Dark Energy Survey Year 6 results: Redshift calibration of the MagLim++ lens sample
In this work, we derive and calibrate the redshift distribution of the MagLim++ lens galaxy sample used in the Dark Energy Survey Year 6 (DES Y6) 3 x 2pt cosmology analysis. The 3 x 2pt analysis combines galaxy clustering from the lens galaxy sample and weak gravitational lensing. The redshift distributions are inferred using the SOMPZ method - a Self-Organizing Map framework that combines deep-field multi-band photometry, wide-field data, and a synthetic source injection ( B alrog) catalog. Key improvements over the DES Year 3 (Y3) calibration include a noise-weighted SOM metric, an expanded Balrog catalogue, and an improved scheme for propagating systematic uncertainties, which allows us to generate O(10 8 ) redshift realizations that collectively span the dominant sources of uncertainty. These realizations are then combined with independent clustering-redshift measurements via importance sampling. The resulting calibration achieves typical uncertainties on the mean redshift of 1-2%, corresponding to a 20-30% average reduction relative to DES Y3. We compress the n(z) uncertainties into a small number of orthogonal modes for use in cosmological inference. Marginalizing over these modes leads to only a minor degradation in cosmological constraints. Here, this analysis establishes the MagLim++ sample as a robust lens sample for precision cosmology with DES Y6 and provides a scalable framework for future surveys.