The Pion Velocity in Dense Skyrmion Matter

We have developed a field theory formalism to calculate $in$-$medium$ properties of hadrons within a unified approach that exploits a single Lagrangian to describe simultaneously both matter background and meson fluctuations. In this paper we discuss the consequences on physical observables of a possible phase transition of hadronic matter taking place in the chiral limit. We pay special attention to the pion velocity $v_\pi$, which controls, through a dispersion relation, the pion propagation in the hadronic medium. The $v_\pi$ is defined in terms of parameters related to the matrix element in matter of the axial-vector current, namely, the in-medium pion decay constants, $f_t$ and $f_s$. Both of the pion decay constants change dramatically with density and even vanish in the chiral limit when chiral symmetry is restored, but the pion velocity does not go to zero, decreasing at most 10% over the whole density range studied. A possible pseudogap structure is indicated.