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.
