Universal short-distance structure of the single-particle spectral function of dilute Fermi gases

We show that the universal 1/k⁴ tail in the momentum distribution of dilute Fermi gases implies that the spectral function A(k,ω) must have weight below the chemical potential for large momentum kkF, with observable consequences in radio-frequency spectroscopy experiments. We find that this incoherent spectral weight is centered around ω-ε(k) in a range of energies of order vFk. 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 in 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.