  We present the first detailed study of Standard Model (SM) neutrino tridents
involving tau leptons at the near detectors of accelerator neutrino facilities.
These processes were previously thought to be negligible, even at future
facilities like DUNE, based on approximations that underestimated the tau
trident cross sections. Our full $2\to 4$ calculation, including both coherent
and incoherent scatterings, reveals that the DUNE near detector will actually
get a non-negligible number of tau tridents, which is an important background
to new physics searches. We identify promising kinematic features that may
allow distinction of tau tridents from the usual neutrino charged-current
background at DUNE, and thus could establish the observation of tau tridents
for the first time. We also comment on the detection prospects at other
accelerator and collider neutrino experiments.
