Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear two-point correlation functions

We perform a blinded cosmology analysis with cosmic shear two-point correlation functions measured from more than 25 million galaxies in the Hyper Suprime-Cam three-year shear catalog in four tomographic redshift bins ranging from 0.3 to 1.5. After conservative masking and galaxy selection, the survey covers 416 deg(2) of the northern sky with an effective galaxy number density of 15 arcmin(-2) over the four redshift bins. The 2PCFs adopted for cosmology analysis are measured in the angular range; 7.1 < theta/arcmin < 56.6 for xi(+) and 31.2 < theta/arcmin < 248 for xi(-), with a total signal-to-noise ratio of 26.6. We apply a conservative, wide, flat prior on the photometric redshift errors on the last two tomographic bins, and the relative magnitudes of the cosmic shear amplitude across four redshift bins allow us to calibrate the photometric redshift errors. With this flat prior on redshift errors, we find Omega(m) = 0.256(-0.044)(+0.056) and S-8 = sigma(8) root Omega(m)/0.3 = 0.769(-0.034)(+0.031) (both 68% C.I.) for a flat. cold dark matter cosmology. We find, after unblinding, that our constraint on S-8 is consistent with the Fourier space cosmic shear and the 3 x 2 pt analyses on the same HSC dataset. We carefully study the potential systematics from astrophysical and systematic model uncertainties in our fiducial analysis using synthetic data, and report no biases (including projection bias in the posterior space) greater than 0.5 sigma in the estimation of S-8. Our analysis hints that the mean redshifts of the two highest tomographic bins are higher than initially estimated. In addition, a number of consistency tests are conducted to assess the robustness of our analysis. Comparing our result with Planck-2018 cosmic microwave background observations, we find a similar to 2 sigma tension for the Lambda CDM model.