# An in-medium chiral power counting for nuclear matter and some applications

## TL;DR

This paper develops a systematic chiral power counting method for nuclear matter, incorporating non-perturbative resummations, and applies it to calculate properties like the equation of state, with implications for neutron star physics.

## Contribution

It introduces a novel in-medium chiral power counting framework combined with non-perturbative techniques for nuclear matter calculations.

## Key findings

- Accurate calculation of pion self-energy and decay constants in nuclear matter.
- Reproduction of realistic nuclear matter equations of state without fine tuning.
- Constraints on neutron star properties consistent with gravitational wave observations.

## Abstract

We review on a chiral power counting for in-medium chiral perturbation theory with nucleons and pions as explicit degrees of freedom coupled to external sources. It allows for a systematic expansion including both local and pion-mediated inter-nucleon interactions. One can identify from this power counting classes of non-perturbative diagrams that require resummation. A non-perturbative method based on Unitary Chiral Perturbation Theory was also developed for performing those resummations. This power counting and non-perturbative techniques were firstly applied to calculate the pion self-energy, the pion-decay constants and the quark condensate in nuclear matter up-to-and-including next-to-leading order (NLO) contributions. The cancellation of the contributions at NLO to the pion self-energy and decay constants from in-medium nucleon-nucleon (NN) interactions was derived. Some NLO NN contributions survive for the quark condensate due to the quark-mass dependence of the pion mass. Next, we discuss the calculation of the energy density in the nuclear medium by employing the in-medium NN scattering amplitudes. For symmetric and neutron matter it reproduces in good agreement, and without fine tuning, calculations from realistic NN potentials with a model for the three-nucleon interaction. These results are applied to derive the equation of state (EOS) for neutron stars and obtain an upper limit for a neutron mass slightly above 2 solar masses. Our results also fulfill other constraints from the detection of the gravitational waves in the event GW170817, like the upper bound on the maximal mass of a neutron star and the allowed interval for the radius of a 1.4-solar-mass neutron star. The knowledge of the neutron-matter EOS is also employed to give an upper bound of the gravitational constant within the strong gravitational field of a 2 solar-mass neutron star.