Reduced regulator dependence of neutron-matter predictions with perturbative chiral interactions

We calculate the energy per particle in infinite neutron matter perturbatively using chiral N${}^3$LO (next-to-next-to-next-to-leading order) two-body potentials plus N${}^2$LO three-body forces. The cutoff dependence of the predictions is investigated by employing chiral interactions with different regulators. We find that the inclusion of three-nucleon forces, which are consistent with the applied two-nucleon interaction, leads to a strongly reduced regulator dependence of the results.

Figure 1

Neutron-proton phase parameters as predicted by chiral N${}^3$LO potentials with different cutoff scale $\Lambda$. Solid (red) curve, $\Lambda =414$ MeV; dashed (blue) curve, $\Lambda =450$ MeV; and dotted (black) curve, $\Lambda =500$ MeV. Partial waves with total angular momentum $J\le 1$ are displayed. The solid dots and open circles are the results from the Nijmegen multienergy $np$ phase shift analysis [14] and the VPI/GWU single-energy $np$ analysis SM99 [15], respectively.

Figure 2

Same as Fig. 1, but $J=2$ phase shifts and $J\le 2$ mixing parameters are shown.

Figure 3

Same as Fig. 1, but some representative peripheral partial waves are shown.

Figure 4

First-, second-, and third-order diagrams of the Goldstone expansion included in our calculations with $V_{NN}$ vertices only. Latin-letter subscripts denote particle states, and Greek-letter subscripts correspond to hole states.

Figure 5

Same as in Fig. 4, but also including ${\overline{V}}_{NNN}$ vertices, which are denoted with thick straight lines.

Figure 6

Neutron-matter energy per particle obtained from the N${}^3$LO 2NF with cutoff $\Lambda =500$ MeV. The first, second, and third order in the perturbative expansion and the Padé approximant $\left[2\right|1]$ are shown as a function of density $\rho$.

Figure 7

Same as in Fig. 6, but including the contribution of the N${}^2$LO 3NF.

Figure 8

Results obtained for the g.s.e. per particle of infinite neutron matter at third-order in perturbation theory for three sets of chiral interactions which differ by the cutoff $\Lambda$.