STAR $\rho^0/\pi^-$ Ratio in Au-Au Peripheral Collisions at RHIC and the Vector Manifestation of Hidden Local Symmetry

Abstract

The hidden local symmetry effective theory, Wilsonian matched to QCD at a matching scale near the chiral scale $\sim 4\pi f_\pi$ as formulated by Harada and Yamawaki, presents a scenario drastically different from the standard scenario of heavy-ion collisions in that as the temperature approaches the critical temperature $T_c$ of chiral restoration from below, the mass of the vector mesons and their widths go to zero in the chiral limit or nearly zero otherwise, proportionally to some power of the quark condensate at what is called "vector manifestation (VM) fixed point". This scenario makes a striking prediction that as the fire-ball expands and cools from $T_c$ down toward the freezeout temperature $T_{freezeout}$ in heavy ion collisions, what we call "hadronic freedom" sets in in which hadrons do not interact or barely interact. We suggest that this scenario is testable at RHIC and as a specific example, we provide an astonishingly simple explanation in terms of the vector manifestation suitably extended to include axial-vector mesons for the anomalously large $\rho^0/\pi^-$ ratio measured in peripheral collisions by STAR.