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

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.