The Role of the Dilaton in Dense Skyrmion Matter

In this note, we report on a remarkable and surprising interplay between the ω meson and the dilaton χ in the structure of a single skyrmion as well as in the phase structure of dense skyrmion matter which may have a potentially important consequence on the properties of compact stars. In our continuing effort to understand hadronic matter at high density, we have developed a unified field theoretic formalism for dense skyrmion matter using a single Lagrangian to describe simultaneously both matter and meson fluctuations and studied in-medium properties of hadrons. The effective theory used is the Skyrme model Lagrangian gauged with the vector mesons ρ and ω, implemented with the dilaton field that describes the spontaneously broken scale symmetry of QCD, in a form consistent with the symmetries of QCD and our expectations regarding the high density limit. We analyze the restoration of scale invariance and chiral symmetry as the density of the system increases. In order to preserve the restoration of scale symmetry and chiral symmetry, signalled in our case by the vanishing of the expectation value of the dilaton, and to be consistent with the “vector manifestation” of hidden local symmetry, a density dependent ω coupling is introduced. We uncover the crucial role played by both the dilaton and the ω meson in the phase structure of dense medium and discover how two different phase transition regimes arise as we “dial” the dilaton mass. Pacs: 12.39-x, 13.60.Hb, 14.65-q, 14.70Dj