Hyper Suprime-Cam Y3 results: Photo- z bias calibration with lensing shear ratios and cosmological constraints from cosmic shear

We present an independent calibration of the photometric redshift (photo-$z$) distributions for source galaxies in the HSC-Y3 weak lensing survey using small-scale galaxy-galaxy lensing. By measuring the tangential shear around spectroscopic lens galaxies from GAMA, SDSS, and DESI, divided into fifteen narrow redshift bins, we compute shear ratios that are sensitive to the mean redshift of source galaxies. Using a blinded analysis, we derive constraints on the photo-$z$ bias parameters in source bins 2, 3 and 4, achieving signal-to-noise ratios of 59, 75, and 62, respectively. Our constraints for $Δz_2$, $Δz_3$ and $Δz_4$ are consistent with those from HSC-Y3 cosmic shear modeling. We observe a mild shift in the $Δz_3$--$Δz_4$ plane due to the heterogeneous depth of the lens sample, which disappears when using only DESI-DR1 lenses. Combining shear-ratio measurements with cosmic shear data, we obtain joint constraints on cosmological parameters: $Ω_{\rm m} = 0.304_{-0.029}^{+0.03}$ and $S_8 = 0.773_{-0.031}^{+0.031}$, consistent with cosmic shear-only results. This work demonstrates the utility of small-scale lensing as an independent probe for calibrating photometric redshift bias in weak lensing cosmology.