Majoron Searches in Neutrinoless Double $\beta $ Decay

INSPIRE   PDGID:
S029MT
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} $ $\bf{90}$ $\bf{{}^{128}\mathrm {Te}}$ CNTR 1
BERNATOWICZ
1992
• • We do not use the following data for averages, fits, limits, etc. • •
$ >120 $ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ CUPID-0 2
AZZOLINI
2023
$ >640 $ $90$ ${}^{76}\mathrm {Ge}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ GERDA 3
AGOSTINI
2022
$ >4300 $ $90$ ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ EXO-200 4
AL-KHARUSI
2021
$ >4.4 $ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 5
ARNOLD
2019
$ >37 $ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 6
ARNOLD
2018
$ >420 $ $90$ ${}^{76}\mathrm {Ge}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ GERDA 7
AGOSTINI
2015A
$ >400 $ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 8
ARNOLD
2015
$ >1200 $ $90$ ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ EXO-200 9
ALBERT
2014A
$ >2600 $ $90$ ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ KamLAND-Zen 10
GANDO
2012
$ >16 $ $90$ ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 11
ARNOLD
2011
$ >1.9 $ $90$ ${}^{96}\mathrm {Zr}$ 2${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 12
ARGYRIADES
2010
$ >1.52 $ $90$ ${}^{150}\mathrm {Nd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 13
ARGYRIADES
2009
$ >27 $ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 14
ARNOLD
2006
$ >15 $ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 15
ARNOLD
2006
$ >14 $ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 16
ARNOLD
2004
$ >12 $ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO-3 17
ARNOLD
2004
$ >2.2 $ $90$ ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ Cryog. det. 18
ARNABOLDI
2003
$ >0.9 $ $90$ ${}^{130}\mathrm {Te}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ Cryog. det. 19
ARNABOLDI
2003
$ >8 $ $90$ ${}^{116}\mathrm {Cd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ CdWO$_{4}$ scint. 20
DANEVICH
2003
$ >0.8 $ $90$ ${}^{116}\mathrm {Cd}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ CdWO$_{4}$ scint. 21
DANEVICH
2003
$ >500 $ $90$ ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ Liquid Xe Scint. 22
BERNABEI
2002D
$ >5.8 $ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ ELEGANT V 23
FUSHIMI
2002
$ >0.32 $ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ Liq. Ar ioniz. 24
ASHITKOV
2001
$ >0.0035 $ $90$ ${}^{160}\mathrm {Gd}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ ${}^{160}\mathrm {Gd}_{2}$SiO$_{5}$:Ce 25
DANEVICH
2001
$ >0.013 $ $90$ ${}^{160}\mathrm {Gd}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ ${}^{160}\mathrm {Gd}_{2}$SiO$_{5}$:Ce 26
DANEVICH
2001
$ >2.3 $ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO 2 27
ARNOLD
2000
$ >0.31 $ $90$ ${}^{96}\mathrm {Zr}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO 2 28
ARNOLD
2000
$ >0.63 $ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ NEMO 2 29
ARNOLD
2000
$ >0.063 $ $90$ ${}^{96}\mathrm {Zr}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ NEMO 2 29
ARNOLD
2000
$ >0.16 $ $90$ ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ NEMO 2 29
ARNOLD
2000
$ >2.4 $ $90$ ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}1{{\mathit \chi}}$ NEMO 2 30
ARNOLD
1998
$ >7.2 $ $90$ ${}^{136}\mathrm {Xe}$ 0${{\mathit \nu}}2{{\mathit \chi}}$ TPC 31
LUESCHER
1998
$ >7.91 $ $90$ ${}^{76}\mathrm {Ge}$ SPEC 32
GUENTHER
1996
$ >17 $ $90$ ${}^{76}\mathrm {Ge}$ CNTR
BECK
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  AZZOLINI 2023 use 9.95 kg$\cdot{}$yr of data, collected by the CUPID-0 experiment, to place a limit on the single Majoron mode of the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{82}\mathrm {Se}$. Various limits on modes involving the emission of multiple Majorons are given too. The resulting constraint on the Majoron-neutrino coupling constant is $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}$ $<$ $1.8 - 4.4 \times 10^{-5}$. The range is due to the variability of the used nuclear matrix elements.
3  AGOSTINI 2022 use 32.8 kg$\cdot{}$yr of GERDA phase 2 data to derive a limit of $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}$ $<$ $1.8 - 4.4 \times 10^{-5}$ on the neutrino-Majoron coupling. The range reflects the author's evaluation of the spread of nuclear matrix elements.
4  AL-KHARUSI 2021 utilize the complete dataset of the EXO-200 experiment, corresponding to an exposure of 234 kg yr, to place a limit on the one Majoron mode of the neutrinoless double beta decay of ${}^{136}\mathrm {Xe}$. Several limits are reported, the one given here corresponds to a spectral index of 1, resulting in a limit of $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}<$ $0.4 - 0.9 \times 10^{-5}$ on the Majoron-neutrino coupling constant. The range reflects the spread of the nuclear matrix elements.
5  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.
6  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.
7  AGOSTINI 2015A analyze a 20.3 kg yr of data set of the GERDA calorimeter to determine $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}<$ $3.4 - 8.7 \times 10^{-5}$ on the Majoron-neutrino coupling constant. The range reflects the spread of the nuclear matrix elements.
8  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 $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}<$ $1.6 - 3.0 \times 10^{-4}$. The spread reflects different nuclear matrix elements. Supersedes ARNOLD 2006.
9  ALBERT 2014A utilize 100 kg yr of exposure of the EXO-200 tracking calorimeter to place a limit on the $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}<$ $0.8 - 1.7 \times 10^{-5}$ on the Majoron-neutrino coupling constant. The range reflects the spread of the nuclear matrix elements.
10  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 $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}<$ $0.8 - 1.6 \times 10^{-5}$ depending on the nuclear matrix elements used.
11  ARNOLD 2011 use the NEMO-3 detector to obtain the reported limit on Majoron emission. It implies that the coupling constant ${{\mathit g}}_{{{\mathit \nu}} {{\mathit \chi}}}$ $<$ $0.6 - 1.6 \times 10^{-4}$ depending on the nuclear matrix element used. Supercedes ARNABOLDI 2003.
12  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.
13  ARGYRIADES 2009 use ${}^{150}\mathrm {Nd}$ data taken with the NEMO-3 tracking detector. The reported limit corresponds to $\langle $ $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}\rangle <$ $1.7 - 3.0 \times 10^{-4}$ using a range of nuclear matrix elements that include the effect of nuclear deformation.
14  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.
15  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.
16  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.
17  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.
18  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.
19  Supersedes ALESSANDRELLO 2000. Cryogenic calorimeter search.
20  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.
21  Limit for the 0${{\mathit \nu}}2{{\mathit \chi}}$ decay of ${}^{116}\mathrm {Cd}$. Supersedes DANEVICH 2000.
22  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.
23  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: $\langle \mathit g_{{{\mathit \nu}} {{\mathit \chi}}}\rangle <(6.3 - 360){\times }10^{-5}$.
24  ASHITKOV 2001 result for 0${{\mathit \nu}}{{\mathit \chi}}$ of ${}^{100}\mathrm {Mo}$ is less stringent than ARNOLD 2000.
25  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.
26  DANEVICH 2001 obtain limit for the 0${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with 2 Majoron emission of ${}^{160}\mathrm {Gd}$.
27  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.
28  Using ${}^{96}\mathrm {Zr}$ source: $\langle \mathit g_{{{\mathit \nu}} {{\mathit \chi}}}\rangle <2.6 \times 10^{-4}$. Matrix element from ARNOLD 1999.
29  ARNOLD 2000 reports limit for the 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with two Majoron emission derived from tracking calorimeter NEMO$~$2.
30  ARNOLD 1998 determine the limit for 0${{\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.
31  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 $2.0 \times 10^{-4}$.
32  See Table$~$1 in GUENTHER 1996 for limits on the Majoron coupling in different models.
References