#### Limits on $\vert {{\mathit U}}$ $_{ {{\mathit \mu}} {{\mathit x}} }\vert ^2$

Quoted limits are either the best limit near the kinematic threshold of the experiment, or a characteristic value in the mass range of the experimental sensitivity
VALUE CL% DOCUMENT ID TECN  COMMENT
$<1 \times 10^{-3}$ 95 1
 2021 AA
LHCB ${\mathit m}_{{{\mathit \nu}_{{x}}}}\sim{}5 - 50$ GeV, ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$<2 \times 10^{-4}$ 95 2
 2021 AA
LHCB ${\mathit m}_{{{\mathit \nu}_{{x}}}}\sim{}5 - 50$ GeV, ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$<5 \times 10^{-9}$ 90 3, 4
 2021
NA62 Near ${\mathit m}_{{{\mathit K}}}–{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<1 \times 10^{-7}$ 90 5
 2020
MBNE Near ${\mathit m}_{{{\mathit K}}}–{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<0.02$ 90 6
 2020
BELL ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 1 GeV
$<2 \times 10^{-5}$ 95 7
 2019 F
ATLS ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $10 - 50$ GeV
$<2 \times 10^{-6}$ 95 8
 2019 F
ATLS ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 10 GeV
$<1 \times 10^{-9}$ 90 9
 2019 B
T2K Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<5 \times 10^{-6}$ 90 10, 11
 2019 B
PIEN ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $16 - 30$ MeV
$<1 \times 10^{-5}$ 90 11
 2019 B
PIEN Near ${\mathit m}_{{{\mathit \pi}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<3 \times 10^{-7}$ 90 3
 2018
NA62 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $250 - 350$ MeV
$<3 \times 10^{-6}$ 90 3
 2017 A
NA62 Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<0.05$ 90 12
 2016
BELL ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 1.4 GeV
$<1 \times 10^{-8}$ 90 3
 2015 A
B949 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $200 - 300$ MeV
$<3 \times 10^{-5}$ 90 13
 2013
BELL Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $2 - 2.5$ GeV
$<2.0 \times 10^{-8}$ 95 14
 2000
KARM ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ = 33.905 MeV
$<8 \times 10^{-8}$ 90 15
 1999
CCFR Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<6 \times 10^{-8}$ 90 16
 1999
CCFR Near ${\mathit m}_{{{\mathit D}_{{s}}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<3 \times 10^{-5}$ 95 17
 1997 I
DLPH ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $6 - 50$ GeV
$<2 \times 10^{-5}$ 95 18
 1997 I
DLPH Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 3.5 GeV
$<3 \times 10^{-5}$ 90 19
 1995 C
CHM2 Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<3 \times 10^{-8}$ 20, 21
 1988
CNTR Near ${\mathit m}_{{{\mathit \mu}}}+{\mathit m}_{{{\mathit \pi}}}$ kin. thres.
$<2 \times 10^{-9}$ 21, 22
 1988
CNTR Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<1 \times 10^{-7}$ 90 23
 1986
CHRM Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<1 \times 10^{-7}$ 90 24
 1985
BEBC Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
 1 Limit from prompt lepton number conserving ${{\mathit W}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \mu}}{{\mathit j}}$ search.
 2 Limit from prompt lepton number violating ${{\mathit W}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \mu}}{{\mathit j}}$ search .
 3 Search for ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ .
 4 Assumes a lifetime exceeding 50 ns, and searches over ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ range $200 - 384$ MeV.
 5 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \pi}^{+}}$ , in the mass range ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $260 - 385$ MeV. ABRATENKO 2020 also considers ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \pi}^{-}}$ for the case of Majorana HNL.
 6 Search for ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ in the mass range ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0 - 1.5$ GeV .
 7 Limit from prompt lepton number violating trilepton search.
 8 Limit from displaced lepton violating or conserving trilepton searches.
 9 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}$ $_{ {{\mathit \mu}} {{\mathit x}} }$. ABE 2019B also considers bounds on $\vert {{\mathit U}}$ $_{ {{\mathit \ell}} {{\mathit x}} }{{\mathit U}}$ $_{ {{\mathit \ell}^{\,'}} {{\mathit x}} }\vert$ for combinations of lepton flavors in the ${{\mathit \nu}_{{x}}}$ decay final state.
 10 Limit requires muon kinetic energy $>$ 1.2 MeV.
 11 Search for ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ .
 12 PARK 2016 quotes an approximate limit B( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ ) $<$ $3 \times 10^{-6}$ in the mass range ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.2 - 1.4$ GeV.
 13 Search for ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ .
 14 DAUM 2000 quotes a branching ratio bound B( ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ ) $<$ $6.0 \times 10^{-10}$ at 95$\%$ CL.
 15 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit X}}$ .
 16 ${{\mathit D}_{{s}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit X}}$ .
 17 Search for prompt ${{\mathit \nu}_{{x}}}$ decay signatures.
 18 Search for displaced ${{\mathit \nu}_{{x}}}$ decay signatures.
 19 Search for Heavy Neutral Leptons produced by neutral current muon neutrino interactions, with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \nu}_{{\mu}}}$ .
 20 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}$ $_{ {{\mathit \mu}} {{\mathit x}} }$ and ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $<$ ${\mathit m}_{{{\mathit \mu}}}$ + ${\mathit m}_{{{\mathit \pi}}}$.
 21 BERNARDI 1988 also considers bounds on $\vert {{\mathit U}}$ $_{ {{\mathit e}} {{\mathit x}} }{{\mathit U}}$ $_{ {{\mathit \mu}} {{\mathit x}} }\vert$.
 22 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \pi}^{+}}$ .
 23 ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ .
 24 ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ or ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \pi}^{+}}$ .
References:
 AAIJ 2021AA
EPJ C81 248 Search for heavy neutral leptons in $W^+\to\mu^{+}\mu^{\pm}\text{jet}$ decays
 CORTINA-GIL 2021
PL B816 136259 Search for $K^+$ decays to a muon and invisible particles
 ABRATENKO 2020
PR D101 052001 Search for Heavy Neutral Leptons Decaying into Muon-Pion Pairs in the MicroBooNE Detector
 PRIM 2020
PR D101 032007 Search for $B^+ \to \mu^+\, \nu_\mu$ and $B^+ \to \mu^+\, N$ with inclusive tagging
 AAD 2019F
JHEP 1910 265 Search for heavy neutral leptons in decays of $W$ bosons produced in 13 TeV $pp$ collisions using prompt and displaced signatures with the ATLAS detector
 ABE 2019B
PR D100 052006 Search for heavy neutrinos with the T2K near detector ND280
 AGUILAR-AREVALO 2019B
PL B798 134980 Search for heavy neutrinos in $\pi \to \mu\nu$ decay
 CORTINA-GIL 2018
PL B778 137 Search for heavy neutral lepton production in $K^+$ decays
 LAZZERONI 2017A
PL B772 712 Search for Heavy Neutrinos in ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{\mu}}}$ Decays
 PARK 2016
PR D94 012003 Search for a Massive Invisible Particle ${{\mathit X}^{0}}$ in ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit X}^{0}}$ and ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit X}^{0}}$ Decays
 ARTAMONOV 2015A
PR D91 052001 Search for Heavy Neutrinos in ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{H}}}$ Decays
 LIVENTSEV 2013
PR D87 071102 Search for Heavy Neutrinos at Belle
 Also
PR D95 099903 (errat.) Erratum to LIVENTSEV 2013 : Search for Heavy Neutrinos at Belle
 DAUM 2000
PRL 85 1815 The KARMEN Time Anomaly: Search for a Neutral Particle of Mass 33.9 MeV in Pion Decay
 VAITAITIS 1999
PRL 83 4943 Search for Neutral Heavy Leptons in a High Energy Neutrino Beam
 ABREU 1997I
ZPHY C74 57 Search for Neutral Heavy Leptons Produced in ${{\mathit Z}}$ Decays
 Also
ZPHY C75 580 (errat.) Erratum: ABREU 1997I Search for Neutral Heavy Leptons Produced in ${{\mathit Z}}$ Decays
 VILAIN 1995C
PL B351 387 Search for Heavy Isosinglet Neutrinos
 Also
PL B343 453 Search for Heavy Isosinglet Neutrinos
 BERNARDI 1988
PL B203 332 Further Limit on Heavy Neutrino Coupling
 DORENBOSCH 1986
PL 166B 473 A Search for Decays of Heavy Neutrinos in the Mass Range of 0.5 $−$ 2.8 GeV
 COOPER-SARKAR 1985
PL 160B 207 Search for Heavy Neutrino Decays in the BEBC Beam Dump Experiment