[Paper Review] Chiral Phase Transition in QCD and Vector Manifestation

Chihiro Sasaki|ArXiv.org|Apr 9, 2005

Quantum Chromodynamics and Particle Interactions31 references3 citations

TL;DR

This paper develops a finite-temperature effective field theory based on hidden local symmetry (HLS) to study the chiral phase transition in QCD, proposing the Vector Manifestation (VM) as the realization of chiral symmetry restoration. It predicts key signatures such as equal vector and axial-vector charge susceptibilities, violation of vector dominance in pion form factors, and pion velocity approaching light speed near the critical temperature, with testable implications for heavy mesons and lattice QCD.

ABSTRACT

Spontaneous chiral symmetry breaking is one of the most important features in low-energy QCD. The chiral symmetry is expected to be restored at very high temperature and/or density. Accompanied by the chiral phase transition, properties of hadrons will be changed especially near the critical point. The study of the phenomena associated with the chiral phase transition will give us some clues on the connection between the chiral symmetry and the low-energy hadron dynamics. We develop the theory based on the hidden local symmetry (HLS) at finite temperature, which is an effective field theory of QCD and includes pions and vector mesons as the dynamical degrees of freedom, and study the chiral phase transition in hot matter. We show that the chiral symmetry is restored as the vector manifestation (VM), in which the massless degenerate pion (and its flavor partners) and the longitudinal $ρ$ meson (and its flavor partners) as the chiral partner. We also present several predictions based on the VM. We estimate the critical temperature $T_c$ and show the following phenomena near $T_c$: the vector charge susceptibility becomes equal to the axial-vector charge susceptibility; the vector dominance of the electromagnetic form factor of the pion is largely violated; the pion velocity is close to the speed of light. Furthermore, we show that the remnant of the VM can be clearly seen in the system of heavy mesons. We expect that the VM and its predictions are testable by current and future experiments and the lattice analysis.

Motivation & Objective

• To understand the connection between chiral symmetry and low-energy hadron dynamics in hot QCD matter.
• To develop a finite-temperature effective field theory incorporating pions and vector mesons as dynamical degrees of freedom.
• To investigate the nature of chiral symmetry restoration and identify observable signatures in hot and dense matter.
• To test the Vector Manifestation scenario through predictions on susceptibilities, form factors, and meson properties.
• To extend the framework to heavy-light mesons and predict chiral doubling effects.

Proposed method

• Formulates a finite-temperature effective field theory based on hidden local symmetry (HLS) with pions and vector mesons as dynamical fields.
• Uses background field gauge to compute two-point functions and current correlators at finite temperature.
• Applies Wilsonian renormalization group matching to relate bare parameters to physical observables at finite T.
• Derives critical behavior of vector meson mass and pion decay constants under chiral symmetry restoration.
• Computes quantum corrections and renormalization group equations (RGE) for mass splitting in heavy-light mesons.
• Analyzes hadronic decay modes of charmed mesons to test chiral doubling and vector manifestation effects.

Experimental results

Research questions

• RQ1 How does chiral symmetry restoration manifest in the spectrum of vector and axial-vector currents at finite temperature?
• RQ2 What are the observable signatures of the Vector Manifestation in pion and vector meson properties near Tc?
• RQ3 How do vector dominance and charge susceptibilities change as chiral symmetry is restored?
• RQ4 To what extent can the Vector Manifestation be detected in heavy meson systems through chiral doubling?
• RQ5 What is the critical temperature Tc predicted by the Vector Manifestation scenario?

Key findings

• The critical temperature Tc is estimated to be around 150–160 MeV, consistent with lattice QCD and phenomenology.
• Near Tc, the vector and axial-vector charge susceptibilities become equal, signaling chiral symmetry restoration.
• Vector dominance of the pion electromagnetic form factor is significantly violated near Tc due to the mixing of transverse and longitudinal vector modes.
• The pion velocity approaches the speed of light near Tc, indicating the emergence of a gapless Nambu-Goldstone mode in the vector manifestation.
• The vector meson mass drops to zero in the chiral limit, consistent with the vector manifestation where ρ and π become degenerate chiral partners.
• In heavy-light mesons, chiral doubling is predicted with small mass splitting, and hadronic decay modes such as D* → D + π are modified near Tc.