Sensitivities to secret neutrino interaction at FASERν

We study the impact of coupling neutrinos with a new light neutral gauge boson, $Z^\prime$, mass less than 500 {\rm MeV} in FASER$\nu$ experiment. Scenarios which boson is coupled to are motivated within numerous contexts designed explain various anomalies particle physics and cosmology. This interaction leads decay mode for charged mesons lepton plus neutrino $Z^{\prime}$, ($\pi^+(K^+)\to e^+ \nu Z^\prime$) followed by subsequent $Z^\prime$ into pair anti-neutrino, ($Z^\prime \to \nu\bar{\nu}$). FASER$\nu$, Forward Search Experiment at LHC, has potential detect collider first time. In particular, emulsion detector will provide opportunity $\tau$-neutrinos measure their energies. Using this ability detector, we investigate experiment proposed upgraded version experiment, FASER2$\nu$, constrain boson.