#### Searches for Goldstone Bosons (${{\mathit X}^{0}}$ )

(Including Horizontal Bosons and Majorons.) Limits are for branching ratios.
VALUE CL% DOCUMENT ID TECN  COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$<4.3 \times 10^{-6}$ 90 1
 2021 A
PIEN ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \nu}}{{\mathit X}^{0}}$ , Majoron
$<5.2 \times 10^{-8}$ 90 2
 2021 A
PIEN ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit X}^{0}}$ , Majoron
$<9 \times 10^{-6}$ 90 3
 2020
PIEN ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ , Familon
$<7 \times 10^{-12}$ 90 4
 2020
MEG ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ ), Familon
$<9 \times 10^{-6}$ 90 5
 2015
TWST ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ , Familon
6
 2013
COSM Majoron dark matter decay
7
 2007
RVUE Meson, ${{\mathit \ell}}$ decays to Majoron
8
 1998
THEO ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit X}^{0}}{{\mathit X}^{0}}$ , ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit X}^{0}}{{\mathit X}^{0}}{{\mathit X}^{0}}$ , Majoron
9
 1991
Electron quasi-magnetic interaction
$<0.033$ 95 10
 1990 E
ARG ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit X}^{0}}$ . Familon
$<0.018$ 95 10
 1990 E
ARG ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit e}}{{\mathit X}^{0}}$ . Familon
$<6.4 \times 10^{-9}$ 90 11
 1990
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ . Familon
$<1.4 \times 10^{-5}$ 90 12
 1988
CNTR ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ . Familon
$<1.1 \times 10^{-9}$ 90 13
 1988
CBOX ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \gamma}}{{\mathit X}^{0}}$ . Familon
14
 1988
ASTR Sun, Majoron
15
 1988
ASTR Majoron, SN 1987A
$<5 \times 10^{-6}$ 90 16
 1988
CNTR ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit X}^{0}}$ , Majoron
$<1.3 \times 10^{-9}$ 90 17
 1987
CNTR ${{\mathit \mu}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \gamma}}{{\mathit X}^{0}}$ . Familon
$<3 \times 10^{-4}$ 90 18
 1986 B
RVUE ${{\mathit \mu}}$ $\rightarrow$ ${{\mathit e}}{{\mathit X}^{0}}$ . Familon
$<1 \times 10^{-10}$ 90 19
 1986
SPEC ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ . Familon
$<2.6 \times 10^{-6}$ 90 20
 1986
SPEC ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ . Familon
21
 1985
MRK3 ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit X}^{0}}$ . Familon
22
 1983
COSM ${{\mathit \nu}}$ (hvy) $\rightarrow$ ${{\mathit \nu}}$ (light) ${{\mathit X}^{0}}$
 1 AGUILAR-AREVALO 2021A quoted limit applies to ${\mathit m}_{{{\mathit X}^{0}}}$ = 33.9 MeV. Limits between $4.3 \times 10^{-6}$ and $7.5 \times 10^{-5}$ are obtained for 0 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 33.9 MeV. The lifetime of ${{\mathit X}^{0}}$ is assumed to be long enough. See their Fig. 6 for mass-dependent limits.
 2 AGUILAR-AREVALO 2021A quoted limit applies to ${\mathit m}_{{{\mathit X}^{0}}}$ = 85 MeV. Limits between $5.2 \times 10^{-8}$ and $1.4 \times 10^{-6}$ are obtained for 0 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 120 MeV, which improve the limits of PICCIOTTO 1988 by an order of magnitude. The lifetime of ${{\mathit X}^{0}}$ is assumed to be long enough. See their Fig. 4 for mass-dependent limits.
 3 AGUILAR-AREVALO 2020 obtained limits of order $10^{-5}$ for ${\mathit m}_{{{\mathit X}^{0}}}$ = $47.8 - 95.1$ MeV. The quoted limit applies to ${\mathit m}_{{{\mathit X}^{0}}}$ = 75 MeV. See their Fig. 1 for mass-dependent limits.
 4 BALDINI 2020 obtained limits for ${\mathit m}_{{{\mathit X}^{0}}}$ = $20 - 45$ MeV and $\tau _{{{\mathit X}^{0}} }$ $<$ 40 ps, and supersedes BOLTON 1988 for ${\mathit m}_{{{\mathit X}^{0}}}$ = $20 - 40$ MeV. See their Fig. 17 for mass-dependent limits.
 5 BAYES 2015 limits are the average over ${\mathit m}_{{{\mathit X}^{0}}}$ = $13 - 80$ MeV for the isotropic decay distribution of positrons. See their Fig. 4 and Table II for the mass-dependent limits as well as the dependence on the decay anisotropy. In particular, they find a limit $<$ $58 \times 10^{-6}$ at 90$\%$ CL for massless familons and for the same asymmetry as normal muon decay, a case not covered by JODIDIO 1986 .
 6 LATTANZI 2013 use WMAP 9 year data as well as X-ray and ${{\mathit \gamma}}$ -ray observations to derive limits on decaying majoron dark matter. A limit on the decay width $\Gamma\mathrm {( {{\mathit X}^{0}} \rightarrow {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$ $<$ $6.4 \times 10^{-19}$ s${}^{-1}$ at 95$\%$ CL is found if majorons make up all of the dark matter.
 7 LESSA 2007 consider decays of the form Meson $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}$ Majoron and ${{\mathit \ell}}$ $\rightarrow$ ${{\mathit \ell}^{\,'}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ Majoron and use existing data to derive limits on the neutrino-Majoron Yukawa couplings $\mathit g_{ {{\mathit \alpha}} {{\mathit \beta}} }$ (${{\mathit \alpha}}$ , ${{\mathit \beta}}$ ${{\mathit \mu}}$ ,${{\mathit \tau}}$ ). Their best limits are $\vert \mathit g_{ {{\mathit e}} {{\mathit \alpha}} }$ $\vert ^2<$ $5.5 \times 10^{-6}$, $\vert \mathit g_{ {{\mathit \mu}} {{\mathit \alpha}} }$ $\vert ^2<$ $4.5 \times 10^{-5}$, $\vert \mathit g_{ {{\mathit \tau}} {{\mathit \alpha}} }$ $\vert ^2<$ $0.055$ at CL = 90$\%$.
 8 DIAZ 1998 studied models of spontaneously broken lepton number with both singlet and triplet Higgses. They obtain limits on the parameter space from invisible decay ${{\mathit Z}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit X}^{0}}{{\mathit X}^{0}}{{\mathit X}^{0}}{{\mathit X}^{0}}{{\mathit X}^{0}}$ and ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit H}^{0}}$ with ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit X}^{0}}{{\mathit X}^{0}}$ .
 9 BOBRAKOV 1991 searched for anomalous magnetic interactions between polarized electrons expected from the exchange of a massless pseudoscalar boson (arion). A limit $\mathit x{}^{2}_{{{\mathit e}} }$ $<$ $2 \times 10^{-4}$ (95$\%$CL) is found for the effective anomalous magneton parametrized as $\mathit x_{{{\mathit e}} }(\mathit G_{\mathit F}/8{{\mathit \pi}}$ $\sqrt {2 }){}^{1/2}$.
 10 ALBRECHT 1990E limits are for B( ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit X}^{0}}$ )/B( ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ ). Valid for ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 100 MeV. The limits rise to $7.1\%$ (for ${{\mathit \mu}}$ ), $5.0\%$ (for ${{\mathit e}}$ ) for ${\mathit m}_{{{\mathit X}^{0}}}$ = 500 MeV.
 11 ATIYA 1990 limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ = 0. The limit B $<$ $1 \times 10^{-8}$ holds for ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 95 MeV. For the reduction of the limit due to finite lifetime of ${{\mathit X}^{0}}$ , see their Fig.$~$3.
 12 BALKE 1988 limits are for B( ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ ). Valid for ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 80 MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}$ $>$ $10^{-8}$ sec.
 13 BOLTON 1988 limit corresponds to $\mathit F$ $>$ $3.1 \times 10^{9}$ GeV, which does not depend on the chirality property of the coupling.
 14 CHANDA 1988 find ${{\mathit v}_{{T}}}$ $<$ 10 MeV for the weak-triplet Higgs vacuum expectation value in Gelmini-Roncadelli model, and ${{\mathit v}_{{S}}}$ $>$ $5.8 \times 10^{6}$ GeV in the singlet Majoron model.
 15 CHOI 1988 used the observed neutrino flux from the supernova SN$~$1987A to exclude the neutrino Majoron Yukawa coupling $\mathit h$ in the range $2 \times 10^{-5}$ $<$ $\mathit h$ $<$ $3 \times 10^{-4}$ for the interaction $\mathit L_{{\mathrm {int}}}$ = ${1\over 2}\mathit ih{{\overline{\mathit \psi}}}{}^{\mathit c}_{\nu }\gamma _{5}{{\mathit \psi}_{{\nu}}}$ $\phi _{{\mathrm {X}}}$. For several families of neutrinos, the limit applies for ($\Sigma \mathit h{}^{4}_{\mathit i}){}^{1/4}$.
 16 PICCIOTTO 1988 limit applies when ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 55 MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}$ $>$ 2ns, and it decreases to $4 \times 10^{-7}$ at ${\mathit m}_{{{\mathit X}^{0}}}$ = 125 MeV, beyond which no limit is obtained.
 17 GOLDMAN 1987 limit corresponds to $\mathit F$ $>$ $2.9 \times 10^{9}$ GeV for the family symmetry breaking scale from the Lagrangian $\mathit L_{{\mathrm {int}}}$ = (1/$\mathit F){{\overline{\mathit \psi}}_{{\mu}}}{{\mathit \gamma}}{}^{{{\mathit \mu}} }$ ($\mathit a+\mathit b{{\mathit \gamma}_{{5}}}$ ) ${{\mathit \psi}_{{e}}}$ $\partial{}_{{{\mathit \mu}} }{{\mathit \phi}}$ $_{{{\mathit X}^{0}} }$ with $\mathit a{}^{2}+\mathit b{}^{2}$ = 1. This is not as sensitive as the limit $\mathit F$ $>9.9 \times 10^{9}$ GeV derived from the search for ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ by JODIDIO 1986 , but does not depend on the chirality property of the coupling.
 18 Limits are for $\Gamma\mathrm {( {{\mathit \mu}} \rightarrow {{\mathit e}} {{\mathit X}^{0}} )}/\Gamma\mathrm {( {{\mathit \mu}} \rightarrow {{\mathit e}} {{\mathit \nu}} {{\overline{\mathit \nu}}} )}$. Valid when ${\mathit m}_{{{\mathit X}^{0}}}$ = 0$-$93.4, 98.1$-$103.5 MeV.
 19 EICHLER 1986 looked for ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ followed by ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ . Limits on the branching fraction depend on the mass and and lifetime of ${{\mathit X}^{0}}$ . The quoted limits are valid when ${\mathit \tau}_{{{\mathit X}^{0}}}{ {}\lesssim{} }3. \times 10^{-10}~$s if the decays are kinematically allowed.
 20 JODIDIO 1986 corresponds to $\mathit F$ $>9.9 \times 10^{9}$ GeV for the family symmetry breaking scale with the parity-conserving effective Lagrangian $\mathit L_{{\mathrm {int}}}$ = (1/$\mathit F$) ${{\overline{\mathit \psi}}_{{\mu}}}{{\mathit \gamma}}{}^{{{\mathit \mu}} }{{\mathit \psi}_{{e}}}$ $\partial{}{}^{{{\mathit \mu}} }\phi _{{{\mathit X}^{0}} }$.
 21 BALTRUSAITIS 1985 search for light Goldstone boson(${{\mathit X}^{0}}$ ) of broken U(1). CL = 95$\%$ limits are B( ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit X}^{0}}$ )$/$B( ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}}{{\mathit \nu}}$ ) $<$0.125 and B( ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ )$/$B( ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit \nu}}$ ) $<$0.04. Inferred limit for the symmetry breaking scale is $\mathit m$ $>$3000 TeV.
 22 The primordial heavy neutrino must decay into ${{\mathit \nu}}$ and familon, $\mathit f_{\mathit A}$, early so that the red-shifted decay products are below critical density, see their table. In addition, ${{\mathit K}}$ $\rightarrow$ ${{\mathit \pi}}$ $\mathit f_{\mathit A}$ and ${{\mathit \mu}}$ $\rightarrow$ ${{\mathit e}}$ $\mathit f_{\mathit A}$ are unseen. Combining these excludes ${\mathit m}_{\mathrm {heavy {{\mathit \nu}} }}$ between $5 \times 10^{-5}$ and $5 \times 10^{-4}$ MeV (${{\mathit \mu}}$ decay) and ${\mathit m}_{\mathrm {heavy {{\mathit \nu}} }}$ between $5 \times 10^{-5}$ and 0.1 MeV (${{\mathit K}}$ -decay).
References:
 AGUILAR-AREVALO 2021A
PR D103 052006 Search for three body pion decays ${\pi}^+{\to}l^+{\nu}X$
 AGUILAR-AREVALO 2020
PR D101 052014 Improved search for two body muon decay ${\mu}^+{\rightarrow}e^+X_H$
 BALDINI 2020
EPJ C80 858 Search for lepton flavour violating muon decay mediated by a new light particle in the MEG experiment
 BAYES 2015
PR D91 052020 Search for Two Body Muon Decay Signals
 LATTANZI 2013
PR D88 063528 Updated CMB, X- and Gamma-Ray Constraints on Majoron Dark Matter
 LESSA 2007
PR D75 094001 Revising Limits on Neutrino-Majoron Couplings
 DIAZ 1998
NP B527 44 Seesaw Majoron Model of Neutrino Mass and Novel Signals in Higgs Boson Production at LEP
 BOBRAKOV 1991
JETPL 53 294 An Experimental Limit on the Existence of the Electron Quasimagnetic (Arion) Interaction
 ALBRECHT 1990E
PL B246 278 Determination of the Michel Parameter in ${{\mathit \tau}}$ Decay
 ATIYA 1990
PRL 64 21 Search for the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$
 BALKE 1988
PR D37 587 Precise Measurement of the Asymmetry Parameter $\delta$ in Muon Decay
 BOLTON 1988
PR D38 2077 Search for Rare Muon Decays with the Crystal Box Detector
 Also
PRL 56 2461 Search for the Decay ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \gamma}}$
 Also
PRL 57 3241 Search for the Rare Decay ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \gamma}}{{\mathit \gamma}}$
 CHANDA 1988
PR D37 2714 Astrophysical Constraints on Axion and Majoron Couplings
 CHOI 1988
PR D37 3225 Constraints on the Majoron Interactions from the Supernova SN1987a
 PICCIOTTO 1988
PR D37 1131 Search for Majoron Production and Other Process Associated with ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}$ Decay
 GOLDMAN 1987
PR D36 1543 Light Boson Emission in the Decay of ${{\mathit \mu}^{+}}$
 BRYMAN 1986B
PRL 57 2787 Exotic Muon Decay ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}}$
 EICHLER 1986
PL B175 101 Limits for Short Lived Neutral Particle Emitted in ${{\mathit \mu}^{+}}$ or ${{\mathit \pi}^{+}}$ Decay
 JODIDIO 1986
PR D34 1967 Search for Right Handed Currents in Muon Decay
 Also
PR D37 237 (erratum) Search for Right Handed Currents in Muon Decay
 BALTRUSAITIS 1985
PRL 55 1842 Tau Leptonic Branching Ratios and a Search for Goldstone Decay
 DICUS 1983
PR D28 1778 Upper Bound on the Decay Constant of Familons