Testing the nonunitarity of the leptonic mixing matrix at $\mathrm{FASER}v$ and $\mathrm{FASER}v2$

The $\mathrm{FASER}\nu$ experiment has detected the first neutrino events coming from LHC. Near future high-statistic neutrino samples will allow us to search for new physics within the neutrino sector. Motivated by the forthcoming promising $\mathrm{FASER}\nu$ neutrino data, and its successor, $\mathrm{FASER}\nu 2$, we study its potential for testing the unitarity of the neutrino lepton mixing matrix. Although it would be challenging for $\mathrm{FASER}\nu$ and $\mathrm{FASER}\nu 2$ to have strong constraints on this kind of new physics, we discuss its role in contributing to a future improved global analysis.