Neutrino trident production at the intensity frontier

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We have calculated cross sections for the production of lepton pairs by a neutrino incident on a nucleus using both the equivalent photon approximation, and deep inelastic formalism. We find that production of mixed flavour lepton pairs can have production cross sections as high as 35 times those of the traditional muon pair-production process. Rates are estimated for the SHiP and DUNE intensity frontier experiments. We find that multiple trident production modes, some of which have never been observed, represent observable signals over the lifetime of the detectors. Our estimates indicate that the SHiP collaboration should be able to observe on the order of 300 trident events given $2\cdot 10^{20}$ POT, and that the DUNE collaboration can expect approximately 250 trident events in their near detector given 3X10^{22} POT. We also discuss possible applications of the neutrino trident data to be collected at SHiP and DUNE for SM and BSM physics.