Effective field theory for dilute Fermi systems at fourth order

Abstract

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or $k_{\mathrm{F}}{a}_s$ expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well-converged at this order for $|k_{\mathrm{F}}{a}_s|\lesssim 0.5$. Further, we show that Pad{é}-Borel resummations can improve the convergence for $|k_{\mathrm{F}}{a}_s|\lesssim 1$. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.

18 pages, 5 figures, minor changes, published version