.27 - 0.76}$ ${}^{130}\mathrm {Te}$ $\text{CUORE(CINO)}$ 7
 2016
$\text{< 1.6 - 5.3}$ ${}^{150}\mathrm {Nd}$ $\text{NEMO-3}$ 8
 2016 A
$\text{<0.061 - 0.165}$ ${}^{136}\mathrm {Xe}$ $\text{KamLAND-Zen}$ 9
 2016
$\text{<0.33 - 0.62}$ ${}^{100}\mathrm {Mo}$ $\text{NEMO-3}$ 10
 2015
$\text{<0.19 - 0.45}$ ${}^{136}\mathrm {Xe}$ $\text{EXO-200}$ 11
 2014 B
$\text{<0.89 - 2.43}$ ${}^{82}\mathrm {Se}$ $\text{NEMO-3}$ 12
 2011 A
$\text{< 7.2 - 19.5}$ ${}^{96}\mathrm {Zr}$ $\text{NEMO-3}$ 13
 2010
$\text{<3.5 - 22}$ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint. 14
 2008
$\text{<0.2 - 1.1}$ ${}^{130}\mathrm {Te}$ Cryog. det. 15
 2005
$\text{<0.37 - 1.9}$ ${}^{130}\mathrm {Te}$ Cryog. det. 16
 2004
$\text{<1.5 - 1.7}$ ${}^{116}\mathrm {Cd}$ ${}^{116}\mathrm {Cd}\text{ WO_}{4} \text{ scint.}$ 17
 2003
$\text{<0.350}$ ${}^{76}\mathrm {Ge}$ Enriched HPGe 18
 2001
$<8.3$ ${}^{48}\mathrm {Ca}$ $CaF_{2} \text{ scint.}$
 1991
1  AALSETH 2018 uses the MAJORANA Demonstrator detector to establish this limit.
2  AGOSTINI 2018 uses the GERDA detector to establish this limit.
3  ALBERT 2018 uses the EXO-200 experiment to obtain this limit.
4  ALDUINO 2018 use the combined data of CUORE, CUORE0, and Cuoricino to obtain this limit.
5  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.
6  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.
7  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 .
8  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 .
9  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.
10  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.
11  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 .
12  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 .
13  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.
14  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 .
15  Supersedes ARNABOLDI 2004 . Reported range of limits due to use of different nuclear matrix element calculations.
16  Supersedes ARNABOLDI 2003 . Reported range of limits due to use of different nuclear matrix element calculations.
17  Limit for $\langle {\mathit m}_{{{\mathit \nu}}}\rangle$ is based on the nuclear matrix elements of STAUDT 1990 and ARNOLD 1996 . Supersedes DANEVICH 2000 .
18  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:
 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
 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
 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 ${}^{48}\mathrm {Ca}$
 ARNOLD 2005A
PRL 95 182302 First Results of the Search for Neutrinoless Double-Beta Decay with the NEMO 3 Detector
 ARNOLD 2004
JETPL 80 377 Study of 2${{\mathit \beta}}$ Decay of ${}^{100}\mathrm {Mo}$ and ${}^{82}\mathrm {Se}$ using the NEMO3 Detector
 ARNOLD 2014
PR D89 111101 Search for Neutrinoless Double-beta Decay of ${}^{100}\mathrm {Mo}$ with the NEMO-3 Detector