Constraining the impact of redshift interlopers on the two-point and three-point correlation functions

Since the early 2000s, the study of the Large Scale Structure of the Universe has become central to cosmology. The European Space Agency Euclid mission promises to significantly advance this field by delivering the most extensive and precise galaxy map to date in optical and infrared bands. However, achieving extreme precision in cosmological measurements, demands rigorous control of systematic effects. Errors in redshift determinations due to noise or spectral line mismatches (noise and line interlopers) can degrade the 2PCF and 3PCF signals. In this study, we assess for the first time the impact of interlopers in the measurement of cosmological parameters with the 3PCF. To do that, we derive and test a new expression for the 3PCF estimator that effectively disentangles the cosmological signal from systematic errors. We implement and test new classes and functions in the CosmoBolognaLib C++ libraries to measure the cross-correlation signal from interlopers for both the 2PCF and 3PCF. Additionally, we assess the impact of redshift interlopers on the 2PCF and 3PCF signals using a galaxy sample from the Euclid official simulations (Flagship 2). Moreover, we model the 2PCF and 3PCF signals considering another large set of Euclid-like simulations (EuclidLargeMocks), comparing pure samples to those contaminated by interlopers. We find that interlopers significantly bias the 2PCF and 3PCF signals, lowering them by more than 30%. Furthermore, we find that cross-correlation signals are crucial in recovering the full 2PCF signal, particularly at low redshifts. We also observe that the linear growth factor, for catalogues affected by interloper contamination is reduced by more than 25% and the linear bias parameter is damped by 20-30%. This work represents the first step in a full self-consistent treatment of realistic data considering systematic effects as expected from the Euclid mission, demonstrating that addressing interloper contamination biases is essential.