  The polarimetric observations on the protoplanetary disk around HL Tau have
shown the scattering-induced polarization at ALMA Band 7, which indicates that
the maximum dust size is $\sim 100~{\rm \mu m}$, while the Spectral Energy
Distribution (SED) has suggested that the maximum dust size is $\sim$ mm. To
solve the contradiction, we investigate the impact of differential settling of
dust grains on the SED and polarization. If the disk is optically thick, longer
observing wavelength traces more interior layer which would be dominated by
larger grains. We find that, the SED of the center part of the HL Tau disk can
be explained with mm-sized grains for a broad range of turbulence strength,
while $160~{\rm \mu m}$-sized grains can explain barely only if the turbulence
strength parameter $\alpha_{\rm t}$ is lower than $10^{-5}$. We also find that
the observed polarization fraction can be potentially explained with the
maximum dust size of $1~{\rm mm}$ if $\alpha_{\rm t}\lesssim10^{-5}$, although
models with $160~{\rm \mu m}$-sized grains are also acceptable. However, if the
maximum dust size is $\sim3~{\rm mm}$, the simulated polarization fraction is
too low to explain the observations even if the turbulence strength is
extremely small, indicating the maximum dust size of $\lesssim1$ mm. The
degeneracy between 100 ${\rm \mu m}$-sized and mm-sized grains can be solved by
improving the ALMA calibration accuracy or polarimetric observations at
(sub-)cm wavelengths.
