Multi-tracers, multi-surveys: data-driven EFT prior calibration from the PFS--DESI overlap

Abstract: Marginalizing over roughly 12 effective-field-theory (EFT) nuisance parameters per tracer per redshift bin is the dominant systematic cost in full-shape galaxy power spectrum analyses. Simulation-based priors (SBP) can tighten these parameters but rely on N-body simulations and halo-occupation-distribution (HOD) models. We propose multi-survey priors: a data-driven alternative that calibrates EFT parameters from the multi-tracer analysis of overlapping spectroscopic surveys. In the $\sim!1{,}200\;\text{deg}^2$ Prime Focus Spectrograph (PFS)--Dark Energy Spectroscopic Instrument (DESI) overlap at $0.6<z<1.6$, up to 4 tracers (PFS-ELG, DESI-ELG, DESI-LRG, DESI-QSO) and 10 cross-spectra per redshift bin provide model-independent constraints on the DESI nuisance parameters. Cross-spectra between different galaxy populations carry zero stochastic contribution, cleanly separating shot noise from signal. Exporting the calibrated priors to the full $14{,}000\;\text{deg}^2$ DESI footprint of the DESI LRG1--3, ELG1--2 and QSO samples improves $σ(fσ8)$ by 8\% (7--25\% per sample) and $σ(Mν)$ by 54\% (46--71\% per sample) at $k_{\rm max}=0.20\,h\,\mathrm{Mpc}^{-1}$. A parameter importance decomposition reveals that the dominant driver is the calibration of the $b_1σ8$ prior -- constrained from a flat prior to $σ\approx 0.17$ by the multi-tracer Fisher -- which accounts for $\sim!70\%$ of the $fσ_8$ gain and $\sim!97\%$ of the $Mν$ gain by breaking the $b_1σ_8$--$fσ_8$ degeneracy intrinsic to single-tracer analyses. Multi-survey prior calibration parallels the SBP approach, which tightens $b_1$ through HOD model assumptions; multi-survey priors provide a model-independent consistency check on these assumptions and generalize to arbitrary combinations of overlapping spectroscopic surveys.