Alcock-Paczynski Blinding Scheme for the Ly-$α$ Forest Analysis

We present and validate a blinding method for the Lyman-$\alpha$ (Ly$\alpha$) forest analysis based on a modification of the Alcock-Paczynski test. In order to hide the background expansion history, the method employs a geometrical shift of each quasar (QSO) forest in wavelength space, once the quasar continuum has been fitted and the fluctuation field is extracted. The redshift positions for the QSO sample are also changed in a consistent manner. We show that the method remains effective when applied to real data, where contamination from metals and Lyman-$\beta$ is intrinsically mixed with the Lyman-$\alpha$ forest. This limitation is primarily visible in the 1D correlation function, where other blinding strategies can mitigate the effect. To assess its effectiveness, the prescription is tested against a series of datasets of increasing complexity: from idealized low-noise mocks, to realistic DESI year one synthetic datasets, and finally to data from DESI first data release (DR1), using both the auto (Ly$\alpha\times$Ly$\alpha$) and cross (Ly$\alpha\times$ QSO) correlations. We find that the method robustly shifts the BAO peak position from the 3D correlation functions to the expected value for cosmology changes of around 5\% in the matter content, without altering the shape of the posteriors in the model parameters. In conclusion, this catalog-level blinding strategy is a viable method for cosmological inference with the Lyman-$\alpha$ forest, particularly if a cross-analysis with other tracers using the same blinding strategy is pursued.