Sensitivities to secret neutrino interaction at meson decay and short baseline neutrino experiments

Scenarios in which a light gauge boson with a mass of $mathcal{O}(100)$ MeV is coupled to neutrinos are motivated by numerous contexts which are designed to explain various anomalies in particle physics and cosmology. This interaction leads to a new decay mode for charged mesons to a light lepton plus neutrino and new gauge boson $Z^prime$, ($Mto l nu Z^prime$) followed by the subsequent decay of $Z^prime$ into the pair of neutrino and anti-neutrino, ($Z^primetonubar{nu}$). We investigate the impact of this new coupling in meson decay and short-baseline neutrino experiments. Moreover, we explain how meson decay experiments such as NA62 and PIENU as well as short-baseline experiments such as DUNE near detector and FASER$nu$ can constrain the scenario.