  We compute the energy per particle of infinite symmetric nuclear matter from
chiral N3LO (next-to-next-to-next-to-leading order) two-body potentials plus
N2LO 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 3H-3He 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.
