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

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
$<3 \times 10^{-4}$ 90 1
 2021
ARNT Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}{ {}\lesssim{} }$ 970 MeV
$<3 \times 10^{-6}$ 90 2
 2021
RVUE Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $0.8 - 1.6$ GeV
$<2 \times 10^{-4}$ 90 3
 2002
CHRM Near ${\mathit m}_{{{\mathit D}}}−{\mathit m}_{{{\mathit \tau}}}$ kin. thres.
$<1 \times 10^{-4}$ 90 4
 2002
CHRM ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $200 - 250$ MeV
$<3 \times 10^{-5}$ 95 5
 1997 I
DLPH ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ $6 - 50$ GeV
$<2 \times 10^{-5}$ 95 6
 1997 I
DLPH Near ${\mathit m}_{{{\mathit \nu}_{{x}}}}$ $\sim{}$ 3.5 GeV
 1 Search for ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \nu}}$ .
 2 Reanalysis of CHARM results (cf. ORLOFF 2002 ) to include searches for ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \nu}}{{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ decays, and including the production of HNLs from ${{\mathit \tau}}$ decays.
 3 ${{\mathit D}_{{s}}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \nu}_{{x}}}$ , with ${{\mathit \nu}_{{x}}}$ decay via ${{\mathit U}}$ $_{ {{\mathit \tau}} {{\mathit x}} }$.
 4 ${{\mathit D}_{{s}}}$ $\rightarrow$ ${{\mathit \nu}_{{\tau}}}{{\mathit \tau}^{+}}$ , ${{\mathit \tau}^{+}}$ $\rightarrow$ ${{\mathit \nu}_{{x}}}{{\mathit X}}$ , with ${{\mathit \nu}_{{x}}}$ decay via ${{\mathit U}}$ $_{ {{\mathit \tau}} {{\mathit x}} }$.
 5 Search for prompt ${{\mathit \nu}_{{x}}}$ decay signatures.
 6 Search for displaced ${{\mathit \nu}_{{x}}}$ decay signatures. Kinematical suppression of ${{\mathit \nu}_{{x}}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit X}}$ at lower masses leads to rapid loosening of the $\vert {{\mathit U}}$ $_{ {{\mathit \tau}} {{\mathit x}} }\vert$ bound compared to that for $\vert {{\mathit U}}$ $_{ {{\mathit e}} {{\mathit x}} }\vert$ and $\vert {{\mathit U}}$ $_{ {{\mathit \mu}} {{\mathit x}} }\vert$.
References:
 ACCIARRI 2021
PRL 127 121801
 BOIARSKA 2021
PR D104 095019
 ORLOFF 2002
PL B550 8 Limits on the Mixing of ${{\mathit \tau}}$ Neutrino to Heavy Neutrinos
 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