# Limits on $\vert {{\boldsymbol U}}_{ {{\boldsymbol \mu}} {{\boldsymbol x}} }\vert ^2$ INSPIRE search

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
$<2 \times 10^{-5}$ 95 1
 2019 F
ATLS ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $10 - 50$ GeV
$<2 \times 10^{-6}$ 95 2
 2019 F
ATLS ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 10 GeV
$<1 \times 10^{-9}$ 90 3
 2019 B
T2K Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<5 \times 10^{-6}$ 90 4, 5
 2019 B
PIEN ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $16 - 30$ MeV
$<1 \times 10^{-5}$ 90 5
 2019 B
PIEN Near ${\mathit m}_{{{\mathit \pi}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<3 \times 10^{-7}$ 90 6
 2018
NA62 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $250 - 350$ MeV
$<3 \times 10^{-6}$ 90 6
 2017 A
NA62 Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<1 \times 10^{-8}$ 90 6
 2015 A
B949 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $200 - 300$ MeV
$<2.0 \times 10^{-8}$ 95 7
 2000
KARM ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ = 33.905 MeV
$<8 \times 10^{-8}$ 90 8
 1999
CCFR Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<6 \times 10^{-8}$ 90 9
 1999
CCFR Near ${\mathit m}_{{{\mathit D}_{{s}}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<3 \times 10^{-5}$ 95 10
 1997 I
DLPH ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $6 - 50$ GeV
$<2 \times 10^{-5}$ 95 11
 1997 I
DLPH Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 3.5 GeV
$<3 \times 10^{-5}$ 90 12
 1995 C
CHM2 Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<3 \times 10^{-8}$ 13, 14
 1988
CNTR Near ${\mathit m}_{{{\mathit \mu}}}+{\mathit m}_{{{\mathit \pi}}}$ kin. thres.
$<2 \times 10^{-9}$ 14, 15
 1988
CNTR Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<1 \times 10^{-7}$ 90 16
 1986
CHRM Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
$<1 \times 10^{-7}$ 90 17
 1985
BEBC Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit \mu}}}$ kin. thres.
• • • We do not use the following data for averages, fits, limits, etc. • • •
18
 2016
BELL ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.2 - 1.4$ GeV
1  Limit from prompt lepton number violating trilepton search.
2  Limit from displaced lepton violating or conserving trilepton searches.
3  ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , 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.
4  Limit requires muon kinetic energy $>$ 1.2 MeV.
5  Search for ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ .
6  Search for ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ .
7  DAUM 2000 quotes a branching ratio bound B( ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ ) $<$ $6.0 \times 10^{-10}$ at 95$\%$ CL.
8  ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit X}}$ .
9  ${{\mathit D}_{{s}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit X}}$ .
10  Search for prompt ${{\mathit \nu}_{{x}}}$ decay signatures.
11  Search for displaced ${{\mathit \nu}_{{x}}}$ decay signatures.
12  Search for Heavy Neutral Leptons produced by neutral current muon neutrino interactions, with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \nu}_{{\mu}}}$ .
13  ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}_{ {{\mathit \mu}} {{\mathit x}} }$ and ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $<$ ${\mathit m}_{{{\mathit \mu}}}$ + ${\mathit m}_{{{\mathit \pi}}}$.
14  BERNARDI 1988 also considers bounds on $\vert {{\mathit U}}_{ {{\mathit e}} {{\mathit x}} }{{\mathit U}}_{ {{\mathit \mu}} {{\mathit x}} }\vert$.
15  ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \pi}^{+}}$ .
16  ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ .
17  ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ or ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \pi}^{+}}$ .
18  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.
References:
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
 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
 VILAIN 1995C
PL B351 387 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