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

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In recent years, a number of intensity frontier experiments have been proposed to search for feebly interacting particles with masses in the GeV range. We discuss how the characteristic shape of the experimental sensitivity regions — upper and lower boundaries of the probed region, the maximal mass reach — depends on the parameters of the experiments. We use the SHiP and the MATHUSLA experiments as examples. We find a good agreement of our estimates with the results of the Monte Carlo simulations. This simple approach allows to cross-check and debug Monte Carlo results, to scan quickly over the parameter space of feebly interacting particle models, and to explore how sensitivity depends on the geometry of experiments.