  Recent studies have increasingly recognized the value of analyzing the
post-reconstruction galaxy power spectrum for investigations into redshift
space distortion (RSD) effects. In this paper, we present a novel theoretical
model for the post-reconstruction galaxy power spectrum, designed for RSD
analyses. In particular, we emphasize the importance of accounting for discrete
effects arising from the reconstruction displacement vector, which have been
overlooked. We specifically calculate these discrete effects, i.e., shot noise
terms, within the framework of standard perturbation theory at the 1-loop
level. In addition, we adopt a formulation that accounts for infrared (IR)
effects to accurately model the non-linear damping of the Baryon Acoustic
Oscillation (BAO) signal. Our model comprehensively integrates key physical
phenomena relevant to the post-reconstruction galaxy power spectrum, such as
gravitational non-linearities, RSD effects, bias effects, reconstruction
effects, reconstruction-specific shot-noise effects, and the non-linear damping
of the reconstructed BAO signal, thereby making it applicable to
post-reconstruction RSD analyses.
