Sensitivity to habitable planets in the \textit{Roman} microlensing
  survey
  We study the \textit{Roman} sensitivity to exoplanets in the Habitable Zone
(HZ). The \textit{Roman}~efficiency for detecting habitable planets is
maximized for three classes of planetary microlensing events with close caustic
topologies. (a) The events with the lens distances of $D_{\rm l} \gtrsim 7$
kpc, the host lens masses of $M_{\rm h}\gtrsim 0.6M_{\odot}$. By assuming
Jupiter-mass planets in the HZs, these events have $q\lesssim 0.001$ and
$d\gtrsim 0.17$ ($q$ is their mass ratio and $d$ is the projected planet-host
distance on the sky plane normalized to the Einstein radius). The events with
primary lenses, $M_{\rm h} \lesssim 0.1 M_{\odot}$, while their lens systems
are either (b) close to the observer with $D_{\rm l}\lesssim 1$ kpc or (c)
close to the Galactic bulge, $D_{\rm l}\gtrsim 7$ kpc. For Jupiter-mass planets
in the HZs of the primary lenses, the events in these two classes have
$q\gtrsim 0.01$, $d\lesssim 0.04$. The events in the class (a) make larger
caustics. By simulating planetary microlensing events detectable by
\textit{Roman},~we conclude that the \textit{Roman}~efficiencies for detecting
Earth- and Jupiter-mass planets in the Optimistic HZs (OHZs, which is the
region between $[0.5,~2]$ AU around a Sun-like star) are $0.01\%$ and $5\%$,
respectively. If we assume that one exoplanet orbits each microlens in
microlensing events detectable by \textit{Roman}~( i.e., $\sim 27000$ ),~this
telescope has the potential to detects $35$ exoplanets with the projected
planet-host distances in the OHZs with only one having a mass $\lesssim
10M_{\oplus}$. According to the simulation, $27$ of these exoplanets are
actually in the OHZs.
