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We present the integrated 3-point correlation functions (3PCF) involving boththe cosmic shear and the galaxy density fields. These are a set of higher-orderstatistics that describe the modulation of local 2-point correlation functions(2PCF) by large-scale features in the fields, and which are easy to measurefrom galaxy imaging surveys. Based on previous works on the shear-onlyintegrated 3PCF, we develop the theoretical framework for modelling 5 newstatistics involving the galaxy field and its cross-correlations with cosmicshear. Using realistic galaxy and cosmic shear mocks from simulations, wedetermine the regime of validity of our models based on leading-order standardperturbation theory with an MCMC analysis that recovers unbiased constraints ofthe amplitude of fluctuations parameter $A_s$ and the linear and quadraticgalaxy bias parameters $b_1$ and $b_2$. Using Fisher matrix forecasts for aDES-Y3-like survey, relative to baseline analyses with conventional3$\times$2PCFs, we find that the addition of the shear-only integrated 3PCF canimprove cosmological parameter constraints by $20-40\%$. The subsequentaddition of the new statistics introduced in this paper can lead to furtherimprovements of $10-20\%$, even when utilizing only conservatively large scaleswhere the tree-level models are valid. Our results motivate future work on thegalaxy and shear integrated 3PCFs, which offer a practical way to extendstandard analyses based on 3$\times$2PCFs to systematically probe thenon-Gaussian information content of cosmic density fields.

Beyond 3$\times$2-point cosmology: the integrated shear and galaxy 3-point correlation functions