Hidden local symmetry at loop: A new perspective of composite gauge boson and chiral phase transition

Abstract

We develop an effective field theory of QCD and QCD-like theories beyond the Standard Model, based on the hidden local symmetry (HLS) model for the pseudoscalar mesons ( π) as Nambu–Goldstone bosons and the vector mesons ( ρ) as gauge bosons. The presence of gauge symmetry of HLS is vital to the systematic low energy expansion or the chiral perturbation theory (ChPT) with loops of ρ as well as π. We first formulate the ChPT with HLS in details and further include quadratic divergences which are crucial to the chiral phase transition. Detailed calculations of the one-loop renormalization-group equation of the parameters of the HLS model are given, based on which we show the phase diagram of the full parameter space. The bare parameters (defined at cutoff Λ) of the HLS model are determined by the matching (“Wilsonian matching”) with the underlying QCD at Λ through the operator-product expansion of current correlators. Amazingly, the Wilsonian matching provides the effective field theory with the otherwise unknown information of the underlying QCD such as the explicit N c dependence and predicts low energy phenomenology for the three-flavored QCD in remarkable agreement with the experiments. Furthermore, when the chiral symmetry restoration takes place in the underlying QCD, the Wilsonian matching uniquely leads to the Vector Manifestation (VM) as a new pattern of Wigner realization of chiral symmetry, with the ρ becoming degenerate with the massless π as the chiral partner. In the VM the vector dominance is badly violated. The VM is in fact realized in the large N f QCD when N f → N f crit−0, with the chiral symmetry restoration point N f crit≃5 N c /3 being in rough agreement with the lattice simulation for N c =3. The large N f QCD near the critical point provides a concrete example of a strong coupling gauge theory that generates a theory of weakly coupled light composite gauge bosons. Similarly to the Seiberg duality in the SUSY QCD, the SU( N f ) HLS plays a role of a “magnetic theory” dual to the SU( N c ) QCD as an “electric theory”. The proof of the low energy theorem of the HLS at any loop order is intact even including quadratic divergences. The VM can be realized also in hot and/or dense QCD.