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

Abstract

We review a chiral power-counting scheme 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 taking into account both local as well as pion-mediated internucleon 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 (UChPT) is also developed for performing those needed resummations. The power-counting and non-perturbative techniques are 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 is derived. Some NLO contributions from the in-medium NN interactions 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 derived 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, in agreement with recent observations. Furthermore, our results also fulfill other constraints from the detection of the gravitational waves in the event GW170817 by the LIGO and Virgo Collaborations, like the upper bound on the maximal mass of a neutron star and the allowed interval of values 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.