Cosmology from the integrated shear 3-point correlation function: simulated likelihood analyses with machine-learning emulators

The integrated shear 3-point correlation function zeta +/- measures the correlation between the local shear 2-point function xi +/- and the 1-point shear aperture mass in patches of the sky. Unlike other higher-order statistics, zeta +/- can be efficiently measured from cosmic shear data, and it admits accurate theory predictions on a wide range of scales as a function of cosmological and baryonic feedback parameters. Here, we develop and test a likelihood analysis pipeline for cosmological constraints using zeta +/-. We incorporate treatment of systematic effects from photometric redshift uncertainties, shear calibration bias and galaxy intrinsic alignments. We also develop an accurate neural-network emulator for fast theory predictions in MCMC parameter inference analyses. We test our pipeline using realistic cosmic shear maps based on N-body simulations with a DES Y3-like footprint, mask and source tomographic bins, finding unbiased parameter constraints. Relative to xi +/--only, adding zeta +/- can lead to approximate to 10 - 25% improvements on the constraints of parameters like As (or sigma 8) and w0. We find no evidence in xi +/- + zeta +/- constraints of a significant mitigation of the impact of systematics. We also investigate the impact of the size of the apertures where 'f is measured, and of the strategy to estimate the covariance matrix (N-body vs. lognormal). Our analysis solidifies the strong potential of the Cf statistic and puts forward a pipeline that can be readily used to improve cosmological constraints using real cosmic shear data.