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In the presence of extra neutrino states at high scales, the low-energyeffective $3\times 3$ leptonic mixing matrix (LMM) is in general non-unitary.We revisit the question of what is our current knowledge of individual LMMmatrix elements without assuming unitarity. We define two minimal sets ofexperimental constraints -- direct $+$ inherent bounds and indirect bounds, andanalyze the implications of each set on leptonic non-unitarity. In addition, weclarify the treatment of flux and cross-section predictions, taking intoaccount NP contamination in hadronic inputs. We use the currently runningFASER$\nu$ experiment as a case study in order to demonstrate the sensitivityof collider neutrino experiments to leptonic non-unitarity. We find thatindirect bounds constrain LMM non-unitarity to below the $10^{-3}$ level,stronger than current CKM non-unitarity constraints. Conversely, consideringonly direct and inherent bounds we find that ${\cal O}(1)$ unitarity violationis viable at $2\sigma$, and will be probed by the FASER$\nu$ experiment in thecurrent run of the LHC.

Revisiting leptonic non-unitarity in light of FASER$\nu$