The High-Energy Frontier of the Intensity Frontier: Closing the Dark Photon, Inelastic Dark Matter, and Muon g-2 Windows

We study hidden sector and long-lived particles at past (CHARM and NuCal), present (NA62 and SeaQuest/DarkQuest), and future (LongQuest) experiments that are at the high-energy frontier of the intensity frontier. We focus on exploring the minimal vector portal and variere-lifetime particles (VLP). VLP models have mostly been devised to explain experimental anomalies while avoiding existing constraints, and we demonstrate that proton fixed-target experiments provide one of the most powerful probes for the sub-GeV to few GeV mass range of the VLP models, using inelastic dark matter (iDM) as an example. We consider an iDM model with small mass splitting that yields the observed dark matter (DM) relic abundance, and a scenario with a sizable mass splitting that can also explain the muon $g-2$ anomaly. We set strong limits based on the CHARM and NuCal experiments, which come close to excluding iDM as full-abundance thermal DM candidates in the MeV to GeV mass range, for the mass arrangements and small mass splittings we consider. We also study the future projections based on NA62 and SeaQuest/DarkQuest, and update the constraints of the minimal dark photon parameter space. We found that NuCal sets the only existing constraint in $\epsilon \sim 10^{-8} - 10^{-4}$ regime reaching $\sim$ 800 MeV in dark photon mass due to the resonant enhancement of the proton bremsstrahlung production. Finally, we propose LongQuest, a three-stage thorough retool of the SeaQuest experiment with short ($\lesssim$ 5 m), medium ($\sim$ 5 m), and long baseline ($\gtrsim$ 35 m) tracking stations/detectors, as a multi-purpose machine to explore dark sector particles with a wide range of couplings to the standard model sector.