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

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.

36 pages, 13 figures. Topical review for focus issue on Hadrons & Gravitational Waves After GW170817. Minor changes to match published version

References in corpus (10)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Shapiro delay measurement of a two solar mass neutron star
• Cold Quark Matter
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Constraints on neutron star radii based on chiral effective field theory interactions
• Identification of a Scalar Glueball
• On the Strangeness -1 S-wave Meson-Baryon Scattering
• Dynamical generation of pseudoscalar resonances
• The chiral quark condensate and pion decay constant in nuclear matter at next-to-leading order
• Scales in nuclear matter: Chiral dynamics with pion nucleon form factors

Cited by in corpus (6)

• nEoS: Neutron Star Equation of State from hadron physics alone
• Hadron matter in neutron stars in view of gravitational wave observations
• Brief history of the pion-nucleon sigma term
• Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes
• Unitarization Technics in Hadron Physics with Historical Remarks
• Ultracold spin-balanced fermionic quantum liquids with renormalized $P$-wave interactions