Dark Energy Survey Year 6 Results: Redshift Calibration of the Weak Lensing Source Galaxies

Determining the distribution of redshifts for galaxies in wide-field photometric surveys is essential for robust cosmological studies of weak gravitational lensing. We present the methodology, calibrated redshift distributions, and uncertainties of the final Dark Energy Survey Year 6 (Y6) weak lensing galaxy data, divided into four redshift bins centered at $\langle z \rangle = [0.414, 0.538, 0.846, 1.157]$. We combine independent information from two methods on the full shape of redshift distributions: optical and near-infrared photometry within an improved Self-Organizing Map $p(z)$ (SOMPZ) framework, and cross-correlations with spectroscopic galaxy clustering measurements (WZ), which we demonstrate to be consistent both in terms of the redshift calibration itself and in terms of resulting cosmological constraints within 0.1$\sigma$. We describe the process used to produce an ensemble of redshift distributions that account for several known sources of uncertainty. Among these, imperfection in the calibration sample due to the lack of faint, representative spectra is the dominant factor. The final uncertainty on mean redshift in each bin is $\sigma_{\langle z\rangle} = [0.012, 0.008,0.009, 0.024]$. We ensure the robustness of the redshift distributions by leveraging new image simulations and a cross-check with galaxy shape information via the shear ratio (SR) method.