Euclid preparation. Galaxy 2-point correlation function modelling in redshift space

The Euclid satellite will measure spectroscopic redshifts for tens of millions of emission-line galaxies. In the context of Stage-IV surveys, the 3-dimensional clustering of galaxies plays a key role in providing cosmological constraints. In this paper, we conduct a model comparison for the multipole moments of the galaxy 2-point correlation function (2PCF) in redshift space. We test state-of-the-art models, in particular the effective field theory of large-scale structure (EFT), one based on the velocity difference generating function (VDG$_{\infty}$), and different variants of Lagrangian perturbation theory (LPT) models, such as convolutional LPT (CLPT) and its effective-field-theory extension (CLEFT). We analyse the first three even multipoles of the 2PCF in the Flagship 1 simulation, which consists of four snapshots at $z\in\{0.9,1.2,1.5,1.8\}$. We study both template-fitting and full-shape approaches and find that with the template-fitting approach, only the VDG$_{\infty}$ model is able to reach a minimum fitting scale of $s_{\rm min}=20\,h^{-1}\,{\rm Mpc}$ at $z=0.9$ without biasing the recovered parameters. Indeed, the EFT model becomes inaccurate already at $s_{\rm min}=30\,h^{-1}\,{\rm Mpc}$. Conversely, in the full-shape analysis, the CLEFT and VDG$_{\infty}$ models perform similarly well, but only the CLEFT model can reach $s_{\rm min}=20\,h^{-1}\,{\rm Mpc}$ while the VDG$_{\infty}$ model is unbiased down to $s_{\rm min}=25\,h^{-1}\,{\rm Mpc}$ at the lowest redshift. Overall, in order to achieve the accuracy required by Euclid, non-perturbative modelling such as in the VDG$_{\infty}$ or CLEFT models should be considered. At $z=1.8$, the CLPT model is sufficient to describe the data with high figure of merit. This comparison selects baseline models that perform best in ideal conditions and sets the stage for an optimal analysis of Euclid data in configuration space.