Modelling Galaxy Clustering and Tomographic Galaxy-Galaxy Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model and Redshift Self-Calibration

The combination of galaxy-galaxy weak lensing and galaxy clustering is a powerful probe of the cosmological model, and exploration of how to best model and extract this information from the signals is essential. We present the measurement of the galaxy-galaxy weak lensing signals using the SDSS DR11 spectroscopic galaxies as lens galaxies, and the HSC Y3 shear catalog as source galaxies, binned into four tomographic bins by their photometric redshift. The SDSS DR11 galaxies, with a redshift range $0.15<z<0.7$, are binned into three redshift bins, each as a probe for measuring the projected correlation function, $w_p(R_p)$. We measure the galaxy-galaxy lensing signal $\Delta \Sigma (R_p)$ in 12 lens-source bin pairs and show that there is no evidence for significant systematic biases in the measurement with null testing. We combine our $w_p(R_p)$ and $\Delta \Sigma (R_p)$ ($2\times2$pt) data vectors and perform likelihood inference with a flat $\Lambda$CDM model. For $\Delta \Sigma (R_p)$, we extend the lower limit of the scale cut compared to previous HSC Y3 analyses to $2 h^{-1}$Mpc by including a point-mass correction term in addition to the minimal bias model. We present various tests to validate our model and provide extended consistency tests. In the $\Lambda$CDM context, our fiducial model yields $S_8 = 0.804^{+0.051}_{-0.051}$. The $2\times2$pt data vector provides redshift parameter constraints for the third and fourth redshift bins $\Delta z_3 = -0.079^{+0.074}_{-0.084}$, and $\Delta z_4 = -0.203^{+0.167}_{-0.206}$, which is consistent with results from the previous tomographic cosmic shear studies, and serves as the foundation for a future $3\times 2$pt analysis.