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 $k_{\rm F} a_s$ expansion the ground-state of dilute Fermi gas is calculated to fourth order, both cutoff regularization and dimensional regularization. For case spin one-half we find from a Bayesian analysis that well-converged this order ${| k_{\rm a_s | \lesssim 0.5}$. Further, show Pad{\'e}-Borel resummations can improve convergence 1}$. Our results provide important constraints nonperturbative ultracold atoms neutron matter.