Probabilistic characterization of blending with LSST and application to cluster lensing cosmology

Next-generation galaxy surveys, like the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), will deliver unprecedented depth and sky coverage, enabling precise measurements of cosmic probes such as weak lensing and galaxy clustering. However, increased imaging depth leads to significant blending of galaxy images, particularly in dense fields like galaxy clusters. This blending, exacerbated by atmospheric blurring in ground-based observations, contaminates galaxy property measurements and causes source confusion. To simultaneously capture these effects, we develop a probabilistic framework introducing the blending entropy, a metric quantifying the ambiguity in matching detected objects to true galaxies or external reference sources. Using simulated data from the DESC Data Challenge 2 (DC2), we characterize blending in LSST data and quantify its impact on cluster lensing cosmology around cosmoDC2 halos. We demonstrate that imposing a blending entropy threshold of $S_b