Toward order-by-order calculations of the nuclear and neutron matter equations of state in chiral effective field theory

We calculate the nuclear and neutron matter equations of state from microscopic nuclear forces at different orders in chiral effective field theory and with varying momentum-space cutoff scales. We focus attention on how the order-by-order convergence depends on the choice of resolution scale and the implications for theoretical uncertainty estimates on the isospin asymmetry energy. Specifically we study the equations of state using consistent NLO and (NLO)-L-2 (next-to-next-to-leading order) chiral potentials where the low-energy constants c(D) and c(E) associated with contact vertices in the (NLO)-L-2 chiral three-nucleon force are fitted to reproduce the binding energies of H-3 and He-3 as well as the beta-decay lifetime of H-3. At these low orders in the chiral expansion there is little sign of convergence, while an exploratory study employing the N3LO two-nucleon force together with the (NLO)-L-2 three-nucleon force give first indications for (slow) convergence with low-cutoff potentials and poor convergence with higher-cutoff potentials. The consistent NLO and (NLO)-L-2 potentials described in the present work provide the basis for estimating theoretical uncertainties associated with the order-by-order convergence of nuclear many-body calculations in chiral effective field theory.