  Baryon acoustic oscillations (BAO) provide a robust standard ruler to measure
the expansion history of the Universe through galaxy clustering. Density-field
reconstruction is now a widely adopted procedure for increasing the precision
and accuracy of the BAO detection. With the goal of finding the optimal
reconstruction settings to be used in the DESI 2024 galaxy BAO analysis, we
assess the sensitivity of the post-reconstruction BAO constraints to different
choices in our analysis configuration, performing tests on blinded data from
the first year of DESI observations (DR1), as well as on mocks that mimic the
expected clustering and selection properties of the DESI DR1 target samples.
Overall, we find that BAO constraints remain robust against multiple aspects in
the reconstruction process, including the choice of smoothing scale, treatment
of redshift-space distortions, fiber assignment incompleteness, and
parameterizations of the BAO model. We also present a series of tests that DESI
followed in order to assess the maturity of the end-to-end galaxy BAO pipeline
before the unblinding of the large-scale structure catalogs.
