Dropping ρ and A 1 meson masses at the chiral phase transition in the generalized hidden local symmetry

We study the chiral symmetry restoration using the generalized hidden local symmetry which incorporates the rho and A{sub 1} mesons as the gauge bosons of the generalized hidden local symmetry and the pion as the Nambu-Goldstone boson consistently with the chiral symmetry of QCD. We show that a set of parameter relations, which ensures the first and second Weinberg sum rules, is invariant under the renormalization group evolution. Then, we found that the Weinberg sum rules together with the matching of the vector and axial-vector current correlators inevitably lead to the dropping masses of both rho and A{sub 1} mesons at the symmetry restoration point, and that the mass ratio as well as the mixing angle between the pion and A{sub 1} meson flows into one of three fixed points.