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

INSPIRE   PDGID:
S029GB
(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. • •
1
ADACHI
2023A
 BEL2 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit X}^{0}}$, Familon
2
ADACHI
2023A
 BEL2 ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit X}^{0}}$, Familon
3
FIORILLO
2023
ASTR Majoron, SN 1987A
4
SANDNER
2023
COSM Majoron, CMB
5
COLOMA
2022A
 BORX ${{\mathit \nu}}{{\mathit e}}$ non-standard interactions
$<4.3 \times 10^{-6}$ 90 6
AGUILAR-AREVA..
2021A
 PIEN ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \nu}}{{\mathit X}^{0}}$, Majoron
$<5.2 \times 10^{-8}$ 90 7
AGUILAR-AREVA..
2021A
 PIEN ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit X}^{0}}$, Majoron
$<9 \times 10^{-6}$ 90 8
AGUILAR-AREVA..
2020
PIEN ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$, Familon
$<7 \times 10^{-12}$ 90 9
BALDINI
2020
MEG ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$), Familon
$<9 \times 10^{-6}$ 90 10
BAYES
2015
TWST ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$, Familon
11
LATTANZI
2013
COSM Majoron dark matter decay
12
LESSA
2007
RVUE Meson, ${{\mathit \ell}}$ decays to Majoron
13
FARZAN
2003
ASTR Majoron, SN cooling
14
DIAZ
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
15
BOBRAKOV
1991
Electron quasi-magnetic interaction
$<0.033$ 95 16
ALBRECHT
1990E
 ARG ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit X}^{0}}$. Familon
$<0.018$ 95 16
ALBRECHT
1990E
 ARG ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit e}}{{\mathit X}^{0}}$. Familon
$<6.4 \times 10^{-9}$ 90 17
ATIYA
1990
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$. Familon
$<1.4 \times 10^{-5}$ 90 18
BALKE
1988
CNTR ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$. Familon
$<1.1 \times 10^{-9}$ 90 19
BOLTON
1988
CBOX ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \gamma}}{{\mathit X}^{0}}$. Familon
20
CHANDA
1988
ASTR Sun, Majoron
21
CHOI
1988
ASTR Majoron, SN 1987A
$<5 \times 10^{-6}$ 90 22
PICCIOTTO
1988
CNTR ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit X}^{0}}$, Majoron
$<1.3 \times 10^{-9}$ 90 23
GOLDMAN
1987
CNTR ${{\mathit \mu}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \gamma}}{{\mathit X}^{0}}$. Familon
$<3 \times 10^{-4}$ 90 24
BRYMAN
1986B
 RVUE ${{\mathit \mu}}$ $\rightarrow$ ${{\mathit e}}{{\mathit X}^{0}}$. Familon
$<1 \times 10^{-10}$ 90 25
EICHLER
1986
SPEC ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$. Familon
$<2.6 \times 10^{-6}$ 90 26
JODIDIO
1986
SPEC ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$. Familon
27
BALTRUSAITIS
1985
MRK3 ${{\mathit \tau}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit X}^{0}}$. Familon
28
DICUS
1983
COSM ${{\mathit \nu}}$ (hvy) $\rightarrow$ ${{\mathit \nu}}$ (light) ${{\mathit X}^{0}}$
1  ADACHI 2023A set limits in the range of $1.1 \times 10^{-3} - 9.7 \times 10^{-3}$ for 0 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 1.6 GeV on B( ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit X}^{0}}$)/B( ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{{e}}}}{{\mathit \nu}_{{{\tau}}}}$). See their Fig. 2 for mass-dependent limits.
2  ADACHI 2023A set limits in the range of $7 \times 10^{-4} - 1.22 \times 10^{-2}$ for 0 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 1.6 GeV on B( ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit X}^{0}}$)/B( ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\overline{\mathit \nu}}_{{{\mu}}}}{{\mathit \nu}_{{{\tau}}}}$). See their Fig. 2 for mass-dependent limits.
3  FIORILLO 2023 used data from Kamiokande-II and IMB on the neutrino flux from SN1987A to constrain the universal neutrino Majoron Yukawa coupling, $\mathit g$. They set an upper limit of $\mathit g$ ${\mathit m}_{{{\mathit X}^{0}}}{ {}\lesssim{} }$ $10^{-9}$ MeV for Majoron masses 100 eV ${ {}\lesssim{} }{\mathit m}_{{{\mathit X}^{0}}}{ {}\lesssim{} }$ 100 MeV, using neutrino coalescence as production of Majorons which then decay back to neutrinos. See their Fig. 1 for the mass-dependent limits.
4  SANDNER 2023 study Majoron production via neutrino inverse decay and use Planck data to constrain the neutrino Majoron Yukawa coupling to $\mathit g$ ${ {}\lesssim{} }$ $2 \times 10^{-13} - 1 \times 10^{-12}$ for Majoron masses ${\mathit m}_{{{\mathit X}^{0}}}$ = $1 - 10$ eV. See their Fig. 1 for mass-dependent limits.
5  COLOMA 2022A used the spectral data of Borexino Phase II to constrain the neutrino non-standard interaction with electrons mediated by a scalar or a pseudoscalar. Limits on the universal coupling to neutrinos and electrons between $2 \times 10^{-6}$ and $10^{-4}$ are obtained for ${\mathit m}_{{{\mathit X}^{0}}}$ ${ {}\lesssim{} }$ $30 - 40$ MeV. See their Fig. 6 for mass-dependent limits.
6  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.
7  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.
8  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.
9  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.
10  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.
11  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.
12  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 $\vert \mathit g_{{{\mathit e}} {{\mathit \alpha}}}$ $\vert ^2<$ $5.5 \times 10^{-6}$, $\vert \mathit g_{{{\mathit \mu}} {{\mathit \alpha}}}$ $\vert ^2<$ $4.5 \times 10^{-5}$, $\vert \mathit g_{{{\mathit \tau}} {{\mathit \alpha}}}$ $\vert ^2<$ $5.5 \times 10^{-2}$ at CL = 90$\%$.
13  FARZAN 2003 set limits on the neutrino Majoron Yukawa coupling, $\vert \mathit g_{{{\mathit e}} {{\mathit e}}}\vert $ $<$ $4 \times 10^{-7}$, by considering the SN cooling due to the massless Majoron emission via neutrino coalescence. They also exclude values around $10^{-5}$ for both $\mathit g_{{{\mathit e}} {{\mathit \mu}}}$ and $\mathit g_{{{\mathit \mu}} {{\mathit \mu}}}$ using the process ${{\mathit \nu}}$ ${{\mathit \nu}}$ $\rightarrow$ ${{\mathit X}^{0}}{{\mathit X}^{0}}$. See also their Figs. 3 and 4 for mass-dependent limits.
14  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 ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit X}^{0}}{{\mathit X}^{0}}$.
15  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 $\mathit x_{{{\mathit e}}}(\mathit G_{\mathit F}/8{{\mathit \pi}}\sqrt {2 }){}^{1/2}$.
16  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.
17  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.
18  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.
19  BOLTON 1988 limit corresponds to $\mathit F$ $>$ $3.1 \times 10^{9}$ GeV, which does not depend on the chirality property of the coupling.
20  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.
21  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 ($\Sigma \mathit h{}^{4}_{\mathit i}){}^{1/4}$.
22  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.
23  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.
24  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.
25  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.
26  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/$\mathit F$) ${{\overline{\mathit \psi}}_{{{\mu}}}}{{\mathit \gamma}}{}^{{{\mathit \mu}}}{{\mathit \psi}_{{{e}}}}\partial{}{}^{{{\mathit \mu}}}\phi _{{{\mathit X}^{0}}}$.
27  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.
28  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