  We study the pion velocity at the critical temperature of chiral symmetry
restoration in QCD. Starting from the premise that the bare effective field
theory is to be defined from the underlying QCD, we incorporate the effects of
Lorentz non-invariance into the bare theory by matching an effective field
theory to QCD at a suitable matching scale, and investigate how the Lorentz
non-invariance existing in the bare theory influences physical quantities.
Using the hidden local symmetry model as the effective field theory, where the
chiral symmetry restoration is realized as the vector manifestation (VM), we
find that the pion velocity at the critical temperature receives neither
quantum nor (thermal) hadronic corrections at the critical temperature even
when we start from the bare theory with Lorentz symmetry breaking. This is
likely the manifestation of a new fixed point in the Lorentz non-invariant
formulation of the VM.
