Effective Degrees of Freedom at Chiral Restoration and the Vector Manifestation in HLS theory

Abstract

The question as to what the relevant effective degrees of freedom at the chiral phase transition are remains largely unanswered and must be addressed in confronting both terrestrial and space laboratory observations purporting to probe matter under extreme conditions. We address this question in terms of the vector susceptibility χ_V (VSUS in short) and the axial-vector susceptibility χ_A (ASUS in short) at the temperature-induced chiral transition. We consider two possible, albeit simplified, cases that are contrasting, one that is given by the standard chiral theory where only the pions figure in the vicinity of the transition and the other that is described by hidden local symmetry (HLS) theory with the Harada-Yamawaki vector manifestation (VM) where nearly massless vector mesons also enter. We find that while in the standard chiral theory, the pion velocity v_πproportional to the ratio of the space component f_π^s of the pion decay constant over the time component f_π^t tends to zero near chiral restoration with f_π^t\neq 0, in the presence of the vector mesons with vanishing mass, the result is drastically different: HLS with VM {\it predicts} that χ_V automatically equals χ_A in consistency with chiral invariance and that v_π\sim 1$ with $f_π^t\approx f_π^s\to 0 as T\to T_c. These results are obtained in the leading order in power counting but we expect their qualitative features to remain valid more generally in the chiral limit thanks to the VM point.