Left panel: Marginalised 2D constraints at confidence intervals of 68.3% and 99.5%, on the nuisance parameters (bias and counter-term) from the 2PCF analysis (grey shaded areas) against the joint 2PCF and 3PCF analysis for several values of $r_{\min }^{3\mathrm{PCF}}$ at z = 1.5 (dashed blue lines, dashed orange lines, and green shaded areas). All cases assume η = 3; see Eq. (40). The vertical grey band is an estimate of the linear bias b₁ obtained from a comparison of the galaxy power spectrum with measurements of the matter power spectrum in Euclid Collaboration: Pezzotta et al. (2024). Right panel: Marginalised 2D constraints at confidence intervals of 68.3% and 99.5%, on the nuisance parameters (bias and counter-term) from the joint 2PCF-3PCF analysis at z = 1.5 for $r_{\min }^{3\mathrm{PCF}}=30h^{-1}\mathrm{Mpc}$ (red contours) compared to the same set-up but with the assumption of the b_𝒢2(b₁) bias relation alone (red contours) and the combination of the relations b_𝒢2(b₁) and b_Γ3(b₁) (violet contours).