Flavorful Lepton Number Violation at the EIC

We explore the prospects of detecting flavorful lepton number violation at the Electron-Ion Collider (EIC) through resonant production of heavy neutral leptons (HNLs), resulting in $e^- p \to \ell^+_\alpha + k\, j+X$, where $\alpha \in \{e, \mu, \tau \}$ and $k$ denotes the number of jets. We work in the $\nu$SMEFT framework of the Standard Model Effective Field Theory augmented with $n$ singlet HNLs, one of which is in the mass range $10-100$~GeV, within kinematic reach of the EIC. To explore the EIC sensitivity, we focus on the HNL production mechanism induced by mixing with light neutrinos. We study kinematic distributions for signal and backgrounds, including hadronization and detector effects, and suggest a set of cuts to minimize backgrounds. In the mass range considered, we find that the EIC with muon detection capabilities and an integrated luminosity of $100~\mathrm{fb}^{-1}$ can reach sensitivities comparable to the strongest direct (LHC) and indirect constraints, and is especially relevant in the $\nu$SMEFT framework beyond dimension four. Our study motivates further assessment of muon detection capabilities at the EIC and $\tau$ hadronic reconstruction, as well as a more general theoretical analysis involving production mechanisms mediated by higher-dimensional operators in the effective theory.