Measuring the redshift-space distortions by cross-correlating the density fields before and after reconstruction

In this work, we develop a theoretical model for the cross-power spectrum of the galaxy density field before and after standard baryonic acoustic oscillation (BAO) reconstruction. Using this model, we extract the redshift-space distortion (RSD) parameter from the cross-power spectrum. The model is validated against a suite of high-resolution $N$-body simulations, demonstrating its accuracy and robustness for cosmological analyses.