Dilute Fermi gas at fourth order in effective field theory

Microscopic calculations of nuclear matter have important consequences for nuclear astrophysics as well as finite nuclei. We present an efficient Monte-Carlo framework for perturbative calculations of infinite nuclear matter based many-body forces derived within chiral effective field theory. It enables to incorporate all many-body contributions in a transparent and also straightforward way, making it well-suited for pushing the limits of current state-of-the-art calculations to high orders in both the chiral as well as the many-body expansion. Furthermore, uncertainty estimates can systematically be extracted by order-by-order calculations, which provides important insights into the rate of convergence of each of the two expansions. Taking advantage of the novel framework, we report here on our complete calculation of the fourth-order term in the Fermi-momentum or $k_{\rm F} a_s$ expansion for the ground-state energy of a dilute Fermi gas. The convergence behavior of the expansion for spin one-half fermions is assessed by comparing to quantum Monte-Carlo results.