  We present a search for long-lived Higgs portal scalars (HPS) and heavy
neutral leptons (HNL) decaying in the MicroBooNE liquid-argon time projection
chamber. The measurement is performed using data collected synchronously with
the NuMI neutrino beam from Fermilab's Main Injector with a total exposure
corresponding to $7.01 \times 10^{20}$ protons on target. We set upper limits
at the $90\%$ confidence level on the mixing parameter $\lvert U_{\mu
4}\rvert^2$ ranging from $\lvert U_{\mu 4}\rvert^2<12.9\times 10^{-8}$ for
Majorana HNLs with a mass of $m_{\rm HNL}=246$ MeV to $\lvert U_{\mu
4}\rvert^2<0.92 \times 10^{-8}$ for $m_{\rm HNL}=385$ MeV, assuming $\lvert
U_{e 4}\rvert^2 = \lvert U_{\tau 4}\rvert^2 = 0$ and HNL decays into
$\mu^\pm\pi^\mp$ pairs. These limits on $\lvert U_{\mu 4}\rvert^2$ represent an
order of magnitude improvement in sensitivity compared to the previous
MicroBooNE result. We also constrain the scalar-Higgs mixing angle $\theta$ by
searching for HPS decays into $\mu^+\mu^-$ final states, excluding a contour in
the parameter space with lower bounds of $\theta^2<31.3 \times 10^{-9}$ for
$m_{\rm HPS}=212$ GeV and $\theta^2<1.09 \times 10^{-9}$ for $m_{\rm HPS}=275$
GeV. These are the first constraints on the scalar-Higgs mixing angle $\theta$
from a dedicated experimental search in this mass range.
