Z' Mediated right-handed Neutrinos from Meson Decays at the FASER

We investigate the pair production of right-handed neutrinos mediated by a $Z^\prime$ mainly from the meson decays at the FASER detector of the HL-LHC. The $Z^\prime$ can be the additional gauge boson in either the $U(1)_{B-L}$ or sterile $\nu$-specific $U(1)_s$ model. Taking the gauge coupling or the kinetic mixing at the current limits, we analyse the sensitivity to the masses of the heavy neutrinos, $M_N$, and active-sterile mixing, $|V_{lN}|^2$, of the FASER2. In a background free scenario, for the $U(1)_{B-L}$ case, FASER2 is able to probe $|V_{lN}|^2 \approx 10^{-8}$ when $M_N \sim 0.3$ GeV, which is comparable to the current limits from the beam dump experiments. When comes to the $U(1)_s$ model, FASER2 can probe $|V_{lN}|^2 \approx 10^{-10}$, which is better than the current limits for at least one magnitude, in all three flavours. A proposed long-lived particle detector, FACET, is also studied, while no significant difference from FASER2 is derived.