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Matching the QCD and Hadron Sectors and Medium Dependent Meson Masses; Hadronization in Relativistic Heavy Ion Collisions

The recent developments on the "vector manifestation" of chiral symmetry by Harada and Yamawaki provide a compelling evidence for, and "refine," the in-medium scaling of hadronic properties in dense/hot matter (call it ``BR scaling") proposed by the authors in 1991. We reinterpret the Harada-Yamawaki result obtained in a Wilsonian renormalization-group approach to hidden local symmetry theory matched to QCD at near the chiral scale in terms of the Nambu-Jona-Lasinio model and predict that the vector meson mass in medium should scale $m_ρ^\star/m_ρ\sim (\la\bar{q}q\ra^\star/\la\bar{q}q\ra)^{1/2}$ from $n=0$ up to $\sim n=n_0$ (where $n_0$ is nuclear matter density) and then go over to the linear scaling $m_ρ^\star/m_ρ\sim \la\bar{q}q\ra^\star/\la\bar{q}q\ra$ up to the chiral transition density $n_c$ at which the mass is to vanish (in the chiral limit) according to the vector manifestation fixed point. In the regime of the linear scaling above $n_0$, the (vector) gauge coupling constant should fall linearly in $\la\bar{q}q\ra^\star$, vanishing at the critical point, with the width of the vector meson becoming steeply narrower. We suggest the in-medium vector meson mass, {\em both} parametric and pole, which goes smoothly to zero with increasing density, to be an order parameter for chiral symmetry restoration. Some issues related to recent RHIC observations are qualitatively discussed in the appendices. Our main conclusion that follows from these considerations is that the movement towards chiral restoration can be reliably described in Nambu-Jona-Lasinio mean field, with constituent quarks as variables, although there is probably density discontinuity following chiral restoration.