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.