Lawrence Berkeley National Laboratory

We present precision measurements of the bias parameters of the one-loop power spectrum model of the Lyman-α (Ly-α) forest, derived within the effective field theory (EFT) of large-scale structure. We fit our model to the three-dimensional flux power spectrum measured from the ACCEL2 hydrodynamic simulations. The EFT model fits the data with an accuracy of below 2% up to k=2 h Mpc-1. Further, we analytically derive how nonlinearities in the three-dimensional clustering of the Ly-α forest introduce biases in measurements of the baryon acoustic oscillations (BAOs) scaling parameters in radial and transverse directions. From our EFT parameter measurements, we obtain a theoretical error budget of Δα∥=-0.2% (Δα⊥=-0.3%) for the radial (transverse) parameters at redshift z=2.0. This corresponds to a shift of -0.3% (0.1%) for the isotropic (anisotropic) distance measurements. We provide an estimate for the shift of the BAO peak for Ly-α -quasar cross-correlation measurements assuming analytical and simulation-based scaling relations for the nonlinear quasar bias parameters resulting in a shift of -0.2% (-0.1%) for the radial (transverse) dilation parameters, respectively. This analysis emphasizes the robustness of Ly-α forest BAO measurements to the theory modeling. We provide informative priors and an error budget for measuring the BAO feature - a key science driver of the currently observing Dark Energy Spectroscopic Instrument (DESI). Our work paves the way for full-shape cosmological analyses of Ly-α forest data from DESI and upcoming surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST.