GeV-scale neutrinos: interactions with mesons and DUNE sensitivity

The simplest extension of the SM to account for the observed neutrino masses and mixings is the addition of at least two singlet fermions (or right-handed neutrinos). If their masses lie at or below the GeV scale, such new fermions would be produced in meson decays. Similarly, provided they are sufficiently heavy, their decay channels may involve mesons in the final state. In this work, we provide consistent expressions for the relevant effective operators involving neutrinos and mesons with masses up to 2 GeV. The associated effective Lagrangian has been implemented in FeynRules, allowing for efficient simulation in event generators such as MadGraph5. As an application of this setup, we numerically compute the expected sensitivity of the DUNE near detector to heavy neutrinos in the MeV-GeV range.