Precision measurements of EFT parameters and BAO peak shifts for the Lyman-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math> forest

We present precision measurements of the bias parameters of the one-loop power spectrum model of the Lyman-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>α</a:mi></a:math> (Ly-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>α</c:mi></c:math>) 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msup><e:mrow><e:mi>ACCEL</e:mi></e:mrow><e:mrow><e:mn>2</e:mn></e:mrow></e:msup></e:mrow></e:math> hydrodynamic simulations. The EFT model fits the data with an accuracy of below 2% up to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>k</g:mi><g:mo>=</g:mo><g:mn>2</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>h</g:mi><g:mtext> </g:mtext><g:msup><g:mrow><g:mi>Mpc</g:mi></g:mrow><g:mrow><g:mo>−</g:mo><g:mn>1</g:mn></g:mrow></g:msup></g:mrow></g:math>. Further, we analytically derive how nonlinearities in the three-dimensional clustering of the Ly-<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>α</i:mi></i:math> 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 <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="normal">Δ</k:mi><k:msub><k:mi>α</k:mi><k:mo stretchy="false">∥</k:mo></k:msub><k:mo>=</k:mo><k:mo>−</k:mo><k:mn>0.2</k:mn><k:mo>%</k:mo></k:math> (<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">Δ</o:mi><o:msub><o:mi>α</o:mi><o:mo>⊥</o:mo></o:msub><o:mo>=</o:mo><o:mo>−</o:mo><o:mn>0.3</o:mn><o:mo>%</o:mo></o:math>) for the radial (transverse) parameters at redshift <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>z</r:mi><r:mo>=</r:mo><r:mn>2.0</r:mn></r:math>. This corresponds to a shift of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mo>−</t:mo><t:mn>0.3</t:mn><t:mo>%</t:mo></t:math> (0.1%) for the isotropic (anisotropic) distance measurements. We provide an estimate for the shift of the BAO peak for Ly-<v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>α</v:mi></v:math> -quasar cross-correlation measurements assuming analytical and simulation-based scaling relations for the nonlinear quasar bias parameters resulting in a shift of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mo>−</x:mo><x:mn>0.2</x:mn><x:mo>%</x:mo></x:math> (<z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mo>−</z:mo><z:mn>0.1</z:mn><z:mo>%</z:mo></z:math>) for the radial (transverse) dilation parameters, respectively. This analysis emphasizes the robustness of Ly-<bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi>α</bb:mi></bb:math> 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-<db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>α</db:mi></db:math> forest data from DESI and upcoming surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST.