– referred to as “vector manifestation (VM) fixed point" – is reached when the quark condensate vanishes.*]{}

In HLS$_1$ (as well as HLS$_\infty$) theory, the vector meson masses are generated by the Higgs mechanism, with the scalar $\sigma$ eaten by the vector mesons. The mass formula therefore is m\_V\^2=g\^2 F\_\^2=a g\^2 F\_\^2. It has been shown that near the critical point, either $T_c$ or $n_c$, the coupling $g$ goes to zero proportionally to $\la\bar{q}q\ra$. Therefore at the chiral restoration, the parametric mass behaves m\_V\~g\~|[q]{}q0. This is consistent with Brown-Rho scaling. The physical mass of $V_1$ also vanishes at the critical point.

The parametric pion decay constant does not exhibit any special feature as $\la\bar{q}q\ra\rightarrow 0$. However the physical pion decay constant $f_\pi=F_\pi +\delta f_\pi$ must go to zero as dictated by the low-energy theorem.

Vector dominance violation
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An important consequence for the problem we are concerned with of the VM fixed point is that the vector dominance in the EM form factors of hadrons is drastically affected. To see this, we look at the pion EM form factor. In the HLS$_1$ theory, the photon couples to the point-like pion with a coefficient $(1-a/2)$ and through the $V_1=\rho$ meson with 