Relation of QCD sum rules in matter and the nuclear many-body problem

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Abstract
The method of QCD sum rules provides a powerful technique for the calculation of properties of hadrons in terms of a number of parameters that specify various condensate matrix elements. One may hope that it will be possible to calculate some of the condensate matrix elements using effective Lagrangians. If we concentrate on quark condensates, the Nambu–Jona-Lasinio model may provide a useful model. In this work we study the relation between relativistic nuclear many-body theory and the analysis of the nucleon self-energy in nuclear matter made using QCD sum rules. This is done by introducing the fields of a bosonized version of the Nambu–Jona-Lasinio (NJL) model. Using the simplest version of the QCD sum-rule analysis, we replace the QCD order parameters in matter with related order parameters describing a Lorentz scalar and a vector field. In our mean-field analysis we find that the many-body theory, based upon the bosonization of the NJL model, is consistent with the simplest version of the QCD sum-rule calculation of the nucleon self-energy in matter.

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