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

$\langle{}{\mathit m}_{{{\mathit \nu}}}\rangle{}$ = $\vert \Sigma$ $\mathit U{}{\mathit m}_{{{\mathit \nu}_{{j}}}}\vert$, where the sum goes from 1 to $\mathit n$ and where $\mathit n$ = number of neutrino generations, and ${{\mathit \nu}_{{j}}}$ is a Majorana neutrino. Note that $\mathit U$, not $\vert \mathit U_{{{\mathit e}}\mathit j}\vert ^2$, occurs in the sum. The possibility of cancellations has been stressed. In the following Listings, only best or comparable limits or lifetimes for each isotope are reported.

$\mathit VALUE$ ${\mathrm {(eV)}}$ CL$\%$ ISOTOPE TRANSITION    METHOD DOCUMENT ID
• • • We do not use the following data for averages, fits, limits, etc. • • •
$\text{<1.4 - 2.5}$ $90$ ${}^{116}\mathrm {Cd}$ $0$ $\text{NEMO-3}$ 1
 2017
$\text{<0.27 - 0.76}$ $90$ ${}^{130}\mathrm {Te}$ $0$ $\text{CUORE(CINO)}$ 2
 2016
$\text{< 1.6 - 5.3}$ $90$ ${}^{150}\mathrm {Nd}$ $0$ $\text{NEMO-3}$ 3
 2016 A
$\text{<0.061 - 0.165}$ $90$ ${}^{136}\mathrm {Xe}$ $0$ $\text{KamLAND-Zen}$ 4
 2016
$\text{<0.33 - 0.62}$ $90$ ${}^{100}\mathrm {Mo}$ $0$ $\text{NEMO-3}$ 5
 2015
$\text{<0.19 - 0.45}$ $90$ ${}^{136}\mathrm {Xe}$ $0$ $\text{EXO-200}$ 6
 2014 B
$\text{<0.2 - 0.4}$ $90$ ${}^{76}\mathrm {Ge}$ $0$ $\text{GERDA}$ 7
 2013 A
$\text{<0.3 - 0.6}$ $90$ ${}^{136}\mathrm {Xe}$ $0$ $\text{KamLAND-Zen}$ 8
 2012 A
$\text{<0.89 - 2.43}$ $90$ ${}^{82}\mathrm {Se}$ $0$ $\text{NEMO-3}$ 9
 2011 A
$\text{< 7.2 - 19.5}$ $90$ ${}^{96}\mathrm {Zr}$ $0$ $\text{NEMO-3}$ 10
 2010
$\text{<3.5 - 22}$ $90$ ${}^{48}\mathrm {Ca}$ $0$ CaF$_{2}$ scint. 11
 2008
$\text{<9.3 - 60}$ $90$ ${}^{100}\mathrm {Mo}$ $0$ NEMO-3 12
 2007
$\text{< 6500}$ $90$ ${}^{100}\mathrm {Mo}$ $0$ NEMO-3 13
 2007
$0.32 \pm0.03$ $68$ ${}^{76}\mathrm {Ge}$ $0$ Enriched ${}^{}\mathrm {HPGe}$ 14
 2006 A
$\text{<0.2 - 1.1}$ $90$ ${}^{130}\mathrm {Te}$ Cryog. det. 15
 2005
$\text{<0.7 - 2.8}$ $90$ ${}^{100}\mathrm {Mo}$ $0$ NEMO-3 16
 2005 A
$\text{<1.7 - 4.9}$ $90$ ${}^{82}\mathrm {Se}$ $0$ NEMO-3 17
 2005 A
$\text{<0.37 - 1.9}$ $90$ ${}^{130}\mathrm {Te}$ Cryog. det. 18
 2004
$\text{<0.8 - 1.2}$ $90$ ${}^{100}\mathrm {Mo}$ $0$ NEMO-3 19
 2004
$\text{<1.5 - 3.1}$ $90$ ${}^{82}\mathrm {Se}$ $0$ NEMO-3 19
 2004
$\text{0.1 - 0.9}$ $99.7$ ${}^{76}\mathrm {Ge}$ Enriched HP Ge 20
 2004 A
$\text{<7.2 - 44.7}$ $90$ ${}^{48}\mathrm {Ca}$ CaF$_{2}$ scint. 21
 2004
$\text{< 1.1 - 2.6}$ $90$ ${}^{130}\mathrm {Te}$ $\text{Cryog. det.}$ 22
 2003
$\text{<1.5 - 1.7}$ $90$ ${}^{116}\mathrm {Cd}$ $0$ ${}^{116}\mathrm {Cd}\text{ WO_}{4} \text{ scint.}$ 23
 2003
$\text{<0.33 - 1.35}$ $90$ Enriched HPGe 24
 2002 B
$<2.9$ $90$ ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}$ Liquid Xe Scint. 25
 2002 D
$0.39 {}^{+0.17}_{-0.28}$ ${}^{76}\mathrm {Ge}$ 0${{\mathit \nu}}$ Enriched HPGe 26
 2002 D
$\text{<2.1 - 4.8}$ $90$ ${}^{100}\mathrm {Mo}$ $0$ $\text{ELEGANT V}$ 27
 2001
$\text{<0.35}$ $90$ ${}^{76}\mathrm {Ge}$ Enriched HPGe 28
 2001
$\text{<23}$ $90$ ${}^{96}\mathrm {Zr}$ NEMO-2 29
 1999
$\text{<1.1 - 1.5}$ ${}^{128}\mathrm {Te}$ $\text{Geochem}$ 30
 1992
$<5$ $68$ ${}^{82}\mathrm {Se}$ $\text{TPC}$ 31
 1992
$<8.3$ $76$ ${}^{48}\mathrm {Ca}$ 0${{\mathit \nu}}$ $CaF_{2} \text{ scint.}$
 1991
1  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.
2  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 .
3  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 .
4  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.
5  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.
6  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 .
7  AGOSTINI 2013A is based on 21.6 kg yr of data collected by the GERDA detector. The reported range reflects different nuclear matrix elements. This result is in tension with the evidence for 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$-decay reported in KLAPDOR-KLEINGROTHAUS 2006A and earlier references to that work.
8  GANDO 2012A limit is based on the KamLAND-Zen data. The reported range reflects different nuclear matrix elements. Superseded by GANDO 2013A.
9  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 .
10  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.
11  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 .
12  ARNOLD 2007 use NEMO-3 half life limit for 0${{\mathit \nu}}$-decay of ${}^{100}\mathrm {Mo}$ to the first excited 0${}^{+}_{1}$-state of daughter nucleus to obtain neutrino mass limit. The spread reflects the choice of two different nuclear matrix elements. This limit is not competitive when compared to the decay to the ground state.
13  ARNOLD 2007 use NEMO-3 half life limit for 0${{\mathit \nu}}$-decay of ${}^{100}\mathrm {Mo}$ to the first excited 2${}^{+}$-state of daughter nucleus to obtain neutrino mass limit. This limit is not competitive when compared to the decay to the ground state.
14  Re-analysis of data originally published in KLAPDOR-KLEINGROTHAUS 2004A. Modified pulse shape analysis leads the authors to claim 6$\sigma$ statistical evidence for observation of 0${{\mathit \nu}}$-decay. Authors use matrix element of STAUDT 1990 . Uncertainty of nuclear matrix element is not reflected in stated error. Supersedes KLAPDOR-KLEINGROTHAUS 2004A.
15  Supersedes ARNABOLDI 2004 . Reported range of limits due to use of different nuclear matrix element calculations.
16  Mass limits reported in ARNOLD 2005A are derived from ${}^{100}\mathrm {Mo}$ data, obtained by the NEMO-3 collaboration. The range reflects the spread of matrix element calculations considered in this work. Supersedes ARNOLD 2004 .
17  Neutrino mass limits based on ${}^{82}\mathrm {Se}$ data utilizing the NEMO-3 detector. The range reported in ARNOLD 2005A reflects the spread of matrix element calculations considered in this work. Supersedes ARNOLD 2004 .
18  Supersedes ARNABOLDI 2003 . Reported range of limits due to use of different nuclear matrix element calculations.
19  ARNOLD 2004 limit is based on the nuclear matrix elements of SIMKOVIC 1999 , STOICA 2001 and CIVITARESE 2003 .
20  Supersedes KLAPDOR-KLEINGROTHAUS 2002D. Event excess at ${{\mathit \beta}}{{\mathit \beta}}$ -decay energy is used to derive Majorana neutrino mass using the nuclear matrix elements of STAUDT 1990 . The mass range shown is based on the authors evaluation of the uncertainties of the STAUDT 1990 matrix element calculation. If this uncertainty is neglected, and only statistical errors are considered, the range in $\langle$m$\rangle$ becomes ($0.2 - 0.6$) eV at the 3 ${{\mathit \sigma}}$ level.
21  Calorimetric CaF$_{2}$ scintillator. Range of limits reflects authors' estimate of the uncertainty of the nuclear matrix elements. Replaces YOU 1991 as the most stringest limit based on ${}^{48}\mathrm {Ca}$.
22  Supersedes ALESSANDRELLO 2000 . Cryogenic calorimeter search. Reported a range reflecting uncertainty in nuclear matrix element calculations.
23  Limit for $\langle {\mathit m}_{{{\mathit \nu}}}\rangle$ is based on the nuclear matrix elements of STAUDT 1990 and ARNOLD 1996 . Supersedes DANEVICH 2000 .
24  AALSETH 2002B reported range of limits on $\langle {\mathit m}_{{{\mathit \nu}}}\rangle$ reflects the spread of theoretical nuclear matrix elements. Excludes part of allowed mass range reported in KLAPDOR-KLEINGROTHAUS 2001B.
25  BERNABEI 2002D limit is based on the matrix elements of SIMKOVIC 2002 . The range of neutrino masses based on a variety of matrix elements is $1.1 - 2.9$ eV.
26  KLAPDOR-KLEINGROTHAUS 2002D is a detailed description of the analysis of the data collected by the Heidelberg-Moscow experiment, previously presented in KLAPDOR-KLEINGROTHAUS 2001B. Matrix elements in STAUDT 1990 have been used. See the footnote in the preceding table for further details. See also KLAPDOR-KLEINGROTHAUS 2002B.
27  The range of the reported $\langle{}{\mathit m}_{{{\mathit \nu}}}\rangle{}$ values reflects the spread of the nuclear matrix elements. On axis value assuming $\langle{}\lambda \rangle{}=\langle{}\eta \rangle{}$=0.
28  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.
29  ARNOLD 1999 limit based on the nuclear matrix elements of STAUDT 1990 .
30  BERNATOWICZ 1992 finds these majorana neutrino mass limits assuming that the measured geochemical decay width is a limit on the 0${{\mathit \nu}}$ decay width. The range is the range found using matrix elements from HAXTON 1984 , TOMODA 1987 , and SUHONEN 1991 . Further details of the experiment are given in BERNATOWICZ 1993 .
31  ELLIOTT 1992 uses the matrix elements of HAXTON 1984 .
References:
 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
 AGOSTINI 2013A
PRL 111 122503 Results on neutrinoless double beta decay of ${}^{76}\mathrm {Ge}$ from GERDA Phase I
 GANDO 2012A
PR C85 045504 Measurement of the Double-${{\mathit \beta}}$ Decay Half-Life of ${}^{136}\mathrm {Xe}$ with the KamLAND-Zen Experiment
 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
 ARNOLD 2007
NP A781 209 Measurement of Double beta Decay of ${}^{100}\mathrm {Mo}$ to Excited States in the NEMO-3 Experiment
 KLAPDOR-KLEINGROTHAUS 2006A
MPL A21 1547 The Evidence for the Observation of 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ Decay: the Identification of 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ Events from the Full Spectra
 ARNABOLDI 2005
PRL 95 142501 New Limit on the Neutrinoless $\beta \beta$ Decay of ${}^{130}\mathrm {Te}$
 ARNOLD 2005A
PRL 95 182302 First Results of the Search for Neutrinoless Double-Beta Decay with the NEMO 3 Detector
 ARNABOLDI 2004
PL B584 260 First Results on Neutrinoless Double Beta Decay of ${}^{130}\mathrm {Te}$ with the Calorimetric Cuoricino Experiment
 ARNOLD 2004
JETPL 80 377 Study of 2${{\mathit \beta}}$ Decay of ${}^{100}\mathrm {Mo}$ and ${}^{82}\mathrm {Se}$ using the NEMO3 Detector
 KLAPDOR-KLEINGROTHAUS 2004A
PL B586 198 Search for Neutrinoless Double Beta Decay with Enriched ${}^{76}\mathrm {Ge}$ in Gran Sasso 1990-2003
 OGAWA 2004
NP A730 215 Search for Neutrinoless Double Beta Decay of ${}^{48}\mathrm {Ca}$ by CaF$_{2}$ Scintillator
 ARNABOLDI 2003
PL B557 167 A Calorimetric Search on Double beta Decay of ${}^{130}\mathrm {Te}$
 DANEVICH 2003
PR C68 035501 Search for 2$\beta$ Decay of Cadmium and Tungsten Isotopes: Final Results of the Solotvina Experiment
 AALSETH 2002B
PR D65 092007 The IGEX ${}^{76}\mathrm {Ge}$ Neutrinoless Double beta Decay Experiment: Prospects for Next Generation Experiments
 BERNABEI 2002D
PL B546 23 Investigation of $\beta \beta$ Decay Modes in ${}^{134}\mathrm {Xe}$ and ${}^{135}\mathrm {Xe}$
 KLAPDOR-KLEINGROTHAUS 2002D
FP 32 1181 Neutrinoless Double beta Decay: Status of Evidence
 EJIRI 2001
PR C63 065501 Limits on the Majorana Neutrino Mass and Right-Handed Weak Currents by Neutrinoless Double $\beta$ Decay of ${}^{100}\mathrm {Mo}$
 KLAPDOR-KLEINGROTHAUS 2001
EPJ A12 147 Latest Results from the Heidelberg-Moscow Double $\beta$ Decay Experiment
 ARNOLD 1999
NP A658 299 Double $\beta$ Decay of ${}^{96}\mathrm {Zr}$
 BERNATOWICZ 1992
PRL 69 2341 Neutrino Mass Limits from a Precise Determination of $\beta$ $\beta$ Decay Rates of ${}^{128}\mathrm {Te}$ and ${}^{130}\mathrm {Te}$
 ELLIOTT 1992
PR C46 1535 Double $\beta$ Decay of ${}^{82}\mathrm {Se}$
 YOU 1991
PL B265 53 A Search for Neutrinoless Double $\beta$ Decay of ${}^{48}\mathrm {Ca}$
 HAXTON 1984
PPNP 12 409 Double $\beta$ Decay