fixed point [@HY:PR]. We will call this Harada-Yamawaki theory “HLS/VM" for short.

We should however mention that this is not the only possibility. In fact, certain models can admit a non-zero $F(0)$, hence a non-zero mass, and still preserve chiral symmetry and allow a Goldstone-Wigner phase transition. For instance, one can have a linear sigma model with parity-doublet fermion fields [@parity-doublet]. In this model, the fermion mass can be non-zero in both the Goldstone and Wigner phases. The fermions can be baryons or constituent (quasi) quarks. In the former case, one can have massless mesons while having massive baryons at the critical point. In the latter case, both mesons and baryons as (weakly) bound states of quasiquarks could remain massive at the critical point with the chiral symmetry preserved. At present, neither theory nor experiment can rule out this scenario. However we find it unnatural within the HLS framework we are adopting. We shall not pursue this alternative scenario.

Hidden Local Symmetry (HLS)
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The well-established perturbative QCD cannot access the highly nonperturbative and strong-coupling regime at low energy we are concerned with. The only tool available at present is effective theories that meet Weinberg’s “folk theorem" [@weinberg-folk] on effective 