Sensitivity of the intensity frontier experiments for neutrino and scalar portals: analytic estimates

In recent years, a number of intensity-frontier experiments have been proposed to search for feebly interacting particles with a mass in the GeV range. We show analytically how the characteristic shape of the sensitivity regions of such experiments - upper and lower boundaries of the probed region, the maximal mass reach - depends on the parameters of the experiments, taking the SHiP and the MATHUSLA experiments as an example. We find a good agreement of our estimates with the results of the Monte Carlo simulations.