On the wave optics effect on primordial black hole constraints from
  optical microlensing search
  Microlensing of stars, e.g. in the Galactic bulge and Andromeda galaxy (M31),
is among the most robust, powerful method to constrain primordial black holes
(PBHs) that are a viable candidate of dark matter. If PBHs are in the mass
range $M_{\rm PBH} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}
10^{-10}M_\odot$, its Schwarzschild radius ($r_{\rm Sch}$) becomes comparable
with or shorter than optical wavelength ($\lambda)$ used in a microlensing
search, and in this regime the wave optics effect on microlensing needs to be
taken into account. For a lensing PBH with mass satisfying $r_{\rm Sch}\sim
\lambda$, it causes a characteristic oscillatory feature in the microlensing
light curve, and it will give a smoking gun evidence of PBH if detected,
because any astrophysical object cannot have such a tiny Schwarzschild radius.
Even in a statistical study, e.g. constraining the abundance of PBHs from a
systematic search of microlensing events for a sample of many source stars, the
wave effect needs to be taken into account. We examine the impact of wave
effect on the PBH constraints obtained from the $r$-band (6210\AA) monitoring
observation of M31 stars in Niikura et al. (2019), and find that a finite
source size effect is dominant over the wave effect for PBHs in the mass range
$M_{\rm PBH}\simeq[10^{-11},10^{-10}]M_\odot$. We also discuss that, if a
denser-cadence (10~sec), $g$-band monitoring observation for a sample of white
dwarfs over a year timescale is available, it would allow one to explore the
wave optics effect on microlensing light curve, if it occurs, or improve the
PBH constraints in $M_{\rm PBH}\lower.5ex\hbox{$\; \buildrel < \over \sim \;$}
10^{-11}M_\odot$ even from a null detection.
