Consistency of cosmic shear analyses in harmonic and real space
  Recent cosmic shear studies have reported discrepancies of up to $1\sigma$ on
the parameter ${S_{8}=\sigma_{8}\sqrt{\Omega_{\rm m}/0.3}}$ between the
analysis of shear power spectra and two-point correlation functions, derived
from the same shear catalogs. It is not a priori clear whether the measured
discrepancies are consistent with statistical fluctuations. In this paper, we
investigate this issue in the context of the forthcoming analyses from the
third year data of the Dark Energy Survey (DES-Y3). We analyze DES-Y3 mock
catalogs from Gaussian simulations with a fast and accurate importance sampling
pipeline. We show that the methodology for determining matching scale cuts in
harmonic and real space is the key factor that contributes to the scatter
between constraints derived from the two statistics. We compare the published
scales cuts of the KiDS, Subaru-HSC and DES surveys, and find that the
correlation coefficients of posterior means range from over 80% for our
proposed cuts, down to 10% for cuts used in the literature. We then study the
interaction between scale cuts and systematic uncertainties arising from
multiple sources: non-linear power spectrum, baryonic feedback, intrinsic
alignments, uncertainties in the point-spread function, and redshift
distributions. We find that, given DES-Y3 characteristics and proposed cuts,
these uncertainties affect the two statistics similarly; the differential
biases are below a third of the statistical uncertainty, with the largest
biases arising from intrinsic alignment and baryonic feedback. While this work
is aimed at DES-Y3, the tools developed can be applied to Stage-IV surveys
where statistical errors will be much smaller.
