  The DUNE near detector will collect an unprecedented large number of neutrino
interactions, allowing the precise measurement of rare processes such as
neutrino trident production, i.e. the generation of a lepton-antilepton pair
through the scattering of a neutrino off a heavy nucleus. The event rate of
this process is a powerful probe to a well-motivated parameter space of new
physics beyond the Standard Model. In this paper, we perform a detailed
sensitivity study of the DUNE near detector to neutrino tridents. We provide
state-of-the-art predictions for the Standard Model cross sections and
corresponding event rates at the near detector for the nu_mu -> nu_mu mu^+
mu^-, nu_mu -> nu_mu e^+e^- and nu_mu -> nu_e e^+ mu^- trident interactions
(and the corresponding anti-neutrino modes), discussing their uncertainties. We
analyze all relevant backgrounds, utilize a Geant4-based simulation of the
DUNE-near detector liquid argon TPC (the official DUNE simulation at the time
of writing this paper), and identify a set of selection cuts that would allow
the DUNE near detector to measure the nu_mu -> nu_mu mu^+ mu^- cross section
with a ~25% accuracy after running in neutrino and anti-neutrino modes for ~3
years each. This would lead to the most precise measurement of the trident
process, surpassing the previous measurement by the CCFR collaboration. We show
that this measurement would be highly sensitive to new physics, and, in
particular, we find that the parameter space of models with gauged L_mu - L_tau
that can explain the (g-2)_mu anomaly could be covered almost entirely. As a
byproduct, a new Monte Carlo tool to generate neutrino trident events is made
publicly available.
