June 1995 From Chiral Mean Field to Walecka Mean Field And Kaon Condensation

A unified treatment of normal nuclear matter described by Walecka's mean field theory and kaon condensed matter described by chiral perturbation theory is proposed in terms of mean fields of an effective chiral Lagrangian. The BR scaling is found to play a key role in making the link between the ground state properties of nuclear matter and the fluctuation into the strangeness-flavor direction. A simple prediction for kaon condensation is presented. Kaon-nuclear physics is probably one of the most exciting new directions in nuclear physics. The issues involved are strangeness productions in heavy-ion collisions and kaon condensation in compact star matter [1]. In discussing kaon-nuclear (or in general pseudo-Goldstone boson) interactions appropriate for kaon condensation, chiral Lagrangians are found to be useful in describing the fluctuation in the strangeness direction. While chiral perturbation theory (χPT) is believed to be the most efficient way to implement chiral symmetry of QCD at low energy, there is a subtlety in applying it to nuclear or compact star matter which has not yet been satisfactorily addressed in the literature. This has to do with the consistency in the description of the ground state of the dense matter and of the fluctuation around that background defined by the ground state. In treatments to date, there is no consistency between the two sectors. For instance, the ground state – nuclear matter – is successfully described by Walecka mean-field theory [2] with the parameters of an apparently non-chiral Lagrangian determined from nuclear matter properties while the kaon condensation phenomenon, the physics of which is lodged in an effective action (or potential), is described by low-order chiral perturbation theory with the parameters of a chiral Lagrangian determined mostly by free-space data. Communication between the ground-state sector and the fluctuation sector has been glaringly missing. What would be needed is a formalism that describes both sectors from a given chiral Lagrangian with common parameters operative in both sectors simultaneously. An attractive possibility is that a lump of nuclear matter arises as a nontopological soliton in the form of " chiral liquid " as suggested by Lynn [3] around which fluctuations in various flavor directions could be described. Such a scheme would incorporate chiral symmetry in a self-consistent way in both sectors [1, 4]. Unfortunately such a strategy has not been yet formulated into a workable scheme. In this Letter, we supply the missing link at mean field level with …