Hidden Local Symmetry as an Effective Field Theory of QCD

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

2. 1. Introduction

3. Q C D ? Low Energy hadron Phenomena

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

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

6. ◎ Chiral Perturbation Theory EFT for π J. Gasser and H. Leutwyler, Annals Phys. 158, 142 (1984); NPB 250, 517 (1985) ・leading order Lagrangian + Skyrme term ⇒ stable soliton ☆ many parameters ! ・・・ not determined by the chiral symmetry should be detemined from QCD ☆ Effective Field Theories based on the chiral symmetry of QCD ◎ Hidden Local Symmetry Theory ・・・ EFT for r and p 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 r loop expansion ⇔ derivative expansion e.g., M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) ・leading order Lagrangian ⇒ stable soliton

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

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

9. 3. Wilsonian Matching in the Chiral Limit

10. ☆ Basic Concept of Wilsonian matching matching integrate out ~ 1 GeV Bare theory bare parameters Quantum effects Quantum theory physical quantities M.H. and K.Yamawaki, PRD 64, 014023 (2001) high energy (perturbative treatment) QCD quarks and gluons Both (perturbative) QCD and HLS are applicable L HLS rand p low energy

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

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

13. ◎ ◎ ◎ ☆ Wilsonian Matching Conditions

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

15. 4. Wilsonian Matching with Current Quark Masses M.H., T.Fujimori and C.Sasaki, in preparation

16. ☆ Inclusion of current quark masses in the HLS

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

18. cf: Gelman-Oaks-Renar relation ☆ Matching at Q2 = Λ2 ◎ Wilsonian matching conditions

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

20. 5. Summary ◎ 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