A solution to the MiniBooNE excess invoking rare three-body decays of the
charged pions and kaons to new states in the MeV mass scale was recently
proposed as a dark-sector explanation. This class of solution illuminates the
fact that, while the charged pions were focused in the target-mode run, their
decay products were isotropically suppressed in the beam-dump-mode run in which
no excess was observed. This suggests a new physics solution correlated to the
mesonic sector. We investigate an extended set of phenomenological models that
can explain the MiniBooNE excess as a dark sector solution, utilizing
long-lived particles that might be produced in the three-body decays of the
charged mesons and the two-body anomalous decays of the neutral mesons. Over a
broad set of interactions with the long-lived particles, we show that these
scenarios can be compatible with constraints from LSND, KARMEN, and MicroBooNE,
and evaluate the sensitivity of the ongoing and future data taken by the
Coherent CAPTAIN Mills experiment (CCM) to a potential discovery in this
parameter space.Comment: 15 pages, 14 figures. Planned submission for PR