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 k(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 vertical bar k(F)a(s)vertical bar less than or similar to 0.5. Furthermore, we show that Pade-Borel resummations can improve the convergence for vertical bar k(F)a(s)vertical bar less than or similar to 1. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.