Simulating heavy neutral leptons with general couplings at collider and fixed target experiments

Heavy neutral leptons (HNLs) are motivated by attempts to explain neutrino masses and dark matter. If their masses are in the MeV to several GeV range, HNLs are light enough to be copiously produced at collider and accelerator facilities, but also heavy enough to decay to visible particles on length scales that can be observed in particle detectors. Previous studies evaluating the sensitivities of experiments have often focused on simple but not particularly well-motivated models in which the HNL mixes with only one active neutrino flavor. In this work, we accurately simulate models for HNL masses between 100 MeV and 10 GeV and arbitrary couplings to $e$, $\mu$, and $\tau$ leptons. We include over 150 HNL production channels and over 100 HNL decay modes, including all of the processes that can be dominant in some region of the general parameter space. The result is HNLCalc, a user-friendly, fast, and flexible library to compute the properties of HNL models. As examples, we implement HNLCalc to extend the FORESEE package to evaluate the prospects for HNL discovery at forward LHC experiments. We present sensitivity reaches for FASER and FASER2 in five benchmark scenarios with coupling ratios $|U_e{|}^2:|U_{\mu }{|}^2:|U_{\tau }{|}^2=1:0:0$, $0:1:0$, $0:0:1$, $0:1:1$, and $1:1:1$, where the latter two have not been studied previously. Comparing these to current constraints, we identify regions of parameter space with significant discovery prospects.