Neutrino trident production at the intensity frontier

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 flavor lepton pairs can have production cross sections as high as 35 times those of the traditional nu(mu) -> nu(mu)mu(+) mu(-) 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 x 10(20) protons on target and that the DUNE Collaboration can expect approximately 250 trident events in their near detector given 3 x 10(22) protons on target. We also discuss possible applications of the neutrino trident data to be collected at SHiP and DUNE for Standard Model and beyond the Standard model physics.