Masayasu Harada (Nagoya Univ.) based on M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003) M.H., T.Fujimori and C.Sasaki, in KIAS-Hanyang Joint Workshop on Multifaceted Skyrmions and Effective Field Theory (October 26, 2004 KIAS)

Q C D Low Energy hadron Phenomena

E α s Asymptotic freedom ☆ Difficulty ? QCD ・・・ Strong Coupling Gauge Theory

☆ QCD → Effective Field Theories Chiral Symmetry E α s Effective Field Theory based on chiral symmetry

☆ Effective Field Theories based on the chiral symmetry of QCD EFT for π ◎ Chiral Perturbation Theory J. Gasser and H. Leutwyler, Annals Phys. 158, 142 (1984); NPB 250, 517 (1985) ・ leading order Lagrangian + Skyrme term ⇒ stable soliton ◎ Hidden Local Symmetry Theory ・・・ EFT for  and  M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, PRL (1985) M. Bando, T. Kugo and K. Yamawaki, Phys. Rept. 164, 217 (1988) ρ ・・・ gauge boson of HLS Systematic low-energy expansion including dynamical  loop expansion ⇔ derivative expansion e.g., M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) ・ leading order Lagrangian ⇒ stable soliton ☆ many parameters ! ・・・ not determined by the chiral symmetry should be detemined from QCD

Outline 1. Introduction 2. Hidden Local Symmetry 3. Wilsonian Matching in the Chiral Limit 4. Wilsonian matching with Current Quark Masses 5. Summary

2. Hidden Local Symmetry U = e = ξ ξ 2 i π/ F π L † R F, F ・・・ Decay constants of π and σ πσ h ∈ ［ SU(N ) ］ fV local g ∈ ［ SU(N ) ］ f L,R global ・ Particles in the leading order Lagrangian

QCD quarks and gluons HLS  and   high energy low energy Bare theory bare parameters Quantum effects Quantum theory physical quantities (perturbative treatment) matching ~ 1 GeV Both (perturbative) QCD and HLS are applicable ☆ Basic Concept of Wilsonian matching integrate out M.H. and K.Yamawaki, PRD 64, (2001)

◎ Generating functional in EFT J : external source fields F : parameters of EFT ◎ Generating functional in QCD ☆ Basic Concept of Wilsonian matching ◎ Wilsonian matching bare theory bare parameter

☆ Matching of axial-vector and vector current correlators ◎ QCD (OPE) ◎ HLS Matching

☆ Wilsonian Matching Conditions ◎ ◎ ◎

☆ A typical prediction of Wilsonian Matching ・ bare parameters M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003) ◎ ρ － γ mixing strength good agreement ! + quantum corrections improved by RGEs + + ・・・ π π ρ γ

M.H., T.Fujimori and C.Sasaki, in preparation

☆ Inclusion of current quark masses in the HLS

☆ Axial-vector current correlator ・ 2 components because of the explicit chiral symmetry breaking π-channel matching

☆ Matching at Q 2 = Λ 2 ◎ Wilsonian matching conditions cf: Gelman-Oaks-Renar relation

☆ Typical predictions M.H., T.Fujimori and C.Sasaki, in preparation bare parameters ρ π ρ K + quantum corrections improved by RGEs + + ・・・ + very good agreement !

◎ Wilsonian matching between the HLS and QCD with current quark masses included Matching of axial-vector current correlator Determination of the bare parameters + quantum corrections improved by RGEs Physical predictions very good agreement ! ◎ future direction Application of the WM to hot and/or dense QCD with the effect of current quark masses included