Equation of state of nuclear and neutron matter at third-order in perturbation theory from chiral EFT

TL;DR

This paper calculates the nuclear and neutron matter equation of state at third-order perturbation theory using chiral EFT, providing new insights into uncertainties and the importance of higher-order diagrams.

Contribution

It presents the first third-order perturbative calculation including self-consistent energies with detailed uncertainty analysis in chiral EFT.

Findings

Third-order diagrams reduce low-density uncertainties.

Uncertainties mainly stem from higher-order chiral expansion terms.

Provides semi-analytic expressions for direct interaction terms.

Abstract

We compute from chiral two- and three-nucleon interactions the energy per particle of symmetric nuclear matter and pure neutron matter at third-order in perturbation theory including self-consistent second-order single-particle energies. Particular attention is paid to the third-order particle-hole ring-diagram, which is often neglected in microscopic calculations of the equation of state. We provide semi-analytic expressions for the direct terms from central and tensor model-type interactions that are useful as theoretical benchmarks. We investigate uncertainties arising from the order-by-order convergence in both many-body perturbation theory and the chiral expansion. Including also variations in the resolution scale at which nuclear forces are resolved, we provide new error bands on the equation of state, the isospin-asymmetry energy, and its slope parameter. We find in particular that the inclusion of third-order diagrams reduces the theoretical uncertainty at low densities, while in general the largest error arises from omitted higher-order terms in the chiral expansion of the nuclear forces.