The contribution from small scales on two-point shear analysis: comparison between power spectrum and correlation function

A known problem in cosmic shear two-point statistics is the apparent inconsistency between analyses performed in harmonic space (power spectrum) and real space (angular correlation). This arises mainly from two factors: first, scale cuts in one space correspond to soft cuts in the other, as the relationship between the two spaces is mediated by Bessel functions. For the same reason, astrophysical effects that are compact in one space may not be in the other, which can lead to biased parameter estimates. In this paper, we argue that these two statistics are complementary: we expect a robust theory to provide consistent constraints regardless of the chosen scale cuts. We present the consequences of pushing our analysis to smaller scales in both spaces, accounting for different models of Intrinsic Alignment and Baryonic Feedback in HSC Y3 data: we find that the harmonic-space analysis is significantly less sensitive to the specific modeling of small-scale physics, with model-choice-driven biases in $S_8$ being 2-3 times smaller than in real space. We show that using a flexible, simulation-based emulator for baryonic feedback (BACCO) in combination with the TATT model for intrinsic alignments provides the most consistent cosmological constraints between the two spaces when pushing to the smallest scales. In contrast, the standard HMCode-2016 model results in a $\sim 1.1\sigma$ tension between the two statistics. While harmonic space appears more robust for cosmological inference given current model uncertainties, real-space analyses offer a clearer separation of baryonic effects and will play a crucial role in distinguishing between baryonic feedback models in upcoming surveys.