Halo Zel’dovich model and perturbation theory: Dark matter power spectrum and correlation function

Perturbation theory for dark matter clustering has received a lot of attention in recent years, but its convergence properties remain poorly justified and there is no successful model that works both for correlation functions and for power spectra. Here we present the halo Zel'dovich approach combined with perturbation theory, in which we use standard perturbation theory at one-loop order (SPT) at very low k, and connect it to a version of the halo model, for which we adopt the Zel'dovich approximation plus a Pad\'e expansion of a compensated one-halo term. This low-k matching allows us to determine the one-halo term amplitude and redshift evolution, both of which are in an excellent agreement with simulations, and approximately agree with the expected value from the halo model. Our Pad\'e expansion approach of the one-halo term added to the Zel'dovich approximation identifies a typical halo scale averaged over the halo mass function, the halo radius scale of order of 1 Mpc/h, and a much larger halo mass compensation scale, which can be determined from SPT. The model gives better than one-percent-accurate predictions for the correlation function above 5 Mpc/h at all redshifts, without any free parameters. With three fitted Pad\'e expansion coefficients the agreement in the power spectrum is good to a percent up to k1 h/Mpc, which can be improved to arbitrary k by adding higher-order terms in the Pad\'e expansion.