Cross-correlations between galaxy weak lensing (WL) and Cosmic Microwave Background (CMB) lensing are a powerful tool to probe matter fluctuations at intermediate redshifts and to detect residual systematics in either probe. In this paper, we study the cross-correlation of galaxy WL from the Hyper Suprime-Cam Subaru Strategic Program (HSC) first data release and CMB lensing from the final Planck data release, for HSC source galaxies at 0.3< z < 1.5. HSC is the deepest Stage-III galaxy WL survey, and provides both a great opportunity to study the high-redshift universe and new challenges related to its exceptionally high source density, such as source blending. The cross-correlation signal is measured at a significance level of 3.1$sigma$. The amplitude of our best-fit model with respect to the best-fit 2018 Planck cosmology is $A = 0.81pm 0.25$, consistent with $A=1$. Our result is also consistent with previous CMB lensing and galaxy WL cross-correlation studies using different surveys. We perform tests with respect to the WL $B$-modes, the point-spread-function, photometric redshift errors, and thermal Sunyaev-Zeldovich leakage, and find no significant evidence of residual systematics.
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