Search for Lepton Flavor Violating Decay at FASER

FASER is one of the promising experiments which search for long-lived particles beyond the Standard Model. In this paper, we consider charged lepton flavor violation (CLFV) via a light and weakly interacting boson and discuss the detectability by FASER. We focus on four types of CLFV interactions, i.e., the scalar-, pseudoscalar-, vector-, and dipole-type interaction, and calculate the sensitivity of FASER to each CLFV interaction. We show that, with the setup of FASER2, a wide region of the parameter space can be explored. Particularly, it is found that FASER2 has a sensitivity to very small coupling regions in which the rare muon decays, such as $\mu \rightarrow e\gamma$, cannot place bounds, and that there is a possibility to detect CLFV decays of the new light bosons.