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

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
$<2 \times 10^{-4}$ 95 1
 2021
Near ${\mathit m}_{\mathrm {{}^{7}\mathrm {Be}}}−$ ${\mathit m}_{\mathrm {{}^{7}\mathrm {Li}}}$ kin. thres.
$<1 \times 10^{-9}$ 90 2
 2020
NA62 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $150 - 400$ MeV
$<2 \times 10^{-5}$ 95 3
 2019 F
ATLS ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $15 - 40$ GeV
$<1 \times 10^{-9}$ 90 4
 2019 B
T2K Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres.
$<1 \times 10^{-4}$ 90 5
 2019 AL
BES3 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.3 - 0.7$ GeV
$<1 \times 10^{-8}$ 90 6
 2018 A
PIEN ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $60 - 120$ MeV
$<3 \times 10^{-7}$ 90 7
 2018
NA62 ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $200 - 400$ MeV
$<1 \times 10^{-6}$ 90 8
 2016
BELL ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 1.4 GeV
$<3 \times 10^{-5}$ 90 9
 2013
BELL Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $2 - 2.5$ GeV
$<3 \times 10^{-5}$ 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
$<1 \times 10^{-5}$ 90 12
 1993
Near ${\mathit m}_{{{\mathit \pi}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres.
$<2 \times 10^{-7}$ 90 12
 1993
Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres.
$<1 \times 10^{-7}$ 13, 14
 1988
CNTR Near ${\mathit m}_{{{\mathit \pi}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres.
$<2 \times 10^{-9}$ 15, 14
 1988
CNTR Near ${\mathit m}_{{{\mathit K}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres.
$<1 \times 10^{-7}$ 90 16
 1986
CHRM Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres.
$<1 \times 10^{-7}$ 90 17
 1985
BEBC Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit e}}}$ kin. thres.
 1 Search in electron capture decay ${}^{7}\mathrm {Be}$ $\rightarrow$ ${}^{7}\mathrm {Li}$ ${{\mathit \nu}_{{x}}}$ . Kinematic threshold is $\sim{}$850 keV.
 2 Search for ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ . Assumes lifetime of ${{\mathit \nu}_{{x}}}$ $>$ 50 ns.
 3 Limit from prompt lepton number violating trilepton search.
 4 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}$ $_{ {{\mathit e}} {{\mathit x}} }$. 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.
 5 Searches for a Majorana Heavy Neutral Lepton producing a ${{\mathit \pi}^{-}}{{\mathit e}^{+}}$ resonance in the same sign dilepton decay ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{+}}$ .
 6 Search for ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ .
 7 Search for ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ .
 8 PARK 2016 quotes an approximate limit B( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ ) $<$ $3 \times 10^{-6}$ in the mass range ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.2 - 1.4$ GeV.
 9 Search for ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ .
 10 Search for prompt ${{\mathit \nu}_{{x}}}$ decay signatures.
 11 Search for displaced ${{\mathit \nu}_{{x}}}$ decay signatures.
 12 Searches for ${{\mathit K}}$ or ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \nu}_{{e}}}$ using a beam dump experiment at the 70 GeV Serpukhov proton synchrotron. BARANOV 1993 also considers limits for $\vert {{\mathit U}}$ $_{ {{\mathit e}} {{\mathit x}} }{{\mathit U}}$ $_{ {{\mathit \mu}} {{\mathit x}} }\vert$ from ${{\mathit K}}$ or ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{x}}}$ , ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \nu}_{{e}}}$ .
 13 ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}$ $_{ {{\mathit e}} {{\mathit x}} }$.
 14 BERNARDI 1988 also considers bounds on $\vert {{\mathit U}}$ $_{ {{\mathit e}} {{\mathit x}} }{{\mathit U}}$ $_{ {{\mathit \mu}} {{\mathit x}} }\vert$.
 15 ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay through ${{\mathit U}}$ $_{ {{\mathit e}} {{\mathit x}} }$.
 16 ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ .
 17 ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ or ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit \pi}^{+}}$ .
References:
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PRL 126 021803 Limits on the Existence of sub-MeV Sterile Neutrinos from the Decay of $^7$Be in Superconducting Quantum Sensors
 CORTINA-GIL 2020
PL B807 135599 Search for heavy neutral lepton production in $K^+$ decays to positrons
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
 ABLIKIM 2019AL
PR D99 112002 Search for heavy Majorana neutrino in lepton number violating decays of $D\to K \pi e^+ e^+$
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PR D97 072012 Improved search for heavy neutrinos in the decay $\pi\rightarrow e\nu$
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PL B778 137 Search for heavy neutral lepton production in $K^+$ decays
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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
 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
 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
 BARANOV 1993
PL B302 336 Search for Heavy Neutrinos at the IHEP-JINR Neutrino Detector
 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