Masayasu Harada (Nagoya Univ.)

based on M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003) M.H., T.Fujimori and C.Sasaki, in preparation

@ KIAS-Hanyang Joint Workshop on Multifaceted Skyrmions and Effective Field Theory

(October 26, 2004 KIAS)

Q C D

Low Energy hadron Phenomena

E

αs

Asymptotic freedom

☆ Difficulty ?

QCD ・・・ Strong Coupling Gauge Theory

☆ QCD → Effective Field Theories

Chiral Symmetry

E

αsEffective

Field

Theory

based on

chiral symmetry

☆ Effective Field Theories based on the chiral symmetry of QCD

EFT for π ◎ Chiral Perturbation TheoryJ. 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 54 1215 (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

［SU(N ) ×SU(N ) ］ ×［SU(N ) ］ → ［SU(N ) ］f f fL R Vglobal local Vf global

［SU(N ) ×SU(N ) ］ ×［SU(N ) ］ → ［SU(N ) ］f f fL R Vglobal local Vf global

U = e = ξ ξ2iπ/ F πL†

R

ξ = e e → h ξ g±iπ / Fπiσ / FσL,R L,R L,R

†ξ = e e → h ξ g±iπ / Fπ±iπ / Fπiσ / Fσiσ / FσL,R L,R L,R

†

F , F ・・・ Decay constants of π and σπ σ

h ∈ ［ SU(N ) ］f V local

g ∈ ［ SU(N ) ］fL,R 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 GeVBoth (perturbative) QCD andHLS are applicable

☆ Basic Concept of Wilsonian matching

integrateout

M.H. and K.Yamawaki, PRD 64, 014023 (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 Q2 = Λ2

◎ 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