hidden local symmetry at loops

Masayasu Harada (Nagoya Univ.)

based on (mainly)

M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003)

at University of Tokyo

Other related references

• M.Bando, T.Kugo and K.Yamawaki, Phys. Rept. 164, 217 (1988)

• M.H. and K.Yamawaki, Phys. Lett. B 297, 151 (1992)

• M.H., T.Kugo and K.Yamawaki, Phys. Rev. Lett. 71, 1299 (1993)

• M.H., T.Kugo and K.Yamawaki, Prog. Theor. Phys. 91, 801 (1994)

• M.H. and A.Shibata, Phys. Rev. D 55, 6716 (1997)

• M.H. and K.Yamawaki, Phys. Rev. Lett. 83, 3374 (1999)

• M.H. and K.Yamawaki, Phys. Rev. D 64, 014023 (2001)

• M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001)

• M.H. and K.Yamawaki, Phys. Rev. Lett. 87, 152001 (2001)

• M.H. and C.Sasaki, Phys. Lett. B 537, 280 (2002)

• M.H., Y.Kim and M.Rho, Phys. Rev. D 66, 016003 (2002)

• M.H., Y.Kim, M.Rho and C.Sasaki, Nucl. Phys. A 727, 437 (2003)

• M.H., M.Tanabashi and K.Yamawaki, Phys. Lett. B 568 103 (2003)

• M.H. and C.Sasaki, hep-ph/0304282

• C.Sasaki, hep-ph/030600

• M.H., Y.Kim, M.Rho and C.Sasaki, hep-ph/0308237

Q C D

Low Energy hadron Phenomena

E

αs

Asymptotic freedom

☆ Difficulty ?

QCD ・・・ Strong Coupling Gauge Theory

Limit of Parameters & Symmetry Properties in QCD

Perturbative QCD

Heavy Quark Symmetry

(asymptotic freedom)

Chiral Symmetry

Theory of weakly interacting mesons

☆ QCD → Effective Field Theories

Chiral Symmetry

E

αs

Effective

Field

Theory

based on

chiral symmetry

EFT for π ☆ Chiral Perturbation Theory

based on chiral symmetry of QCD

P-wave ππ scattering

J. Gasser and H. Leutwyler, Annals Phys. 158, 142 (1984); NPB 250, 517 (1985)

1-loop

tree

too many parameters !!

determine from QCD

☆ matching between EFT and QCD (T=μ=0)

QCD quarks and gluons

Bare theory

EFT for hadrons

bare parameters

Quantum effects

Quantum theory

physical quantities

matchingΛ

high energy

low energy

EFT for π ☆ Chiral Perturbation Theory

matching to QCD Λ⇒ ～ 1 GeV

P-wave ππ scattering

J. Gasser and H. Leutwyler, Annals Phys. 158, 142 (1984); NPB 250, 517 (1985)

1-loop

tree

☆ Hidden Local SymmetryEFT for π and ρ

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)

based on chiral symmetry of QCD

ρ gauge boson of HLS

works well for E ～ mρ

reduces to chiral Lagrangian for E ≪ mρ

HLS at tree level

equivalent !!

Other models for vector meson

◎ Matter field method

◎ Massive Yang-Mills method

◎ Anti-symmetric tensor field method

(tree level)

☆ Chiral Perturbation Theory with HLSH.Georgi, PRL 63, 1917 (1989); NPB 331, 311 (1990):

M.Tanabashi, PLB 316, 534 (1993):

M.H. and K.Yamawaki, PRD 64, 014023 (2001)

Systematic low-energy expansion E ～ mρ

loop expansion ⇔ derivative expansion

Applicable for E 1.2 GeV≦

Phenomena for E > mρ

☆ Matching HLS with QCDM.H. and K.Yamawaki, PRD 64, 014023 (2001)

QCD ⇔ HLS

One can study QCD in other conditions

(N > 3)f

Outline

1. Introduction

2. Spontaneous Symmetry Breaking

and Effective Field Theory

3. Brief Review of Chiral Perturbation Theory

4. Hidden Local Symmetry (HLS)

5. Chiral Perturbation Theory with HLS

6. Wilsonian Matching

7. Vector Manifestation (in large flavor QCD)

8. HLS in Hot and/or Dense Matter

9. Vector Manifestation in Hot and/or Dense Matter

10. Effects of Lorentz Violation at Bare Level

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