JWST/NIRSpec Measurements of Extremely Low Metallicities in High Equivalent Width Lyman-$\alpha$ Emitters

Deep VLT/MUSE optical integral field spectroscopy has recently revealed an abundant population of ultra-faint galaxies ($M_{UV} \approx -15$; 0.01 $L_{\star}$) at $z=$2.9$-$6.7 due to their strong Lyman-$\alpha$ emission with no detectable continuum. The implied Lyman-$\alpha$ equivalent widths can be in excess of 100-200 Angstrom, challenging existing models of normal star formation and indicating extremely young ages, small stellar masses, and a very low amount of metal enrichment. We use JWST/NIRSpec's microshutter array to follow-up 45 of these galaxies (11h in G235M/F170LP and 7h in G395M/F290LP), as well as 45 lower-equivalent width Lyman-$\alpha$ emitters. Our spectroscopy covers the range 1.7$-$5.1 micron in order to target strong optical emission lines: H$\alpha$, [N II], [O III], and H$\beta$. Individual measurements as well as stacks reveal line ratios consistent with a metal poor nature (2$-$40% $Z_{\odot}$, depending on the calibration). The galaxies with the highest equivalent widths of Lyman-$\alpha$, in excess of 90 Angstrom, have lower [N II]/H$\alpha$ (1.9-$\sigma$) and [O III]/H$\beta$ (2.2-$\sigma$) ratios than those with lower equivalent widths, implying lower gas-phase metallicities at a combined significance of 2.4-$\sigma$. This implies a selection based on Lyman-$\alpha$ equivalent width is an efficient technique for identifying younger, less chemically enriched systems.