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The polarimetric observations on the protoplanetary disk around HL Tau haveshown the scattering-induced polarization at ALMA Band 7, which indicates thatthe maximum dust size is $\sim 100~{\rm \mu m}$, while the Spectral EnergyDistribution (SED) has suggested that the maximum dust size is $\sim$ mm. Tosolve the contradiction, we investigate the impact of differential settling ofdust grains on the SED and polarization. If the disk is optically thick, longerobserving wavelength traces more interior layer which would be dominated bylarger grains. We find that, the SED of the center part of the HL Tau disk canbe 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 turbulencestrength parameter $\alpha_{\rm t}$ is lower than $10^{-5}$. We also find thatthe observed polarization fraction can be potentially explained with themaximum dust size of $1~{\rm mm}$ if $\alpha_{\rm t}\lesssim10^{-5}$, althoughmodels with $160~{\rm \mu m}$-sized grains are also acceptable. However, if themaximum dust size is $\sim3~{\rm mm}$, the simulated polarization fraction istoo low to explain the observations even if the turbulence strength isextremely small, indicating the maximum dust size of $\lesssim1$ mm. Thedegeneracy between 100 ${\rm \mu m}$-sized and mm-sized grains can be solved byimproving the ALMA calibration accuracy or polarimetric observations at(sub-)cm wavelengths.

Impact of Differential Dust Settling on the SED and Polarization: Application to the Inner Region of the HL Tau Disk