Chiral Effective Field Theory for Nuclear Matter with long- and short-range Multi-Nucleon Interactions

We derive a novel chiral power counting scheme for in-medium chiral perturbation theory with explicit nucleonic and pionic degrees of freedom coupled to external sources. It allows for a systematic expansion taking into account local as well as pion-mediated inter-nucleon interactions. Based on this power counting, one can identify classes of non-perturbative diagrams that require a resummation. Within this scheme, the pion self-energy in asymmetric nuclear matter is analyzed and calculated upto-and-including next-to-leading order (NLO). It is shown that the corrections involving in-medium nucleon-nucleon interactions cancel between each other at NLO. As a result, there are no corrections One of the long-standing issues in nuclear physics is the calculation of atomic nuclei and nuclear matter properties from microscopic inter-nucleon forces in a systematic and controlled way. This is a nonperturbative problem involving the strong interactions. In the last decades, Effective Field Theory (EFT) has proven to be an indispensable tool to accomplish such an ambitious goal. In this work we employ