Unveiling the Cosmic Chemistry: Revisiting the Mass-Metallicity Relation with JWST/NIRSpec at 4 < z < 10

We present star formation rates (SFR), the mass-metallicity relation (MZR), and the SFR-dependent MZR across redshifts 4 to 10 using 81 star-forming galaxies observed by the JWST NIRSpec employing both low-resolution PRISM and medium-resolution gratings, including galaxies from the JADES GOODS-N and GOODS-S fields, the JWST-PRIMAL Legacy Survey, and additional galaxies from the literature in Abell 2744, SMACS-0723, RXJ2129, BDF, COSMOS, and MACS1149 fields. These galaxies span a 3 dex stellar mass range of 10⁷ < M_/M_ < 10^10, with an average SFR of 7. 2 1. 2 M_ yr^-1 and an average metallicity of 12+ log (O/H) = 7. 91 0. 08. Our findings align with previous observations up to z=8 for the MZR and indicate no deviation from local universe FMR up to this redshift. Beyond z=8, we observe a significant deviation 0. 27 dex) in FMR, consistent with recent JWST findings. We also integrate CEERS (135 galaxies) and JADES (47 galaxies) samples with our data to study metallicity evolution with redshift in a combined sample of 263 galaxies, revealing a decreasing metallicity trend with a slope of 0. 067 0. 013, consistent with IllustrisTNG and EAGLE, but contradicts with FIRE simulations. We introduce an empirical mass-metallicity-redshift (MZ-z relation): 12+ log (O/H) =6. 29 + 0. 237 log (M_/M_) - 0. 06 (1+z), which accurately reproduces the observed trends in metallicity with both redshift and stellar mass. This trend underscores the ``Grand Challenge'' in understanding the factors driving high-redshift galactic metallicity trends, such as inflow, outflow, and AGN/stellar feedback -- and emphasizes the need for further investigations with larger samples and enhanced simulations.