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

Neutrino Trident Production at the Intensity Frontier