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

TL;DR

This paper develops a new chiral power counting scheme for nuclear matter, enabling systematic analysis of nucleon interactions and calculating the pion self-energy up to NLO, revealing cancellations that uphold the linear density approximation.

Contribution

It introduces a novel chiral power counting scheme for in-medium chiral perturbation theory with explicit nucleon and pion degrees of freedom.

Findings

Pion self-energy in asymmetric nuclear matter calculated up to NLO.

In-medium nucleon-nucleon interactions cancel at NLO.

No corrections to the linear density approximation at NLO.

Abstract

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 up-to-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 up to this order to the linear density approximation for the in-medium pion self-energy.