Next-to-next-to-leading-order ε expansion for a Fermi gas at infinite scattering length

We extend previous work on applying the $ϵ$ expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio $\ensuremath{\xi}=\ensuremath{\mu}∕{ϵ}_{\mathrm{F}}$ of chemical potential to ideal gas Fermi energy to next-to-next-to-leading-order (NNLO) in $ϵ=4\ensuremath{-}d$, where $d$ is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO.