  We investigate the possible accuracy that can be reached by analytical models
for the matter density power spectrum and correlation function. Using a
realistic description of the power spectrum that combines perturbation theory
with a halo model, we study the convergence rate of several perturbative
expansion schemes and the impact of nonperturbative effects, as well as the
sensitivity to phenomenological halo parameters. We check that the simple
reorganization of the standard perturbative expansion, with a Gaussian damping
prefactor, provides a well-ordered convergence and a finite correlation
function that yields a percent accuracy at the baryon acoustic oscillation peak
(as soon as one goes to second order). Lagrangian-space expansions are somewhat
more efficient, when truncated at low orders, but may diverge at high orders.
We find that whereas the uncertainty on the halo-profile mass-concentration
relation is not a strong limitation, the uncertainty on the halo mass function
can severely limit the accuracy of theoretical predictions for $P(k)$ (this
also applies to the power spectra measured in numerical simulations). The
real-space correlation function provides a better separation between
perturbative and nonperturbative effects, which are restricted to $x \lesssim
10 h^{-1}$Mpc at all redshifts.
