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 epsilon = 4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/epsilon(F) = 1/2 epsilon(3/2) + 1/16 epsilon(5/2) ln epsilon - 0:0246 epsilon(5/2) + (.) (.) (.) and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu = 2 epsilon(-1) - 0:691 + (.) (.) (.) .The minimum of the fermion dispersion curve is located at vertical bar p vertical bar = (2m epsilon(0)) (1/2), where epsilon(0)/mu = 2 + O (epsilon). Extrapolation to d = 3 gives results consistent with Monte Carlo simulations.