Multi-tracers, multi-surveys: a joint Fisher analysis of DESI+PFS

Marginalizing over roughly 12 effective-field-theory (EFT) nuisance parameters per tracer per redshift bin is a dominant systematic cost in full-shape galaxy power spectrum analyses. Simulation-based priors (SBP) tighten these parameters but rely on N-body simulations and halo-occupation-distribution (HOD) models. We propose a multi-tracer Fisher analysis as a model-independent alternative: cross-spectra between galaxy populations calibrate EFT bias and stochastic parameters from data alone, through two channels -- within a survey and across overlapping surveys -- combined in a volume-partitioned joint Fisher. We forecast across the $14{,}000\;\mathrm{deg}^2$ Dark Energy Spectroscopic Instrument (DESI) footprint, including the $\sim\!1{,}200\;\mathrm{deg}^2$ Prime Focus Spectrograph (PFS) overlap at $z\in[0.6,1.6]$ with up to 4 tracers (PFS-ELG, DESI-ELG, DESI-LRG, DESI-QSO). The internal-DESI channel (LRG, ELG, and QSO over the full footprint) provides most of the gain, improving $\sigma(f\sigma_8)$ by 33%, $\sigma(M_\nu)$ by 80%, and $\sigma(\Omega_m)$ by 49% over a single-tracer broad-prior baseline at $k_{\rm max}=0.20\,h\,\mathrm{Mpc}^{-1}$. Adding the PFS$\,\times\,$DESI overlap further tightens these by 9%, 24%, and 9%, respectively, after marginalizing over residual cross-population stochasticity. A parameter-importance decomposition shows that the dominant driver is calibration of the $b_1\sigma_8$ prior, tightened from a flat prior to $\sigma\approx 0.13$, which breaks the $b_1\sigma_8$--$f\sigma_8$ degeneracy of single-tracer analyses. The multi-tracer multi-survey approach targets the same $b_1$ calibration as SBPs, using observed cross-spectra rather than HOD mocks as a model-independent check on SBP-driven $b_1\sigma_8$ shifts. The framework extends to any number of overlapping spectroscopic surveys.