Nuclear-matter equation of state with consistent two- and three-body perturbative chiral interactions

Abstract

We compute the energy per particle of infinite symmetric nuclear matter from chiral N$^{3}\mathrm{LO}$ (next-to-next-to-next-to-leading order) two-body potentials plus N$^{2}\mathrm{LO}$ three-body forces. The low-energy constants of the chiral three-nucleon force that cannot be constrained by two-body observables are fitted to reproduce the triton binding energy and the $^{3}\mathrm{H}$-$^{3}\mathrm{He}$ Gamow-Teller transition matrix element. In this way, the saturation properties of nuclear matter are reproduced in a parameter-free approach. The equation of state is computed up to third order in many-body perturbation theory, with special emphasis on the role of the third-order particle-hole diagram. The dependence of these results on the cutoff scale and regulator function is studied. We find that the inclusion of three-nucleon forces consistent with the applied two-nucleon interaction leads to a reduced dependence on the choice of the regulator only for lower values of the cutoff.