Cosmological inference from the emulator based halo model II: Joint
  analysis of galaxy-galaxy weak lensing and galaxy clustering from HSC-Y1 and
  SDSS
  We present high-fidelity cosmology results from a blinded joint analysis of
galaxy-galaxy weak lensing ($\Delta\!\Sigma$) and projected galaxy clustering
($w_{\rm p}$) measured from the Hyper Suprime-Cam Year-1 (HSC-Y1) data and
spectroscopic Sloan Digital Sky Survey (SDSS) galaxy catalogs in the redshift
range $0.15<z<0.7$. We define luminosity-limited samples of SDSS galaxies to
serve as the tracers of $w_{\rm p}$ in three spectroscopic redshift bins, and
as the lens samples for $\Delta\!\Sigma$. For the $\Delta\!\Sigma$
measurements, we select a single sample of 4 million source galaxies over 140
deg$^2$ from HSC-Y1 with photometric redshifts (photo-$z$) greater than 0.75,
enabling a better handle of photo-$z$ errors by comparing the $\Delta\!\Sigma$
amplitudes for the three lens redshift bins. For cosmological parameter
inference, we use an input galaxy-halo connection model built on the {\tt Dark
Emulator} package with a halo occupation distribution that includes nuisance
parameters to marginalize over modeling uncertainties. We model the
$\Delta\!\Sigma$ and $w_{\rm p}$ measurements on scales from $R\simeq 3$ and
$2\,h^{-1}{\rm Mpc}$, respectively, up to $30\,h^{-1}{\rm Mpc}$ assuming a flat
$\Lambda$CDM cosmology. With various tests using mock catalogs described in
Miyatake et al. (2021), we show that any bias in the clustering amplitude
$S_8\equiv \sigma_8(\Omega_{\rm m}/0.3)^{0.5}$ due to uncertainties in the
galaxy-halo connection is less than $\sim50$\% of the statistical uncertainty
of $S_8$, {\it unless} the assembly bias effect is unexpectedly large. Our
best-fit models have $S_8=0.795^{+0.049}_{-0.042}$ (mode and 68\% credible
interval) for the flat $\Lambda$CDM model; we find tighter constraints on the
quantity $S_8(\alpha=0.17)\equiv\sigma_8(\Omega_{\rm m}/0.3)^{0.17}
=0.745^{+0.039}_{-0.031}$. (abriged)
