Effective Field Theory Constraints on Primordial Black Holes from the High-Redshift Lyman-$α$ Forest

We present updated constraints on the abundance of primordial black holes (PBHs) dark matter from the high-redshift Lyman-$α$ forest data from MIKE/HIRES experiments. Our analysis leverages an effective field theory (EFT) description of the 1D flux power spectrum, allowing us to analytically predict the Lyman-$α$ fluctuations on quasi-linear scales from first principles. Our EFT-based likelihood enables robust inference across redshifts $z = 4.2-5.4$ and down to scales of 100 kpc, within previously unexplored regions of parameter space for this dataset. We derive new bounds on the PBH fraction with respect to the total dark matter $f_{\text{PBH}}$, excluding populations with $f_{\text{PBH}} \gtrsim 10^{-3}$ for masses $M_{\text{PBH}} \sim 10^{4}-10^{16} M_{\odot}$. This offers the leading constraint for PBHs heavier than $10^{9} M_{\odot}$ and highlights the Lyman-$α$ forest as a uniquely sensitive probe of new physics models that modify the structure formation history of our universe.