Lagrangian perturbation theory at one loop order: successes, failures,
  and improvements
  We apply the convolved Lagrangian perturbation theory (CLPT) formalism, in
which one can express the matter density power spectrum in terms of integrals
over a function of cumulants of the displacement field, allowing for a
resummation of the terms, to evaluate the full one loop power spectrum. We keep
the cumulants up to third order, extending the Zel'dovich approximation and
providing the power spectrum analogous to the calculations recently performed
for the correlation function. We compare the results to the N-body simulations
and to the Lagrangian perturbation simulations up to the second order. We find
that the analytic calculations are in a good agreement with the LPT
simulations, but when compared to full N-body simulations, we find that while
one loop calculations improve upon the Zel'dovich approximation in the power
spectrum, they still significantly lack power. As found previously in the
correlation function one loop CLPT improves slightly against Zel'dovich above
30Mpc/h, but is actually worse than Zel'dovich below that. We investigate the
deficiencies of the CLPT approach and argue that main problem of CLPT is its
inability to trap particles inside dark matter halos, which leads to an
overestimate of the small scale power of the displacement field and to an
underestimate of the small scale power from one halo term effects. We model
this using the displacement field damped at a nonlinear scale (CLPTs). To
explore this in more detail we decompose the power spectrum and correlation
function into three additive components: Zel'dovich, residual BAO wiggle, and
residual broad band. One loop CLPT predicts small modifications to BAO wiggles
that are enhanced in CLPTs, with up to 5\% corrections to correlation function
around BAO scale.
