  We present an improved prediction of the nonlinear perturbation theory (PT)
via the Lagrangian picture, which was originally proposed by Matsubara (2008).
Based on the relations between the power spectrum in standard PT and that in
Lagrangian PT, we derive analytic expressions for the power spectrum in
Lagrangian PT up to 2-loop order in both real and redshift spaces. Comparing
the improved prediction of Lagrangian PT with $N$-body simulations in real
space, we find that the 2-loop corrections can extend the valid range of wave
numbers where we can predict the power spectrum within 1% accuracy by a factor
of 1.0 ($z=0.5$), 1.3 (1), 1.6 (2) and 1.8 (3) vied with 1-loop Lagrangian PT
results. On the other hand, in all redshift ranges, the higher-order
corrections are shown to be less significant on the two-point correlation
functions around the baryon acoustic peak, because the 1-loop Lagrangian PT is
already accurate enough to explain the nonlinearity on those scales in $N$-body
simulations.
