Vector mesons and dense skyrmion matter

Abstract

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. Dropping the quartic Skyrme term, we incorporate into our previous Lagrangian the vector mesons ρ and ω in a form which is consistent with the symmetries of QCD. The results that we have obtained, reported here, expose a hitherto unsuspected puzzle associated with the role the ω meson plays at short distance. Since the ω meson couples to baryon density, it leads to a pseudo-gap scenario for the chiral symmetry phase transition, which is at variance with standard scenario of QCD at the phase transition. We find that in the presence of the ω mesons, the scale-anomaly dilaton field is prevented from developing a vanishing vacuum expectation value at the chiral restoration, as a consequence of which the in-medium pion decay constant does not vanish. This seems to indicate that the ω degree of freedom obstructs the “vector manifestation” which is considered to be a generic feature of effective field theories matched to QCD.