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

LHCB

${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ )

$<3.7 \times 10^{-8}$

AHN

KOTO

${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}$ ${{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$ = 135 MeV

$<6 \times 10^{-11}$

BATLEY

NA48

${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ ${{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ )

⁴

WON

2016

BELL

${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}$ ${{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ )

$<1 \times 10^{-9}$

⁵

2015

LHCB

${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{*0}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ )

$<1.5 \times 10^{-6}$

⁶

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

$<2$

⁷

BABUSCI

2013

KLOE

${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )

⁸

ARCHILLI

KLOE

${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit X}^{0}}$ , ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$

$<2 \times 10^{-15}$

⁹

BDMP

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )

$<3 \times 10^{-14}$

¹⁰

BDMP

${{\mathit \eta}}({{\mathit \eta}^{\,'}}$) $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )

$<7 \times 10^{-10}$

¹¹

B787

${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$

$<7.3 \times 10^{-11}$

¹²

ANISIMOVSKY

B949

${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$

$<4.5 \times 10^{-11}$

¹³

2002

B787

${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$

$<4 \times 10^{-5}$

¹⁴

B787

${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit A}^{0}}$

$<4.9 \times 10^{-5}$

AMMAR

CLEO

${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ (${{\mathit K}^{\pm}}){{\mathit X}^{0}}$

$<5.3 \times 10^{-5}$

AMMAR

CLEO

${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit X}^{0}}$

$<3.3 \times 10^{-5}$

¹⁵

ALTEGOER

1998

NOMD

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}<120$ MeV

$<5.0 \times 10^{-8}$

¹⁶

KITCHING

1997

B787

${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ )

$<5.2 \times 10^{-10}$

¹⁷

B787

${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$

$<2.8 \times 10^{-4}$

¹⁸

CBAR

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}<$ 65 MeV

$<3 \times 10^{-4}$

¹⁸

CBAR

${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$= $50 - 200$ MeV

$<4 \times 10^{-5}$

¹⁸

CBAR

${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$= $50 - 925$ MeV

$<6 \times 10^{-5}$

¹⁸

CBAR

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}=65 - 125$ MeV

$<6 \times 10^{-5}$

¹⁸

CBAR

${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}=200 - 525$ MeV

$<7 \times 10^{-3}$

¹⁹

CNTR

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$=25 MeV

$<2 \times 10^{-3}$

¹⁹

CNTR

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$ , ${\mathit m}_{{{\mathit X}^{0}}}$=100 MeV

$<2 \times 10^{-7}$

²⁰

1993

B787

Sup. by ADLER 2004

$<3 \times 10^{-13}$

²¹

1993

COSM

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$

$<1.1 \times 10^{-8}$

²²

ALLIEGRO

SPEC

${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$ ( ${{\mathit X}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )

$<5 \times 10^{-4}$

²³

B787

${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}^{0}}$

$<1 \times 10^{-12}$

²⁴

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

$<1 \times 10^{-12}$

²⁵

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

$<1 \times 10^{-11}$

²⁶

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

$<1 \times 10^{-14}$

²⁷

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

$<4 \times 10^{-6}$

²⁸

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

$<1 \times 10^{-7}$

²⁹

1990

B787

Sup. by KITCHING 1997

$<1.3 \times 10^{-8}$

³⁰

KORENCHENKO

1987

SPEC

${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit A}^{0}}$ ( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ )

$<1 \times 10^{-9}$

³¹

EICHLER

1986

SPEC

Stopped ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\mathit A}^{0}}$

$<2 \times 10^{-5}$

³²

YAMAZAKI

1984

SPEC

For 160$<\mathit m<$260 MeV

$<(1.5-4){\times }\text{ 10^}{-6}$

³²

YAMAZAKI

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

CNTR

Stopped ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$

³⁵

ZHITNITSKII

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:

2017AQ

PR D95 071101

Search for Long-Lived Scalar Particles in ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \chi}}$ (${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$)} Decays

AHN

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

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

2015AZ

PRL 115 161802

Search for Hidden-Sector Bosons in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{*0}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ Decays

ADLARSON

2013

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

PL B706 251

Search for a Vector Gauge Boson in ${{\mathit \phi}}$ Meson Decays with the KLOE Detector

2012B

PL B713 244

Constraints on sub-GeV Hidden Sector Gauge Bosons from a Search for Heavy Neutrino Decays

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

PRL 93 031801

Improved Measurement on the ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}$ Branching Ratio

2002C

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 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$

1996B

ZPHY C70 219

Search for a New Light Gauge Boson in ${{\mathit \pi}^{0}}$, ${{\mathit \eta}}$ and ${{\mathit \eta}^{\,'}}$ Decays

1994B

PL B333 271

Search for a New Light Gauge Boson in Decays of ${{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$

PR D49 4937

Search for the Decay ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$

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 ${\mathrm {MeV}}/\mathit c{}^{2}$

1993

PR D48 2941

Cosmological Bound on the Decay ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$

ALLIEGRO

PRL 68 278

Study of the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit e}^{+}}{{\mathit e}^{-}}$

PRL 69 733

Search for the Decay ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit X}}$

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

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

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 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit X}^{0}}$

1982

PL 113B 195

A New Experimental Limit for the Decay ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \gamma}}{{\mathit \gamma}}$