Non-local contribution from small scales in galaxy-galaxy lensing: Comparison of mitigation schemes

Recent cosmological analyses with large-scale structure and weak lensing measurements, usually referred to as 3$\times$2pt, had to discard a lot of signal-to-noise from small scales due to our inability to accurately model non-linearities and baryonic effects. Galaxy-galaxy lensing, or the position-shear correlation between lens and source galaxies, is one of the three two-point correlation functions that are included in such analyses, usually estimated with the mean tangential shear. However, tangential shear measurements at a given angular scale $\theta$ or physical scale $R$ carry information from all scales below that, forcing the scale cuts applied in real data to be significantly larger than the scale at which theoretical uncertainties become problematic. Recently there have been a few independent efforts that aim to mitigate the non-locality of the galaxy-galaxy lensing signal. Here we perform a comparison of the different methods, including the Y-transformation, the Point-Mass marginalization methodology and the Annular Differential Surface Density statistic. We do the comparison at the cosmological constraints level in a combined galaxy clustering and galaxy-galaxy lensing analysis. We find that all the estimators yield equivalent cosmological results assuming a simulated Rubin Observatory Legacy Survey of Space and Time (LSST) Year 1 like setup and also when applied to DES Y3 data. With the LSST Y1 setup, we find that the mitigation schemes yield $\sim$1.3 times more constraining $S_8$ results than applying larger scale cuts without using any mitigation scheme.