  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
function and for power spectrum. Here we present Halo Zeldovich approach
combined with perturbation theory (HZPT), 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 Zeldovich approximation plus a Pade
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 Pade expansion approach of the one halo
term added to Zeldovich approximation identifies two typical halo scales
averaged over the halo mass function, the halo radius scale of order of 1Mpc/h,
and the halo mass compensation scale of order 26Mpc/h. The model gives better
than one percent accurate predictions for the correlation function above 5Mpc/h
at all redshifts, without any free parameters. With three fitted Pade expansion
coefficients the agreement in power spectrum is good to a percent up to $k \sim
1$h/Mpc, which can be improved to arbitrary $k$ by adding higher order terms in
Pade expansion.
