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Using effective field theory methods, we calculate for the first time thecomplete fourth-order term in the Fermi-momentum or $k_{\rm F} a_s$ expansionfor the ground-state energy of a dilute Fermi gas. The convergence behavior ofthe expansion is examined for the case of spin one-half fermions and comparedagainst quantum Monte-Carlo results, showing that the Fermi-momentum expansionis well-converged at this order for $| k_{\rm F} a_s | \lesssim 0.5$.

Dilute Fermi gas at fourth order in effective field theory