Pion Velocity near the Chiral Phase Transition

Abstract

We study the pion velocity near the critical temperature $T_c$ of chiral symmetry restoration in QCD. Using the hidden local symmetry (HLS) model as the effective field theory, where the chiral symmetry restoration is realized as the vector manifestation (VM), we show that the pion velocity for $T \to T_c$ receives neither quantum nor (thermal) hadronic corrections at the critical temperature even when we start from the bare theory with Lorentz symmetry breaking. We show that this is related to a new fixed point structure originated in the VM. Further we match at a matching scale the axial-vector current correlator in the HLS with the one in the operator product expansion for QCD, and present the matching condition to determine the bare pion velocity. We find that the pion velocity is close to the speed of light, $v_\pi (T) = 0.83 - 0.99$.