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Hidden Local Symmetry at Loops

Hidden Local Symmetry at Loops. An Effective Field Theory for QCD. Masayasu Harada (Nagoya Univ.). at University of Tokyo. based on (mainly) M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003). Other related references. M.Bando, T.Kugo and K.Yamawaki, Phys. Rept. 164 , 217 (1988)

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Hidden Local Symmetry at Loops

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  1. Hidden Local Symmetry at Loops An Effective Field Theory for QCD Masayasu Harada (Nagoya Univ.) at University of Tokyo based on (mainly) M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003)

  2. 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

  3. 1. Introduction

  4. Q C D ? Low Energy hadron Phenomena

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

  6. Perturbative QCD (asymptotic freedom) Heavy Quark Symmetry Chiral Symmetry Theory of weakly interacting mesons Limitof Parameters &SymmetryProperties in QCD

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

  8. P-waveππ scattering ☆ Chiral Perturbation Theory EFT for π J. Gasser and H. Leutwyler, Annals Phys. 158, 142 (1984); NPB 250, 517 (1985) based on chiral symmetry of QCD too many parameters !! determine from QCD 1-loop tree

  9. ☆ matching between EFT and QCD (T=μ=0) high energy QCD quarks and gluons Λ matching EFT for hadrons Bare theory bare parameters Quantum effects low energy Quantum theory physical quantities

  10. P-waveππ scattering ☆ Chiral Perturbation Theory EFT for π J. Gasser and H. Leutwyler, Annals Phys. 158, 142 (1984); NPB 250, 517 (1985) matching to QCD ⇒ Λ～ 1 GeV 1-loop tree

  11. EFT for π and ρ ρ gauge boson of HLS based on chiral symmetry of QCD works well forE～ m ρ reduces to chiral Lagrangian forE ≪ m ρ ☆ Hidden Local Symmetry 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)

  12. (tree level) Other models for vector meson ◎ Matter field method ◎ Massive Yang-Mills method ◎ Anti-symmetric tensor field method HLS at tree level equivalent !!

  13. Systematic low-energy expansion E～ m ρ Phenomena for E > m ρ ☆ Chiral Perturbation Theory with HLS H.Georgi, PRL 63, 1917 (1989); NPB 331, 311 (1990): M.Tanabashi, PLB 316, 534 (1993): M.H. and K.Yamawaki, PRD 64, 014023 (2001) loop expansion ⇔ derivative expansion Applicable for E ≦ 1.2 GeV

  14. Wilsonian Matching ☆ Matching HLS with QCD M.H. and K.Yamawaki, PRD 64, 014023 (2001)

  15. (N > 3) f large flavor QCD QCD ⇔ HLS Wilsonian Matching One can study QCD in other conditions Hot and/or Dense QCD

  16. 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

  17. 2. Spontaneous Symmetry Breaking and Effective Field Theory

  18. -

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