The JADES Mass-Metallicity and Fundamental Metallicity Relations at $z\gtrsim2$ Using New High-Redshift Metallicity Calibrations

We present measurements of the mass-metallicity relation (MZR) and fundamental metallicity relation (FMR) at $1.4<z<7.0$ using stacked JWST/NIRSpec spectra of 601 star-forming galaxies from the JWST Advanced Deep Extragalactic Survey (JADES). Using the most up-to-date strong-line metallicity calibrations based on high-redshift galaxies, we derive gas-phase metallicities from composite spectra binned by stellar mass, redshift, and star-forming main sequence (SFMS) offset. We find that the MZR slope evolves weakly from $z\sim0$ out to $z\sim5$, with $\gamma\sim0.21\pm0.03$, while the normalization decreases smoothly with redshift at a rate of $d\log(\mathrm{O/H})/dz\sim-0.1$ out to $z\sim4$. Beyond $z\gtrsim5$, the low-mass end continues to decline in metallicity while the high-mass end remains broadly consistent with lower-redshift relations, producing a steeper overall MZR. We additionally find evidence for a shallow anti-correlation between deviations from the MZR and SFMS at fixed stellar mass at $z\sim1.4-5$. This anti-correlation, albeit with weaker SFR coupling than observed locally, suggests that an FMR is already beginning to emerge by $z\sim5$. Comparisons with recent observations and cosmological simulations show broad agreement, though no single simulation simultaneously reproduces the observed slopes and normalizations across all redshifts. Our results support a picture in which bursty star formation and strong stellar feedback increasingly shape the regulation of galaxy growth at high redshift, while also highlighting the need for substantially larger spectroscopic samples to robustly constrain the evolution of galaxy scaling relations at high-redshift.