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Majoron Searches in Neutrinoless Double $\beta $ Decay

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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

• • We do not use the following data for averages, fits, limits, etc. • •

$ \text{> 16 - 24} $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}1{{\mathit \chi}}$

CUPID-Mo

$ >120 $

$90$

${}^{82}\mathrm {Se}$

0${{\mathit \nu}}1{{\mathit \chi}}$

CUPID-0

$ >640 $

$90$

${}^{76}\mathrm {Ge}$

0${{\mathit \nu}}1{{\mathit \chi}}$

GERDA

$ >4300 $

$90$

${}^{136}\mathrm {Xe}$

0${{\mathit \nu}}1{{\mathit \chi}}$

EXO-200

$ >4.4 $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >37 $

$90$

${}^{82}\mathrm {Se}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >420 $

$90$

${}^{76}\mathrm {Ge}$

0${{\mathit \nu}}1{{\mathit \chi}}$

GERDA

$ >400 $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >1200 $

$90$

${}^{136}\mathrm {Xe}$

0${{\mathit \nu}}1{{\mathit \chi}}$

EXO-200

$ >2600 $

$90$

${}^{136}\mathrm {Xe}$

0${{\mathit \nu}}1{{\mathit \chi}}$

KamLAND-Zen

$ >16 $

$90$

${}^{130}\mathrm {Te}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >1.9 $

$90$

${}^{96}\mathrm {Zr}$

2${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >1.52 $

$90$

${}^{150}\mathrm {Nd}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >27 $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >15 $

$90$

${}^{82}\mathrm {Se}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >14 $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >12 $

$90$

${}^{82}\mathrm {Se}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO-3

$ >2.2 $

$90$

${}^{130}\mathrm {Te}$

0${{\mathit \nu}}1{{\mathit \chi}}$

Cryog. det.

$ >0.9 $

$90$

${}^{130}\mathrm {Te}$

0${{\mathit \nu}}2{{\mathit \chi}}$

Cryog. det.

$ >8 $

$90$

${}^{116}\mathrm {Cd}$

0${{\mathit \nu}}1{{\mathit \chi}}$

CdWO$_{4}$ scint.

$ >0.8 $

$90$

${}^{116}\mathrm {Cd}$

0${{\mathit \nu}}2{{\mathit \chi}}$

CdWO$_{4}$ scint.

$ >500 $

$90$

${}^{136}\mathrm {Xe}$

0${{\mathit \nu}}1{{\mathit \chi}}$

Liquid Xe Scint.

$ >5.8 $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}1{{\mathit \chi}}$

ELEGANT V

$ >0.32 $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}1{{\mathit \chi}}$

Liq. Ar ioniz.

$ >0.0035 $

$90$

${}^{160}\mathrm {Gd}$

0${{\mathit \nu}}1{{\mathit \chi}}$

${}^{160}\mathrm {Gd}_{2}$SiO$_{5}$:Ce

$ >0.013 $

$90$

${}^{160}\mathrm {Gd}$

0${{\mathit \nu}}2{{\mathit \chi}}$

${}^{160}\mathrm {Gd}_{2}$SiO$_{5}$:Ce

$ >2.3 $

$90$

${}^{82}\mathrm {Se}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO 2

$ >0.31 $

$90$

${}^{96}\mathrm {Zr}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO 2

$ >0.63 $

$90$

${}^{82}\mathrm {Se}$

0${{\mathit \nu}}2{{\mathit \chi}}$

NEMO 2

$ >0.063 $

$90$

${}^{96}\mathrm {Zr}$

0${{\mathit \nu}}2{{\mathit \chi}}$

NEMO 2

$ >0.16 $

$90$

${}^{100}\mathrm {Mo}$

0${{\mathit \nu}}2{{\mathit \chi}}$

NEMO 2

$ >2.4 $

$90$

${}^{82}\mathrm {Se}$

0${{\mathit \nu}}1{{\mathit \chi}}$

NEMO 2

$ >7.2 $

$90$

${}^{136}\mathrm {Xe}$

0${{\mathit \nu}}2{{\mathit \chi}}$

TPC

$ >7.91 $

$90$

${}^{76}\mathrm {Ge}$

SPEC

$ >17 $

$90$

${}^{76}\mathrm {Ge}$

CNTR

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

AUGIER 2024 make use of 1.47 kg$\cdot{}$yr of ${}^{100}\mathrm {Mo}$ exposure of the CUPID-Mo scintillating cryogenic calorimeter, operated at the Laboratoire Souterrain de Modane to place a range of limits on the single Majoron mode of the 0${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{100}\mathrm {Mo}$. The range is due to the use of two different analysis strategies. Various limits on modes involving the emission of multiple Majorons are given too. The derived range of constraints on the Majoron-neutrino coupling constant is $\mathit g_{{{\mathit \nu}} {{\mathit \chi}}}$ $<$ $4.0 - 8.5 \times 10^{-5}$, reflecting the variability of the used nuclear matrix elements and of the two data analysis strategies.

³

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.

⁴	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.

⁵

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.

⁶	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.

⁷	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.

⁸	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.

⁹	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.

¹⁰	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.

¹¹	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.

¹²	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.

¹³	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.

¹⁴

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.

¹⁵	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.

¹⁶	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.

¹⁷	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.

¹⁸	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.

¹⁹	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.

²⁰	Supersedes ALESSANDRELLO 2000. Cryogenic calorimeter search.

²¹	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.

²²	Limit for the 0${{\mathit \nu}}2{{\mathit \chi}}$ decay of ${}^{116}\mathrm {Cd}$. Supersedes DANEVICH 2000.

²³	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.

²⁴

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: $\langle \mathit g_{{{\mathit \nu}} {{\mathit \chi}}}\rangle <(6.3 - 360){\times }10^{-5}$.

²⁵	ASHITKOV 2001 result for 0${{\mathit \nu}}{{\mathit \chi}}$ of ${}^{100}\mathrm {Mo}$ is less stringent than ARNOLD 2000.

²⁶	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.

²⁷	DANEVICH 2001 obtain limit for the 0${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with 2 Majoron emission of ${}^{160}\mathrm {Gd}$.

²⁸	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.

²⁹	Using ${}^{96}\mathrm {Zr}$ source: $\langle \mathit g_{{{\mathit \nu}} {{\mathit \chi}}}\rangle <2.6 \times 10^{-4}$. Matrix element from ARNOLD 1999.

³⁰	ARNOLD 2000 reports limit for the 0 ${{\mathit \nu}}$2 ${{\mathit \chi}}$ decay with two Majoron emission derived from tracking calorimeter NEMO$~$2.

³¹	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.

³²

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 $2.0 \times 10^{-4}$.

³³	See Table$~$1 in GUENTHER 1996 for limits on the Majoron coupling in different models.

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