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Majoron Searches in Neutrinoless Double $\beta $ Decay

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. • •

$ >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

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.

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