Effective field theory for dilute Fermi systems at fourth order

We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or kFaₛ 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 |kFaₛ|0.5. Furthermore, we show that Pad\'e-Borel resummations can improve the convergence for |kFaₛ|1. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.