Vector Manifestation and Violation of Vector Dominance in Hot Matter

Abstract

We show the details of the calculation of the hadronic thermal corrections to the two-point functions in the effective field theory of QCD for pions and vector mesons based on the hidden local symmetry (HLS) in hot matter using the background field gauge. We study the temperature dependence of the pion velocity in the low temperature region determined from the hadronic thermal corrections, and show that, due to the presence of the dynamical vector meson, the pion velocity is smaller than the speed of the light already at one-loop level, in contrast to the result obtained in the ordinary chiral perturbation theory including only the pion at one-loop. Including the intrinsic temperature dependences of the parameters of the HLS Lagrangian determined from the underlying QCD through the Wilsonian matching, we show how the vector manifestation (VM), in which the massless vector meson becomes the chiral partner of pion, is realized at the critical temperature. We present a new prediction of the VM on the direct photon-$π$-$π$ coupling which measures the validity of the vector dominance (VD) of the electromagnetic form factor of the pion: We find that the VD is largely violated at the critical temperature, which indicates that the assumption of the VD made in several analyses on the dilepton spectra in hot matter may need to be weakened for consistently including the effect of the dropping mass of the vector meson.