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

TL;DR

This paper advances the theoretical understanding of a unitary Fermi gas by calculating the chemical potential ratio to NNLO in epsilon-expansion, providing insights into corrections beyond NNLO.

Contribution

It extends the epsilon-expansion method to NNLO for a Fermi gas at infinite scattering length, offering more precise theoretical predictions.

Findings

Calculated the ratio xi = mu/epsilon_F to NNLO in epsilon

Analyzed the nature of higher-order corrections beyond NNLO

Enhanced the theoretical framework for universal Fermi gas properties

Abstract

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