Universal Short-Distance Structure of the Single-Particle Spectral Function of Dilute Fermi Gases

We show that the universal $1\mathrm{/}{k}^4$ tail in the momentum distribution of dilute Fermi gases implies that the spectral function $A(\text{kk},\omega )$ must have weight below the chemical potential for large momentum $k\gg k_F$, with observable consequences in RF spectroscopy experiments. We find that this incoherent spectral weight is centered about $\omega \simeq -ϵ(\text{kk})$ in a range of energies of order $v_{F}k$. This “bending back” in the dispersion, while natural for superfluids, is quite surprising for normal gases. This universal structure is present in the hard-sphere gas as well as the Fermi liquid ground state of the highly imbalanced, attractive gas near unitarity. We argue that, even in the BCS superfluid, this bending back at large $k$ is dominated by interaction effects which do not reflect the pairing gap.