# ${{\boldsymbol A}^{0}}$ (Axion) and Other Light Boson (${{\boldsymbol X}^{0}}$) Searches in Hadron Decays INSPIRE search

Limits are for branching ratios.
VALUE CL% DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<2 \times 10^{-10}$ 95 1
 2017 AQ
LHCB ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ )
$<3.7 \times 10^{-8}$ 90 2
 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 3
 2017
NA48 ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ ${{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ )
4
 2016
BELL ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}$ ${{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ )
$<1 \times 10^{-9}$ 95 5
 2015 AZ
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 6
 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
$<2$ 90 7
 2013 B
KLOE ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )
8
 2012
KLOE ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit X}^{0}}$ , ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$
$<2 \times 10^{-15}$ 90 9
 2012 A
BDMP ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )
$<3 \times 10^{-14}$ 90 10
 2012 B
BDMP ${{\mathit \eta}}({{\mathit \eta}^{\,'}}$) $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )
$<7 \times 10^{-10}$ 90 11
 2004
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<7.3 \times 10^{-11}$ 90 12
 2004
B949 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<4.5 \times 10^{-11}$ 90 13
 2002 C
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<4 \times 10^{-5}$ 90 14
 2001
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit A}^{0}}$
$<4.9 \times 10^{-5}$ 90
 2001 B
CLEO ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ (${{\mathit K}^{\pm}}){{\mathit X}^{0}}$
$<5.3 \times 10^{-5}$ 90
 2001 B
CLEO ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit X}^{0}}$
$<3.3 \times 10^{-5}$ 90 15
 1998
NOMD ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}<120$ MeV
$<5.0 \times 10^{-8}$ 90 16
 1997
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ )
$<5.2 \times 10^{-10}$ 90 17
 1996
B787 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
$<2.8 \times 10^{-4}$ 90 18
 1996 B
CBAR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}<$ 65 MeV
$<3 \times 10^{-4}$ 90 18
 1996 B
CBAR ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$= $50 - 200$ MeV
$<4 \times 10^{-5}$ 90 18
 1996 B
CBAR ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$= $50 - 925$ MeV
$<6 \times 10^{-5}$ 90 18
 1994 B
CBAR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}=65 - 125$ MeV
$<6 \times 10^{-5}$ 90 18
 1994 B
CBAR ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}=200 - 525$ MeV
$<7 \times 10^{-3}$ 90 19
 1994
CNTR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$=25 MeV
$<2 \times 10^{-3}$ 90 19
 1994
CNTR ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$=100 MeV
$<2 \times 10^{-7}$ 90 20
 1993 B
$<3 \times 10^{-13}$ 21
 1993
COSM ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$
$<1.1 \times 10^{-8}$ 90 22
 1992
SPEC ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )
$<5 \times 10^{-4}$ 90 23
 1992
B787 ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$
$<1 \times 10^{-12}$ 95 24
 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 25
 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 26
 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 27
 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 28
 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 29
 1990 B
B787 Sup. by KITCHING 1997
$<1.3 \times 10^{-8}$ 90 30
 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 31
 1986
SPEC Stopped ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit A}^{0}}$
$<2 \times 10^{-5}$ 90 32
 1984
SPEC For 160$<\mathit m<$260 MeV
$<(1.5-4){\times }\text{ 10^}{-6}$ 90 32
 1984
SPEC ${{\mathit K}}$ decay, ${\mathit m}_{{{\mathit X}^{0}}}{}\ll$100 MeV
33
 1982
CNTR Stopped ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
34
 1981 B
CNTR Stopped ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
35
 1979
Heavy axion
1  The 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.
2  The limit as a function of ${\mathit m}_{{{\mathit X}^{0}}}$ from 0 to 250 MeV is provided in their Fig. 5 .
3  The 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.
4  WON 2016 look for a vector boson coupled to baryon number. Derived limits on ${{\mathit \alpha}^{\,'}}$ $<$ for ${\mathit m}_{{{\mathit X}^{0}}}$ = $290 - 520$ MeV at 95$\%$ CL. See their Fig. 4 for mass-dependent limits.
5  The 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.
6  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.
7  The 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).
8  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.
9  This 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.
10  This 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.
11  This 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.
12  ANISIMOVSKY 2004 bound is for ${\mathit m}_{{{\mathit X}^{0}}}$=0.
13  ADLER 2002C bound is for ${\mathit m}_{{{\mathit X}^{0}}}<$60 MeV. See Fig.$~$2 for limits at higher masses.
14  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.
15  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.
16  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.
17  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.
18  AMSLER 1994B and AMSLER 1996B looked for a peak in missing-mass distribution.
19  The 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.
20  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.
21  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 ${{\mathit X}^{0}}$.
22  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.
23  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.
24  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.
25  Limits between $1 \times 10^{-12}$ and $1$ are obtained for 4 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 69 MeV.
26  Limits between $1 \times 10^{-11}$ and $5 \times 10^{-3}$ are obtained for 4 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 63 MeV.
27  Limits between $1 \times 10^{-14}$ and $1$ are obtained for 3 $<$ ${\mathit m}_{{{\mathit X}^{0}}}$ $<$ 82 MeV.
28  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.
29  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.
30  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.
31  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.
32  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.
33  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.
34  ASANO 1981B is KEK experiment. Set B( ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ ) $<3.8 \times 10^{-8}$ at CL = 90$\%$.
35  ZHITNITSKII 1979 argue that a heavy axion predicted by YANG 1978 (3 $<\mathit m$ $<$40 MeV) contradicts experimental muon anomalous magnetic moments.
References:
 AAIJ 2017AQ
PR D95 071101 Search for Long-Lived Scalar Particles in ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \chi}}$ (${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$)} Decays
 AHN 2017
PTEP 2017 021C01 A New Search for the ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ and ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit X}^{0}}$ Decays
 BATLEY 2017
PL B769 67 Searches for Lepton Number Violation and Resonances in ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \mu}}{{\mathit \mu}}$ Decays
 WON 2016
PR D94 092006 Search for a Dark Vector Gauge Boson Decaying to ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ using ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ Decays
 AAIJ 2015AZ
PRL 115 161802 Search for Hidden-Sector Bosons in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{*0}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ Decays
PL B726 187 Search for a Dark Photon in the ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ Decay
 BABUSCI 2013B
PL B720 111 Limit on the Production of a Light Vector Gauge Boson in ${{\mathit \phi}}$ Meson Decays with the KLOE Detector
 ARCHILLI 2012
PL B706 251 Search for a Vector Gauge Boson in ${{\mathit \phi}}$ Meson Decays with the KLOE Detector
 GNINENKO 2012B
PL B713 244 Constraints on sub-GeV Hidden Sector Gauge Bosons from a Search for Heavy Neutrino Decays
 GNINENKO 2012A
PR D85 055027 Stringent Limits on the ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$ , ${{\mathit X}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Decay from Neutrino Experiments and Constraints on New Light Gauge Bosons
PR D70 037102 Further Search for the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ in the Momentum Region P $<$ 195 MeV/$\mathit c$
 ANISIMOVSKY 2004
PRL 93 031801 Improved Measurement on the ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}$ Branching Ratio
PL B537 211 Search for the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ in the Momentum Region P$_{{{\mathit \pi}}}$ $<$ 195-MeV/$\mathit c$
PR D63 032004 Search for the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$
 AMMAR 2001B
PRL 87 271801 Search for the Familon via ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit X}^{0}}$ , ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit X}^{0}}$ , and ${{\mathit B}^{0}}$ ${{\mathit X}^{0}}$ Decays
 ALTEGOER 1998
PL B428 197 Search for a New Gauge Boson in ${{\mathit \pi}^{0}}$ Decays
 KITCHING 1997
PRL 79 4079 Observation of the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \gamma}}{{\mathit \gamma}}$
PRL 76 1421 Search for Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$
 AMSLER 1996B
ZPHY C70 219 Search for a New Light Gauge Boson in ${{\mathit \pi}^{0}}$, ${{\mathit \eta}}$ and ${{\mathit \eta}^{\,'}}$ Decays
 AMSLER 1994B
PL B333 271 Search for a New Light Gauge Boson in Decays of ${{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$
 MEIJERDREES 1994
PR D49 4937 Search for the Decay ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$
 ATIYA 1993B
PR D48 1 Search for the Decays ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ and ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ for 150 $<$ $\mathit M_{{{\mathit X}^{0}}}$ $<$ 250 ${\mathrm {MeV}}/\mathit c{}^{2}$
 NG 1993
PR D48 2941 Cosmological Bound on the Decay ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$
 ALLIEGRO 1992
PRL 68 278 Study of the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit e}^{+}}{{\mathit e}^{-}}$
 ATIYA 1992
PRL 69 733 Search for the Decay ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$
 BARABASH 1992
PL B295 154 Restraints on Light Higgs Boson Mass from ${{\mathit \pi}}$-, ${{\mathit K}}$-, and ${{\mathit \eta}^{\,'}{(958)}}$-Meson Decays in Proton Beam-Dump Experiment
 MEIJERDREES 1992
PRL 68 3845 Search for Weakly Interacting Neutral Bosons Produced in ${{\mathit \pi}^{-}}{{\mathit p}}$ Interactions at Rest and Decaying into ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Pairs
 ATIYA 1990B
PRL 65 1188 Search for the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \gamma}}{{\mathit \gamma}}$
 KORENCHENKO 1987
SJNP 46 192 On Decays ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}$ ( ${{\mathit e}^{+}}{{\mathit e}^{-}}$), ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit e}^{+}}{{\mathit e}^{+}}{{\mathit \nu}}$
 EICHLER 1986
PL B175 101 Limits for Short Lived Neutral Particle Emitted in ${{\mathit \mu}^{+}}$ or ${{\mathit \pi}^{+}}$ Decay
 YAMAZAKI 1984
PRL 52 1089 Search for a Neutral Boson in a Two Body Decay of ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$
 ASANO 1982
PL 113B 195 A New Experimental Limit for the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \gamma}}{{\mathit \gamma}}$
 ASANO 1981B
PL 107B 159 Search for a Rare Decay Mode ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ and Axion
 ZHITNITSKII 1979
SJNP 29 517 Does Yang's Heavy Axion Exist?