Describing Nuclear Matter with Effective Field Theories

Nuclear forces have been studied in depth over the past fifty years, leading to excellent phenomenological descriptions. A recent resurgence of interest in this field has been fueled by the promise of systematic results from an effective field theory (EFT) analysis [1]. EFT techniques adapted to many-body systems may give new insight into the properties of nuclei and their connection to QCD. The EFT lagrangian consists of long-range interactions constrained by chiral symmetry and the most general short-range interactions consistent with QCD symmetries. The coefficients of these short-range terms may eventually be derived from QCD, but at present must be fit by matching calculated and experimental observables in a momentum expansion. This effective lagrangian can then be used to systematically predict other observables, including inelastic processes. The predictability of an EFT relies on an organizational scheme, called power counting, to determine the importance of any contribution to a calculation. This can be illustrated by using the familiar one-boson-exchange representation of the NN force as a model of the true underlying physics. One-pion exchange (OPE) is taken to be the long-range physics, as its contribution to the EFT is dictated by chiral symmetry. Exchanges of the heavier mesons will be considered short-range physics, which must be included generically in the EFT. For example, for center-of-mass momenta below the sigma mass, p < mσ, the heavy-meson propagators are well approximated by momentum-dependent contact interactions,