Interpretation of the scalar fields of the relativistic Brueckner-Hartree-Fock formalism

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Abstract
We discuss matrix elements of the axial current and the Gell-Mann-Oakes-Renner relation in the presence of nuclear matter. The density dependence of hadron masses and of the pion decay constant is also considered. We define a scalar order parameter that describes the modification of the quark scalar density in the presence of nuclear matter and go on to relate that parameter to the scalar field that appears in the relativistic Brueckner-Hartree-Fock (RBHF) theory. We suggest that the field-theoretic formulation provides a value for only the Hartree term in the calculation of the nucleon self-energy and present some estimates of how exchange (Fock) terms and short-range correlations modify the value obtained for the nucleon self-energy when calculations are made in the RBHF formalism. [Because of various cancellations, it is seen that the magnitude of the scalar part of the nucleon self-energy is largely unchanged when exchange (Fock) terms and short-range correlations are taken into account.]