Pion Velocity near the Chiral Phase Transition

An enhancement of dielectron mass spectra below ρ/ω resonance observed at CERN SPS3) can be explained by the dropping mass of ρ meson4) following the Brown-Rho scaling.5) There is a scenario which certainly requires the dropping mass of the vector meson and supprots the Brown-Rho scaling, named the vector manifestation (VM)6) where the massless vector meson becomes the chiral partner of pion at the critical point. By using the effective field theory based on the hidden local symmetry (HLS), which includes both pions and vector mesons as the dynamical degrees of freedom, and performing the Wilsonian matching which is one of the methods to determine the bare theory from the underlying QCD, the VM has been formulated.6) As pointed out in Ref. 7), in the chiral phase transition in hot and/or dense matter, the intrinsic temperature and/or density dependences of the parameters of the HLS Lagrangian, which are obtained by integrating out the high energy modes (i.e., the quarks and gluons above the matching scale) in medium, play the essential roles to realize the chiral symmetry restoration consistently. Further, the intrinsic temperature and/or density dependences cause the effect of Lorentz symmetry breaking to the bare parameters. In Ref. 1), starting from the bare HLS theory without Lorentz invariance, it was proven that the non-renormalization property on the pion velocity in hot matter, which is protected by the VM. This can be understood based on the idea of chiral partners: Away from Tc, the contribution from the longitudinal mode of thermal vector meson ρL is suppressed owing to the Boltzmann factor exp[−Mρ/T ], and only the thermal pion contributes to the pion velocity. Then there exists the hadronic thermal correction to the pion velocity. On the other hand, when we approach the critical temperature, the vector meson mass goes to zero due to the VM. Thus exp[−Mρ/T ] is no longer the suppression factor. As a result, the hadronic thermal correction to the pion velocity is absent due to the exact cancellation between the contribution from pion and that from its chiral partner ρL. Similarly, the quantum correction generated from the pion loop is exactly cancelled by that from the ρL loop. Accordingly we conclude