${{\mathit A}^{0}}$ (Axion) and Other Light Boson (${{\mathit X}^{0}}$) Searches in Hadron Decays

INSPIRE   JSON  (beta) PDGID:
S029AD2
Limits are for branching ratios.
VALUE CL% DOCUMENT ID TECN  COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$<1 \times 10^{-4}$ 90 1
ABLIKIM
2024AK
 BES3 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit A}^{0}}$, ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$
2
ABLIKIM
2024G
 BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit X}^{0}}$
$<0.5 \times 10^{-6}$ 90 3
ABLIKIM
2024M
 BES3 ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$
$<2 \times 10^{-9}$ 90 4
CORTINA-GIL
2024
NA62 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit A}^{0}}$, ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$
$<2 \times 10^{-7}$ 90 5
SADOVSKY
2024
OKA ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit A}^{0}}$
$<4 \times 10^{-8}$ 95 6
ADACHI
2023K
 BEL2 ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit X}^{0}}$
$<9 \times 10^{-8}$ 95 7
ADACHI
2023K
 BEL2 ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}^{0}}{{\mathit X}^{0}}$ (${{\mathit K}^{*}{(892)}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$)
$<3.7 \times 10^{-10}$ 95 8
CORTINA-GIL
2023B
 NA62 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit A}^{0}}{{\mathit A}^{0}}$, ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$
$<4.2 \times 10^{-8}$ 90 9
LEES
2022B
 BABR ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit A}^{0}}$ (${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$)
$<7 \times 10^{-13}$ 95 10
ABRATENKO
2021
MCBN ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$)
$<1.5 \times 10^{-7}$ 90 11
CORTINA-GIL
2021
NA62 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}}{{\mathit X}^{0}}$
$<5 \times 10^{-11}$ 90 12
CORTINA-GIL
2021A
 NA62 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<9 \times 10^{-10}$ 90 13
CORTINA-GIL
2021C
 NA62 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<1.5 \times 10^{-8}$ 90 14
PARK
2021
BELL ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit X}^{0}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$, ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$)
$<2.4 \times 10^{-9}$ 90 15
AHN
2019
KOTO ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}$ ${{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}$ = 135 MeV
$<2 \times 10^{-10}$ 95 16
AAIJ
2017AQ
 LHCB ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$)
$<3.7 \times 10^{-8}$ 90 17
AHN
2017
KOTO ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}$ ${{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}$ = 135 MeV
$<6 \times 10^{-11}$ 90 18
BATLEY
2017
NA48 ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ ${{\mathit X}^{0}}({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$)
19
WON
2016
BELL ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}$ ${{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$)
$<1 \times 10^{-9}$ 95 20
AAIJ
2015AZ
 LHCB ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{*0}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$)
$<1.5 \times 10^{-6}$ 90 21
ADLARSON
2013
WASA ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$), ${\mathit m}_{{{\mathit X}^{0}}}$ = 100 MeV
$<2 \times 10^{-8}$ 90 22
BABUSCI
2013B
 KLOE ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$)
23
ARCHILLI
2012
KLOE ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit X}^{0}}$, ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$
$<2 \times 10^{-15}$ 90 24
GNINENKO
2012A
 BDMP ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$)
$<3 \times 10^{-14}$ 90 25
GNINENKO
2012B
 BDMP ${{\mathit \eta}}({{\mathit \eta}^{\,'}}$) $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$)
$<7 \times 10^{-10}$ 90 26
ADLER
2004
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<7.3 \times 10^{-11}$ 90 27
ANISIMOVSKY
2004
B949 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<4.5 \times 10^{-11}$ 90 28
ADLER
2002C
 B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<4 \times 10^{-5}$ 90 29
ADLER
2001
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit A}^{0}}$
$<4.9 \times 10^{-5}$ 90
AMMAR
2001B
 CLEO ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}({{\mathit K}^{\pm}}){{\mathit X}^{0}}$
$<5.3 \times 10^{-5}$ 90
AMMAR
2001B
 CLEO ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit X}^{0}}$
$<3.3 \times 10^{-5}$ 90 30
ALTEGOER
1998
NOMD ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}<120$ MeV
$<5.0 \times 10^{-8}$ 90 31
KITCHING
1997
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$)
$<5.2 \times 10^{-10}$ 90 32
ADLER
1996
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<2.8 \times 10^{-4}$ 90 33
AMSLER
1996B
 CBAR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}<$ 65 MeV
$<3 \times 10^{-4}$ 90 33
AMSLER
1996B
 CBAR ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}$= $50 - 200$ MeV
$<4 \times 10^{-5}$ 90 33
AMSLER
1996B
 CBAR ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}$= $50 - 925$ MeV
$<6 \times 10^{-5}$ 90 33
AMSLER
1994B
 CBAR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}=65 - 125$ MeV
$<6 \times 10^{-5}$ 90 33
AMSLER
1994B
 CBAR ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}=200 - 525$ MeV
$<7 \times 10^{-3}$ 90 34
MEIJERDREES
1994
CNTR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}$=25 MeV
$<2 \times 10^{-3}$ 90 34
MEIJERDREES
1994
CNTR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$, ${\mathit m}_{{{\mathit X}^{0}}}$=100 MeV
$<2 \times 10^{-7}$ 90 35
ATIYA
1993B
 B787 Sup. by ADLER 2004
$<3 \times 10^{-13}$ 36
NG
1993
COSM ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$
$<1.1 \times 10^{-8}$ 90 37
ALLIEGRO
1992
SPEC ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$)
$<5 \times 10^{-4}$ 90 38
ATIYA
1992
B787 ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$
$<1 \times 10^{-12}$ 95 39
BARABASH
1992
BDMP ${{\mathit \pi}^{\pm}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit \nu}}{{\mathit X}^{0}}({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \gamma}}{{\mathit \gamma}}$), ${\mathit m}_{{{\mathit X}^{0}}}$ = 8 MeV
$<1 \times 10^{-12}$ 95 40
BARABASH
1992
BDMP ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ ${{\mathit X}^{0}}({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \gamma}}{{\mathit \gamma}}$), ${\mathit m}_{{{\mathit X}^{0}}}$ = 10 MeV
$<1 \times 10^{-11}$ 95 41
BARABASH
1992
BDMP ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}$ ${{\mathit X}^{0}}({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \gamma}}{{\mathit \gamma}}$), ${\mathit m}_{{{\mathit X}^{0}}}$ = 10 MeV
$<1 \times 10^{-14}$ 95 42
BARABASH
1992
BDMP ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}$ ${{\mathit X}^{0}}({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \gamma}}{{\mathit \gamma}}$), ${\mathit m}_{{{\mathit X}^{0}}}$ = 10 MeV
$<4 \times 10^{-6}$ 90 43
MEIJERDREES
1992
SPEC ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ (${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$), ${\mathit m}_{{{\mathit X}^{0}}}$= 100 MeV
$<1 \times 10^{-7}$ 90 44
ATIYA
1990B
 B787 Sup. by KITCHING 1997
$<1.3 \times 10^{-8}$ 90 45
KORENCHENKO
1987
SPEC ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit A}^{0}}$ (${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$)
$<1 \times 10^{-9}$ 90 46
EICHLER
1986
SPEC Stopped ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit A}^{0}}$
$<2 \times 10^{-5}$ 90 47
YAMAZAKI
1984
SPEC For 160$<\mathit m<$260 MeV
$<(1.5-4){\times }\text{ 10}$$^{-6}$ 90 47
YAMAZAKI
1984
SPEC ${{\mathit K}}$ decay, ${\mathit m}_{{{\mathit X}^{0}}}{}\ll$100 MeV
48
ASANO
1982
CNTR Stopped ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
49
ASANO
1981B
 CNTR Stopped ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
50
ZHITNITSKII
1979
Heavy axion
1  ABLIKIM 2024AK search for ${{\mathit \eta}^{\,'}}$ decays to axions in the mass range 0 to 500 MeV using the BESIII detector at the Beijing Electron-Positron Collider. See Fig. 9b for mass-dependent limits.
2  ABLIKIM 2024G search for muonphilic vector or scalar ${{\mathit X}^{0}}$ particles with masses between 1 and 1000 MeV in ${{\mathit J / \psi}}$ decays at the BESIII detector. See their Fig. 3 for mass-dependent limits on the scalar/vector couplings under three different models.
3  ABLIKIM 2024M search for ${{\mathit \eta}}$ and ${{\mathit \eta}^{\,'}}$ decays to dark photons in the mass range 0 to 0.7 GeV using the BESIII detector at the Beijing Electron-Positron Collider. The quoted limit is for ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$. See Fig. 7 a and b for mass-dependent limits.
4  CORTINA-GIL 2024 use ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \gamma}}{{\mathit \gamma}}$ events in NA62 to constrain 210 to 350 MeV-mass axions coupled to gluons, which promptly decay to ${{\mathit \gamma}}{{\mathit \gamma}}$. See their Fig. 8 for mass-dependent limits.
5  SADOVSKY 2024 report results from the OKA collaboration on a missing-mass search for invisible axions in ${{\mathit K}^{+}}$ decays to pions. The quoted limit applies at ${\mathit m}_{{{\mathit A}^{0}}}$ $\simeq{}$ 200 MeV. See their Fig. 6 for mass-dependent limits up to 200 MeV.
6  ADACHI 2023K quoted limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ $\simeq{}$ 3 GeV, $\mathit c\tau _{{{\mathit X}^{0}}}$ = 1 cm, and the decay channel ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$. See their Fig. 2 for limits with different lifetimes and decay channels, ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit K}^{+}}{{\mathit K}^{-}}$.
7  ADACHI 2023K quoted limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ $\simeq{}$ 2 GeV, $\mathit c\tau _{{{\mathit X}^{0}}}$ = 1 cm, and the decay channel ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$. See their Fig. 2 for limits with different lifetimes and decay channels, ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit K}^{+}}{{\mathit K}^{-}}$.
8  CORTINA-GIL 2023B limit extends over $10 - 170$ MeV in mass. Quoted limit is at 155 MeV.
9  LEES 2022B quoted limit is for ${\mathit m}_{{{\mathit A}^{0}}}$ = 3.9 GeV, assuming the promptly decaying axion. Limits of O($10^{-7}$) are obtained for ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.175 - 4.78$ GeV. See their Figs.3 and 4 for mass and lifetime dependent limits.
10  ABRATENKO 2021 quoted limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ = 150 MeV and the lifetime $\mathit c\tau _{{{\mathit X}^{0}}}$ = 80 m. See their Fig. 4 for the limits in the range of ${\mathit m}_{{{\mathit X}^{0}}}$ = $10 - 210$ MeV.
11  CORTINA-GIL 2021 quoted limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ = 370 MeV. Limits from O($10^{-5}$) and O($10^{-6}$) are obtained for ${\mathit m}_{{{\mathit X}^{0}}}$ = $10 - 370$ MeV (see their Fig. 7).
12  CORTINA-GIL 2021A quoted limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ = $160 - 250$ MeV. Limits between $5 \times 10^{-11}$ and $2 \times 10^{-10}$ are obtained in the range of ${\mathit m}_{{{\mathit X}^{0}}}$ = $0 - 110$ and $154 - 260$ MeV, assuming stable or invisibly decaying ${{\mathit X}^{0}}$. See their Fig. 4 for mass- and lifetime-dependent limits.
13  CORTINA-GIL 2021C quoted limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ = $130 - 140$ MeV, and limits of $9 \times 10^{-10} - 6 \times 10^{-7}$ are obtained in the mass range of ${\mathit m}_{{{\mathit X}^{0}}}$ = $110 - 155$ MeV, assuming ${{\mathit X}^{0}}$ escapes detection. See their Fig. 6 for mass- and lifetime-dependent limits.
14  PARK 2021 look for dark photons produced by decays of ${{\mathit B}^{0}}$ through off-shell Higgs-dark Higgs mixing. See their Fig. 5 for limits in the range of ${\mathit m}_{{{\mathit X}^{0}}}$ = $0.01 - 2.62$ GeV.
15  AHN 2019 is an update of AHN 2017 from a new data set. See their Fig. 4 for the limits in the range of ${\mathit m}_{{{\mathit X}^{0}}}$ = $0 - 250$ MeV.
16  AAIJ 2017AQ limit is for ${\mathit \tau}_{{{\mathit X}^{0}}}$ = 10 ps. See their Fig. 4 for limits in the range of ${\mathit m}_{{{\mathit X}^{0}}}$ = $250 - 4700$ MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}$ = $0.1 - 1000$ ps.
17  AHN 2017 limit as a function of ${\mathit m}_{{{\mathit X}^{0}}}$ from 0 to 250 MeV is provided in their Fig. 5.
18  BATLEY 2017 limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ = 216 MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}{}\leq{}$ 10 ps. See their Fig. 4(c) for limits in the range of ${\mathit m}_{{{\mathit X}^{0}}}$ = $211 - 354$ MeV and longer lifetimes.
19  WON 2016 look for a vector boson coupled to baryon number. Derived limits on ${{\mathit \alpha}^{\,'}}$ $<$ $10^{-3} - 10^{-2}$ for ${\mathit m}_{{{\mathit X}^{0}}}$ = $290 - 520$ MeV at 95$\%$ CL. See their Fig. 4 for mass-dependent limits.
20  AAIJ 2015AZ limit is for ${\mathit \tau}_{{{\mathit X}^{0}}}$ = 10 ps and ${\mathit m}_{{{\mathit X}^{0}}}$ = $214 - 4350$ MeV. See their Fig. 4 for mass- and lifetime-dependent limits.
21  ADLARSON 2013 limits between $2.0 \times 10^{-5}$ and $1.5 \times 10^{-6}$ are obtained for ${\mathit m}_{{{\mathit X}^{0}}}$ = $20 - 100$ MeV (see their Fig. 8). Angular momentum conservation requires that ${{\mathit X}^{0}}$ has spin ${}\geq{}$ 1.
22  BABUSCI 2013B limit is for B(${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit X}^{0}})\cdot{}B({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$) and applies to ${\mathit m}_{{{\mathit X}^{0}}}$ = 410 MeV. It is derived by analyzing ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$. Limits between $1 \times 10^{-6}$ and $2 \times 10^{-8}$ are obtained for ${\mathit m}_{{{\mathit X}^{0}}}{}\leq{}$ 450 MeV (see their Fig. 6).
23  ARCHILLI 2012 analyzed ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ decays. Derived limits on ${{\mathit \alpha}^{\,'}}/{{\mathit \alpha}}$ $<$ $2 \times 10^{-5}$ for ${\mathit m}_{{{\mathit X}^{0}}}$ = $50 - 420$ MeV at 90$\%$ CL. See their Fig. 8 for mass-dependent limits.
24  GNINENKO 2012A limit is for B(${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}})\cdot{}B({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$) and applies for ${\mathit m}_{{{\mathit X}^{0}}}$ = 90 MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}$ $\simeq{}$ $1 \times 10^{-8}$ sec. Limits between $10^{-8}$ and $2 \times 10^{-15}$ are obtained for ${\mathit m}_{{{\mathit X}^{0}}}$ = $3 - 120$ MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}$ = $1 \times 10^{-11} - 1$ sec. See their Fig. 3 for limits at different masses and lifetimes.
25  GNINENKO 2012B limit is for B(${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}})\cdot{}B({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$) and applies for ${\mathit m}_{{{\mathit X}^{0}}}$ = 100 MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}$ $≅$ $6 \times 10^{-9}$ sec. Limits between $10^{-5}$ and $3 \times 10^{-14}$ are obtained for ${\mathit m}_{{{\mathit X}^{0}}}{ {}\lesssim{} }$ 550 MeV and ${\mathit \tau}_{{{\mathit X}^{0}}}$ = $10^{-10} - 10$ sec. See their Fig. 5 for limits at different mass and lifetime and for ${{\mathit \eta}^{\,'}}$ decays.
26  ADLER 2004 limit applies for a mass near 180 MeV. For other masses in the range ${\mathit m}_{{{\mathit X}^{0}}}$ = $150 - 250$ MeV the limit is less restrictive, but still improves ADLER 2002C and ATIYA 1993B.
27  ANISIMOVSKY 2004 bound is for ${\mathit m}_{{{\mathit X}^{0}}}$=0.
28  ADLER 2002C bound is for ${\mathit m}_{{{\mathit X}^{0}}}<$60 MeV. See Fig.$~$2 for limits at higher masses.
29  The quoted limit is for ${\mathit m}_{{{\mathit X}^{0}}}$ = $0 - 80$ MeV. See their Fig. 5 for the limit at higher mass. The branching fraction limit assumes pure phase space decay distributions.
30  ALTEGOER 1998 looked for ${{\mathit X}^{0}}$ from ${{\mathit \pi}^{0}}$ decay which penetrate the shielding and convert to ${{\mathit \pi}^{0}}$ in the external Coulomb field of a nucleus.
31  KITCHING 1997 limit is for B(${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}})\cdot{}B({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$) and applies for ${\mathit m}_{{{\mathit X}^{0}}}\simeq{}$50 MeV, $\tau _{{{\mathit X}^{0}}}<10^{-10}~$s. Limits are provided for 0$<{\mathit m}_{{{\mathit X}^{0}}}<100$ MeV, $\tau _{{{\mathit X}^{0}}}<10^{-8}~$s.
32  ADLER 1996 looked for a peak in missing-mass distribution. This work is an update of ATIYA 1993. The limit is for massless stable ${{\mathit X}^{0}}$ particles and extends to ${\mathit m}_{{{\mathit X}^{0}}}$=80 MeV at the same level. See paper for dependence on finite lifetime.
33  AMSLER 1994B and AMSLER 1996B looked for a peak in missing-mass distribution.
34  MEIJERDREES 1994 limit is based on inclusive photon spectrum and is independent of ${{\mathit X}^{0}}$ decay modes. It applies to $\tau\mathrm {({{\mathit X}^{0}})}>10^{-23}~$sec.
35  ATIYA 1993B looked for a peak in missing mass distribution. The bound applies for stable ${{\mathit X}^{0}}$ of ${\mathit m}_{{{\mathit X}^{0}}}=150 - 250$ MeV, and the limit becomes stronger ($10^{-8}$) for ${\mathit m}_{{{\mathit X}^{0}}}=180 - 240$ MeV.
36  NG 1993 studied the production of ${{\mathit X}^{0}}$ via ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ in the early universe at $\mathit T\simeq{}$1 MeV. The bound on extra neutrinos from nucleosynthesis $\Delta {{\mathit N}_{{{\nu}}}}<0.3$ (WALKER 1991) is employed. It applies to ${\mathit m}_{{{\mathit X}^{0}}}{}\ll$1 MeV in order to be relativistic down to nucleosynthesis temperature. See paper for heavier ${{\mathit X}^{0}}$.
37  ALLIEGRO 1992 limit applies for ${\mathit m}_{{{\mathit X}^{0}}}=150 - 340$ MeV and is the branching ratio times the decay probability. Limit is $<1.5 \times 10^{-8}$ at 99$\%$CL.
38  ATIYA 1992 looked for a peak in missing mass distribution. The limit applies to ${\mathit m}_{{{\mathit X}^{0}}}=0 - 130$ MeV in the narrow resonance limit. See paper for the dependence on lifetime. Covariance requires ${{\mathit X}^{0}}$ to be a vector particle.
39  BARABASH 1992 is a beam dump experiment that searched for a light Higgs. Limits between $1 \times 10^{-12}$ and $1 \times 10^{-7}$ are obtained for 3 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 40 MeV.
40  Limits between $1 \times 10^{-12}$ and $1$ are obtained for 4 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 69 MeV.
41  Limits between $1 \times 10^{-11}$ and $5 \times 10^{-3}$ are obtained for 4 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 63 MeV.
42  Limits between $1 \times 10^{-14}$ and $1$ are obtained for 3 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 82 MeV.
43  MEIJERDREES 1992 limit applies for ${\mathit \tau}_{{{\mathit X}^{0}}}$ = $10^{-23} - 10^{-11}~$sec. Limits between $2 \times 10^{-4}$ and $4 \times 10^{-6}$ are obtained for ${\mathit m}_{{{\mathit X}^{0}}}$ = $25 - 120$ MeV. Angular momentum conservation requires that ${{\mathit X}^{0}}$ has spin ${}\geq{}$1.
44  ATIYA 1990B limit is for B(${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}})\cdot{}B({{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$) and applies for ${\mathit m}_{{{\mathit X}^{0}}}$ = 50 MeV, ${\mathit \tau}_{{{\mathit X}^{0}}}$ $<$ $10^{-10}~$s. Limits are also provided for 0 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 100 MeV, ${\mathit \tau}_{{{\mathit X}^{0}}}$ $<$ $10^{-8}~$s.
45  KORENCHENKO 1987 limit assumes ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.7$ MeV, ${\mathit \tau}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $10^{-12}$ s, and B(${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$) = 1.
46  EICHLER 1986 looked for ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit A}^{0}}$ followed by ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$. Limits on the branching fraction depend on the mass and and lifetime of ${{\mathit A}^{0}}$. The quoted limits are valid when $\tau\mathrm {({{\mathit A}^{0}})}{ {}\gtrsim{} }3. \times 10^{-10}$s if the decays are kinematically allowed.
47  YAMAZAKI 1984 looked for a discrete line in ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}$ X. Sensitive to wide mass range (5$-$300 MeV), independent of whether X decays promptly or not.
48  ASANO 1982 at KEK set limits for B(${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$) for ${\mathit m}_{{{\mathit X}^{0}}}$ $<$100 MeV as BR $<4. \times 10^{-8}$ for $\tau\mathrm {({{\mathit X}^{0}} \rightarrow {{\mathit n}} )}$ $>1. \times 10^{-9}$ s, BR $<1.4 \times 10^{-6}$ for $\tau $ $<1. \times 10^{-9}$s.
49  ASANO 1981B is KEK experiment. Set B(${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$) $<3.8 \times 10^{-8}$ at CL = 90$\%$.
50  ZHITNITSKII 1979 argue that a heavy axion predicted by YANG 1978 (3 $<\mathit m$ $<$40 MeV) contradicts experimental muon anomalous magnetic moments.
References