ϵ Expansion for a Fermi Gas at Infinite Scattering Length

We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over ϵ=4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be μ/ε_F=1/2ϵ^3/2+1/16ϵ^5/2ln⁡ϵ-0.0246ϵ^5/2+⋯ and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Δ/μ=2ϵ^-1-0.691+⋯. The minimum of the fermion dispersion curve is located at |p|=(2mε₀)^1/2, where ε₀/μ=2+O(ϵ). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.