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The integrated shear 3-point correlation function $\zeta_{\pm}$ measures thecorrelation between the local shear 2-point function $\xi_{\pm}$ and the1-point shear aperture mass in patches of the sky. Unlike other higher-orderstatistics, $\zeta_{\pm}$ can be efficiently measured from cosmic shear data,and it admits accurate theory predictions on a wide range of scales as afunction of cosmological and baryonic feedback parameters. Here, we develop andtest a likelihood analysis pipeline for cosmological constraints using$\zeta_{\pm}$. We incorporate treatment of systematic effects from photometricredshift uncertainties, shear calibration bias and galaxy intrinsic alignments.We also develop an accurate neural-network emulator for fast theory predictionsin MCMC parameter inference analyses. We test our pipeline using realisticcosmic shear maps based on $N$-body simulations with a DES Y3-like footprint,mask and source tomographic bins, finding unbiased parameter constraints.Relative to $\xi_{\pm}$-only, adding $\zeta_{\pm}$ can lead to $\approx10-25\%$ improvements on the constraints of parameters like $A_s$ (or$\sigma_8$) and $w_0$. We find no evidence in $\xi_{\pm} + \zeta_{\pm}$constraints of a significant mitigation of the impact of systematics. We alsoinvestigate the impact of the size of the apertures where $\zeta_{\pm}$ ismeasured, and of the strategy to estimate the covariance matrix ($N$-body vs.lognormal). Our analysis solidifies the strong potential of the $\zeta_{\pm}$statistic and puts forward a pipeline that can be readily used to improvecosmological constraints using real cosmic shear data.

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