  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
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 ${| k_{\rm F} a_s | \lesssim
0.5}$. Further, we show that Pad{\'e}-Borel resummations can improve the
convergence for ${| k_{\rm F} a_s | \lesssim 1}$. Our results provide important
constraints for nonperturbative calculations of ultracold atoms and dilute
neutron matter.
