  This thesis covers a range of experimental and theoretical efforts to
elucidate the origin of the $4.8\sigma$ MiniBooNE low energy excess (LEE). We
begin with the follow-up MicroBooNE experiment, which took data along the BNB
from 2016 to 2021. This thesis specifically presents MicroBooNE's search for
$\nu_e$ charged-current quasi-elastic (CCQE) interactions consistent with
two-body scattering. The two-body CCQE analysis uses a novel reconstruction
process, including a number of deep-learning-based algorithms, to isolate a
sample of $\nu_e$ CCQE interaction candidates with $75\%$ purity. The analysis
rules out an entirely $\nu_e$-based explanation of the MiniBooNE excess at the
$2.4\sigma$ confidence level. We next perform a combined fit of MicroBooNE and
MiniBooNE data to the popular $3+1$ model; even after the MicroBooNE results,
allowed regions in $\Delta m^2$-$\sin^2 2_{\theta_{\mu e}}$ parameter space
exist at the $3\sigma$ confidence level. This thesis also demonstrates that the
MicroBooNE data are consistent with a $\overline{\nu}_e$-based explanation of
the MiniBooNE LEE at the $<2\sigma$ confidence level. Next, we investigate a
phenomenological explanation of the MiniBooNE excess combining the $3+1$ model
with a dipole-coupled heavy neutral lepton (HNL). It is shown that a 500 MeV
HNL can accommodate the energy and angular distributions of the LEE at the
$2\sigma$ confidence level while avoiding stringent constraints derived from
MINER$\nu$A elastic scattering data. Finally, we discuss the Coherent
CAPTAIN-Mills experiment--a 10-ton light-based liquid argon detector at Los
Alamos National Laboratory. The background rejection achieved from a novel
Cherenkov-based reconstruction algorithm will enable world-leading sensitivity
to a number of beyond-the-Standard Model physics scenarios, including
dipole-coupled HNLs.
