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

TL;DR

This paper investigates the order-by-order convergence of nuclear and neutron matter equations of state in chiral effective field theory, highlighting the impact of cutoff scales and providing insights into theoretical uncertainties.

Contribution

It provides a systematic analysis of convergence behavior in chiral EFT calculations for nuclear matter, using consistent NLO and N2LO potentials and exploring cutoff dependencies.

Findings

Little convergence at low orders in chiral expansion.

Slow convergence observed with N3LO two-nucleon force and N2LO three-nucleon force.

The study offers a basis for estimating theoretical uncertainties in nuclear matter calculations.

Abstract

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 N2LO (next-to-next-to-leading order) chiral potentials where the low-energy constants cD and cE associated with contact vertices in the N2LO chiral three-nucleon force are fitted to reproduce the binding energies of 3H and 3He as well as the beta-decay lifetime of 3H. 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 N2LO three-nucleon force give first indications for (slow) convergence with low-cutoff potentials and poor convergence with higher-cutoff potentials. The consistent NLO and N2LO 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.