Finite density chiral effective field theory in nuclear physics

Abstract

In the present work, we develop an Effective Field Theory for nuclear matter at zero temperature that is valid up to about twice the nuclear matter saturation density. For that, a novel in-medium power counting will be derived with explicit nucleonic and pionic degrees of freedom coupled to external sources. It allows for a systematic expansion taking into account short- and long-range multi-nucleon interactions, which are mediated by nucleon contact-terms and pion exchanges, respectively. In order to implement the in-medium power counting in actual calculations we develop non-perturbative methods based on Unitary Chiral Perturbation Theory for performing required resummations. Employing our framework, we find that the main trends for symmetric nuclear matter and pure neutron matter are already reproduced at next-to-leading order. In particular, we are able to reproduce the empirical saturation point and the compressibility of nuclear matter, while the energy per nucleon as a function of density agrees with so-called sophisticated many-body calculations from the literature. Interestingly, we also find cancellations of nucleon-nucleon contributions for the in-medium pion self-energy, the in-medium chiral quark condensate and the in-medium pion decay consant. This actually explains the successful applications of previous approaches employing Effective Field Theories.