The streaming model for the three-point correlation function and its connection to standard perturbation theory

Redshift-space distortions present a significant challenge in building models for the three-point correlation function (3PCF). We compare two possible lines of attack: the streaming model and standard perturbation theory (SPT). The two approaches differ in their treatment of the non-linear mapping from real to redshift space: SPT expands this mapping perturbatively, while the streaming model retains its non-linear form but relies on simplifying assumptions about the probability density function (PDF) of line-of-sight velocity differences between pairs or triplets of tracers. To assess the quality of the predictions and the validity of the assumptions of these models, we measure the monopole of the matter 3PCF and the first two moments of the pair- and triplewise velocity PDF from a suite of N-body simulations. We also evaluate the large-scale limit of the streaming model and determine under which conditions it aligns to SPT. On scales $>10\,h^{-1}\mathrm{Mpc}$, we find that the streaming model for the 3PCF monopole is dominated by the first two velocity moments, making the exact shape of the PDF irrelevant. This model can match the accuracy of a Stage-IV galaxy survey, if the velocity moments are measured directly from the simulations. However, replacing the measurements with perturbative expressions to leading order generates large errors already on scales of $60-70 h^{-1}\mathrm{Mpc}$. This is the main drawback of the streaming model. Conversely, the SPT model for the 3PCF cannot account for the significant velocity dispersion that is present at all scales, and consequently provides predictions with limited accuracy. We demonstrate that this issue can be addressed by isolating the large-scale limit of the dispersion, which leads to typical Fingers-of-God damping functions. Overall, the SPT model with a damping function provides the best deal in terms of accuracy and computing time.