Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition

TL;DR

This paper develops an effective field theory based on hidden local symmetry to describe chiral phase transitions in QCD, predicting the vector manifestation where rho mesons become chiral partners with pions.

Contribution

It introduces a novel formulation of the HLS model with loop corrections and quadratic divergences, providing a unified description of chiral symmetry restoration and the vector manifestation.

Findings

Wilsonian matching predicts low energy QCD phenomenology accurately.

The vector manifestation predicts rho as a chiral partner of pions at the phase transition.

Large Nf QCD supports the realization of the VM near the critical number of flavors.

Abstract

We develop an effective field theory of QCD and QCD-like theories, based on the hidden local symmetry (HLS) model. We formulate the chiral perturbation theory with loops of rho as well as pi 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, with the bare parameters (defined at cutoff Lambda) determined by the matching (``Wilsonian matching'') with the underlying QCD at Lambda through the operator-product expansion of current correlators. The Wilsonian matching predicts low energy phenomenology for the three-flavored QCD in remarkable agreement with the experiments. When the chiral symmetry restoration takes place in the underlying QCD, the HLS model uniquely leads to the Vector Manifestation (VM) as a new pattern of Wigner realization of chiral symmetry, with the rho becoming degenerate with the massless pi as the chiral partner. The VM is in fact realized in the large Nf QCD when Nf to Nf^{crit}-0, with Nf^{crit} = 5 Nc/3 being in rough agreement with the lattice simulation for Nc=3. The VM can be realized also in hot and/or dense QCD.