Non-perturbative methods for a chiral effective field theory of finite density nuclear systems

TL;DR

This paper introduces a non-perturbative approach based on Unitary Chiral Perturbation Theory within a novel chiral power counting scheme to accurately describe nuclear matter properties at next-to-leading order.

Contribution

It develops a non-perturbative resummation method for a chiral effective field theory of nuclear matter, enabling systematic calculations of the energy density and equation of state.

Findings

Reproduces main trends of nuclear matter energy density at NLO.

Accurately describes neutron matter equation of state.

Reproduces empirical saturation point and incompressibility.

Abstract

Recently we have developed a novel chiral power counting scheme for an effective field theory of nuclear matter with nucleons and pions as degrees of freedom [1]. It allows for a systematic expansion taking into account both local as well as pion-mediated multi-nucleon interactions. We apply this power counting in the present study to the evaluation of the pion self-energy and the energy density in nuclear and neutron matter at next-to-leading order. To implement this power counting in actual calculations we develop here a non-perturbative method based on Unitary Chiral Perturbation Theory for performing the required resummations. We show explicitly that the contributions to the pion self-energy with in-medium nucleon-nucleon interactions to this order cancel. The main trends for the energy density of symmetric nuclear and neutron matter are already reproduced at next-to-leading order. In addition, an accurate description of the neutron matter equation of state, as compared with sophisticated many-body calculations, is obtained by varying only slightly a subtraction constant around its expected value. The case of symmetric nuclear matter requires the introduction of an additional fine-tuned subtraction constant, parameterizing the effects from higher order contributions. With that, the empirical saturation point and the nuclear matter incompressiblity are well reproduced while the energy per nucleon as a function of density closely agrees with sophisticated calculations in the literature.