# Majoron Searches in Neutrinoless Double $\beta$ Decay INSPIRE search

Limits are for the half-life of neutrinoless ${{\mathit \beta}}{{\mathit \beta}}$ decay with a Majoron emission. No experiment currently claims any such evidence. Only the best or comparable limits for each isotope are reported.

$\mathit t_{1/2}$ ($10^{21}$ yr) CL$\%$ ISOTOPE TRANSITION METHOD DOCUMENT ID
$\bf{>7200}$ 90 $\bf{{}^{128}\mathrm {Te}}$ CNTR 1
 1992
• • • We do not use the following data for averages, fits, limits, etc. • • •
$>4.4$ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 2
 2019
$>37$ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 3
 2018
$>420$ 90 ${}^{76}\mathrm {Ge}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ GERDA 4
 2015 A
$>400$ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 5
 2015
$>1200$ 90 ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ EXO-200 6
 2014 A
$>2600$ 90 ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ KamLAND-Zen 7
 2012
$>16$ 90 ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 8
 2011
$>1.9$ 90 ${}^{96}\mathrm {Zr}$ 2${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 9
 2010
$>1.52$ 90 ${}^{150}\mathrm {Nd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 10
 2009
$>27$ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 11
 2006
$>15$ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 12
 2006
$>14$ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 13
 2004
$>12$ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 14
 2004
$>2.2$ 90 ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ Cryog. det. 15
 2003
$>0.9$ 90 ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ Cryog. det. 16
 2003
$>8$ 90 ${}^{116}\mathrm {Cd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ CdWO$_{4}$ scint. 17
 2003
$>0.8$ 90 ${}^{116}\mathrm {Cd}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ CdWO$_{4}$ scint. 18
 2003
$>500$ 90 ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ Liquid Xe Scint. 19
 2002 D
$>5.8$ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ ELEGANT V 20
 2002
$>0.32$ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ Liq. Ar ioniz. 21
 2001
$>0.0035$ 90 ${}^{160}\mathrm {Gd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ ${}^{160}\mathrm {Gd}_{2}$SiO$_{5}$:Ce 22
 2001
$>0.013$ 90 ${}^{160}\mathrm {Gd}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ ${}^{160}\mathrm {Gd}_{2}$SiO$_{5}$:Ce 23
 2001
$>2.3$ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO 2 24
 2000
$>0.31$ 90 ${}^{96}\mathrm {Zr}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO 2 25
 2000
$>0.63$ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ NEMO 2 26
 2000
$>0.063$ 90 ${}^{96}\mathrm {Zr}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ NEMO 2 26
 2000
$>0.16$ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ NEMO 2 26
 2000
$>2.4$ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO 2 27
 1998
$>7.2$ 90 ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ TPC 28
 1998
$>7.91$ 90 ${}^{76}\mathrm {Ge}$ SPEC 29
 1996
$>17$ 90 ${}^{76}\mathrm {Ge}$ CNTR
 1993
1  BERNATOWICZ 1992 studied double-$\beta$ decays of ${}^{128}\mathrm {Te}$ and ${}^{130}\mathrm {Te}$, and found the ratio $\tau ({}^{130}\mathrm {Te})/\tau ({}^{128}\mathrm {Te}$) = ($3.52$ $\pm0.11$) $\times 10^{-4}$ in agreement with relatively stable theoretical predictions. The bound is based on the requirement that Majoron-emitting decay cannot be larger than the observed double-beta rate of ${}^{128}\mathrm {Te}$ of ($77$ $\pm4$) $\times 10^{23}$ year. We calculated 90$\%$ CL limit as ($7.7 - 1.28{\times }0.4=7.2){\times }10^{24}$.
2  ARNOLD 2019 uses the NEMO-3 tracking calorimeter to determine limits for the Majoron emitting double beta decay, with spectral index n = 3. The limit corresponds to the range of the ${{\mathit g}_{{ee}}}$ coupling of $0.013 - 0.035$; dependimg on the nuclear matrix elements used.
3  ARNOLD 2018 use the NEMO-3 tracking detector. The limit corresponds to $\langle {{\mathit g}_{{ee}}}\rangle$ $<$ $3.2 - 8.0 \times 10^{-5}$; the range corresponds to different nuclear matrix element calculations.
4  AGOSTINI 2015A analyze a 20.3 kg yr of data set of the GERDA calorimeter to determine $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $3.4 - 8.7$ on the Majoron-neutrino coupling constant. The range reflects the spread of the nuclear matrix elements.
5  ARNOLD 2015 use the NEMO-3 tracking calorimeter with 3.43 kg yr exposure to determine the limit on Majoron emission. The limit corresponds to $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $1.6 - 3.0$. The spread reflects different nuclear matrix elements. Supersedes ARNOLD 2006 .
6  ALBERT 2014A utilize 100 kg yr of exposure of the EXO-200 tracking calorimeter to place a limit on the $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $0.8 - 1.7$ on the Majoron-neutrino coupling constant. The range reflects the spread of the nuclear matrix elements.
7  GANDO 2012 use the KamLAND-Zen detector to obtain the limit on the 0${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission. It implies that the coupling constant $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }<$ $0.8 - 1.6$ depending on the nuclear matrix elements used.
8  ARNOLD 2011 use the NEMO-3 detector to obtain the reported limit on Majoron emission. It implies that the coupling constant ${{\mathit g}}_{ {{\mathit \nu}} {{\mathit \chi}} }$ $<$ $0.6 - 1.6$ depending on the nuclear matrix element used. Supercedes ARNABOLDI 2003 .
9  ARGYRIADES 2010 use the NEMO-3 tracking detector and ${}^{96}\mathrm {Zr}$ to derive the reported limit. No limit for the Majoron electron coupling is given.
10  ARGYRIADES 2009 use ${}^{150}\mathrm {Nd}$ data taken with the NEMO-3 tracking detector. The reported limit corresponds to $\langle$ $\mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <$ $1.7 - 3.0$ using a range of nuclear matrix elements that include the effect of nuclear deformation.
11  ARNOLD 2006 use ${}^{100}\mathrm {Mo}$ data taken with the NEMO-3 tracking detector. The reported limit corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.4 - 1.8){\times }10^{-4}$ using a range of matrix element calculations. Superseded by ARNOLD 2015 .
12  NEMO-3 tracking calorimeter is used in ARNOLD 2006 . Reported half-life limit for ${}^{82}\mathrm {Se}$ corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.66 - 1.9){\times }10^{-4}$ using a range of matrix element calculations. Supersedes ARNOLD 2004 .
13  ARNOLD 2004 use the NEMO-3 tracking detector. The limit corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.5 - 0.9)10^{-4}$ using the matrix elements of SIMKOVIC 1999 , STOICA 2001 and CIVITARESE 2003 . Superseded by ARNOLD 2006 .
14  ARNOLD 2004 use the NEMO-3 tracking detector. The limit corresponds to $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ ($0.7 - 1.6)10^{-4}$ using the matrix elements of SIMKOVIC 1999 , STOICA 2001 and CIVITARESE 2003 .
15  Supersedes ALESSANDRELLO 2000 . Array of TeO$_{2}$ crystals in high resolution cryogenic calorimeter. Some enriched in ${}^{130}\mathrm {Te}$. Derive $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ $<$ $17 - 33 \times 10^{-5}$ depending on matrix element.
16  Supersedes ALESSANDRELLO 2000 . Cryogenic calorimeter search.
17  Limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission of ${}^{116}\mathrm {Cd}$ using enriched CdWO$_{4}$ scintillators. $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <4.6 - 8.1 \times 10^{-5}$ depending on the matrix element. Supersedes DANEVICH 2000 .
18  Limit for the 0${{\mathit \nu}}2{{\mathit \chi}}$ decay of ${}^{116}\mathrm {Cd}$. Supersedes DANEVICH 2000 .
19  BERNABEI 2002D obtain limit for 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission of ${}^{136}\mathrm {Xe}$ using liquid Xe scintillation detector. They derive $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <2.0 - 3.0 \times 10^{-5}$ with several nuclear matrix elements.
20  Replaces TANAKA 1993 . FUSHIMI 2002 derive half-life limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ $~$decay by means of tracking calorimeter ELEGANT$~$V. Considering various matrix element calculations, a range of limits for the Majoron-neutrino coupling is given: $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <(6.3 - 360){\times }10^{-5}$.
21  ASHITKOV 2001 result for 0 ${{\mathit \nu}}{{\mathit \chi}}$ of ${}^{100}\mathrm {Mo}$ is less stringent than ARNOLD 2000 .
22  DANEVICH 2001 obtain limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission of ${}^{160}\mathrm {Gd}$ using Gd$_{2}$SiO$_{5}$:Ce crystal scintillators.
23  DANEVICH 2001 obtain limit for the 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with 2 Majoron emission of ${}^{160}\mathrm {Gd}$.
24  ARNOLD 2000 reports limit for the 0 ${{\mathit \nu}}{{\mathit \chi}}$ decay with Majoron emission derived from tracking calorimeter NEMO$~$2. Using ${}^{82}\mathrm {Se}$ source: $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <1.6 \times 10^{-4}$. Matrix element from GUENTHER 1996 .
25  Using ${}^{96}\mathrm {Zr}$ source: $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle <2.6 \times 10^{-4}$. Matrix element from ARNOLD 1999 .
26  ARNOLD 2000 reports limit for the 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with two Majoron emission derived from tracking calorimeter NEMO$~$2.
27  ARNOLD 1998 determine the limit for 0${{\mathit \nu}_{{\chi}}}$ decay with Majoron emission of ${}^{82}\mathrm {Se}$ using the NEMO-2 tracking detector. They derive $\langle \mathit g_{{{\mathit \nu}_{{\chi}}}}\rangle$ $<2.3 - 4.3 \times 10^{-4}$ with several nuclear matrix elements.
28  LUESCHER 1998 report a limit for the 0${{\mathit \nu}}$ decay with Majoron emission of ${}^{136}\mathrm {Xe}$ using ${}^{}\mathrm {Xe}$ TPC. This result is more stringent than BARABASH 1989 . Using the matrix elements of ENGEL 1988 , they obtain a limit on $\langle \mathit g_{ {{\mathit \nu}} {{\mathit \chi}} }\rangle$ of $2.0 \times 10^{-4}$.
29  See Table$~$1 in GUENTHER 1996 for limits on the Majoron coupling in different models.
References:
 ARNOLD 2019
EPJ C79 440 Detailed studies of $^{100}$Mo two-neutrino double beta decay in NEMO-3
 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
 AGOSTINI 2015A
EPJ C75 416 Results on ${{\mathit \beta}}{{\mathit \beta}}$ Decay with Emission of Two Neutrinos or Majorons in ${}^{76}\mathrm {Ge}$ from GERDA Phase I
 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 2014A
PR D90 092004 Search for Majoron-Emitting Modes of Double-Beta Decay of ${}^{136}\mathrm {Xe}$ with EXO-200
 GANDO 2012
PR C86 021601 Limits on Majoron-Emitting Double-${{\mathit \beta}}$ Decays of ${}^{136}\mathrm {Xe}$ in the KamLAND-Zen Experiment
 ARNOLD 2011
PRL 107 062504 Measurement of the ${{\mathit \beta}}{{\mathit \beta}}$ Decay Half-Life of ${}^{130}\mathrm {Te}$ 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 C80 032501 Measurement of the Double-${{\mathit \beta}}$ Decay Half-Life of ${}^{150}\mathrm {Nd}$ and Search for Neutrinoless Decay Modes with the NEMO-3 Detector
 ARNOLD 2006
NP A765 483 Limits on Different Majoron Decay Modes of ${}^{100}\mathrm {Mo}$ and ${}^{82}\mathrm {Se}$ for Neutrinoless Double Beta Decays in the NEMO-3 Experiment
 ARNOLD 2004
JETPL 80 377 Study of 2${{\mathit \beta}}$ Decay of ${}^{100}\mathrm {Mo}$ and ${}^{82}\mathrm {Se}$ using the NEMO3 Detector
 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
 BERNABEI 2002D
PL B546 23 Investigation of $\beta \beta$ Decay Modes in ${}^{134}\mathrm {Xe}$ and ${}^{135}\mathrm {Xe}$
 FUSHIMI 2002
PL B531 190 Limits on Majoron Emitting Neutrinoless Double-beta Decay of ${}^{100}\mathrm {Mo}$
 ASHITKOV 2001
JETPL 74 529 Double beta Decay in ${}^{100}\mathrm {Mo}$
 DANEVICH 2001
NP A694 375 Quest for Double $\beta$ Decay of ${}^{160}\mathrm {Gd}$ and ${}^{}\mathrm {Ce}$ Isotopes
 ARNOLD 2000
NP A678 341 Limits on Different Majoron Decay Modes of ${}^{100}\mathrm {Mo}$, ${}^{116}\mathrm {Cd}$, ${}^{82}\mathrm {Se}$ and ${}^{96}\mathrm {Zr}$ for Neutrinoless Double $\beta$ Decay in the NEMO-2 Experiment
 ARNOLD 1998
NP A636 209 Double beta Decay of ${}^{82}\mathrm {Se}$
 LUESCHER 1998
PL B434 407 Search for $\beta$ $\beta$ Decay in ${}^{136}\mathrm {Xe}$: New Results from the Gotthard Experiment
 GUENTHER 1996
PR D54 3641 Bounds on New Majoron Models from the Heidelberg-Moscow Experiment
 BECK 1993
PRL 70 2853 Investigation of the Majoron Accompanied Double $\beta$ Decay Mode of ${}^{76}\mathrm {Ge}$
 BERNATOWICZ 1992
PRL 69 2341 Neutrino Mass Limits from a Precise Determination of $\beta$ $\beta$ Decay Rates of ${}^{128}\mathrm {Te}$ and ${}^{130}\mathrm {Te}$