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Masayasu Harada (Nagoya Univ.)

Vector Manifestation and the Hidden Local Symmetry. Masayasu Harada (Nagoya Univ.). at International Conference on QCD and Hadronic Physics (June 18, 2005, Beijing). based on (mainly) M.H. and K.Yamawaki, Phys. Rev. Lett. 86 , 757 (2001)

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Masayasu Harada (Nagoya Univ.)

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  1. Vector Manifestation and the Hidden Local Symmetry Masayasu Harada(Nagoya Univ.) at International Conference on QCD and Hadronic Physics (June 18, 2005, Beijing) based on (mainly) M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001) M.H. and C.Sasaki, Phys. Lett. B 537, 280 (2002) M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003) M.H. and C.Sasaki, Nucl. Phys. A 736, 300 (2004) M.H., Y.Kim, M.Rho and C.Sasaki, Nucl. Phys. A 730, 379 (2004) M.H., T.Fujimori and C.Sasaki, in preparation

  2. 1. Introduction

  3. ☆ In-medium modification of r/w mesons KEK-PS E325 CERES/CERN CB/TAPS@ELSA

  4. R.Rapp-J.Wambach, ANP 25,1 (2000) dropping r mass based on Brown-Rho scaling ☆ Dropping r/w mass (Brown-Rho scaling) can explain KEK-PS E325 CB/TAPS@ELSA

  5. Theoretical description of dropping r mass ? ☆ Vector Manifestation M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001) near chiral restoration point longitudinal r= Chiral partner of p Dropping r mass ・・・ necessary for the VM. ☆ Brown-Rho scaling implies dropping rmass ⇔ chiral symmetry restoration

  6. Outline 1. Introduction 2. Hidden Local Symmetry Theory 3. Vector Manifestation of Chiral Symmetry 4. Formulation of the Vector Manifestation in Hot Matter 5. Summary

  7. 2. Hidden Local Symmetry Theory 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) M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003) M.H., T.Fujimori and C.Sasaki, in preparation

  8. ◎ 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) M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) based on chiral symmetry of QCD ρ ・・・ gauge boson of the HLS

  9. ☆ 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 ρμ = ρμaTa・・・ HLS gauge boson π=πaTa・・・ NG boson of ［SU(Nf)L×SU(Nf)R］global symmetry breaking σ=σaTa・・・ NG boson of ［SU(Nf)V］local symmetry breaking

  10. ◎ Hidden Local Symmetry Theory ・・・ EFT for r and p ◎ Chiral Perturbation Theory with HLS H.Georgi, PRL 63, 1917 (1989); NPB 331, 311 (1990): M.H. and K.Yamawaki, PLB297, 151 (1992) M.Tanabashi, PLB 316, 534 (1993): M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) Systematic low-energy expansion including dynamical r loop expansion ⇔ derivative expansion 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) M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) based on chiral symmetry of QCD r・・・ gauge boson of the HLS

  11. ☆ Validity of the expansion ? ? ☆ Expansion Parameter ◎ ordinary ChPT for p chiral symmetry breaking scale ◎ ChPT with HLS

  12. ? ・・・ justified in the large Nc QCD This is true for any models ! This is NOT enough for a systematic expansion !!

  13. ２ may cause 1/m corrections ◎ e.g., in Matter Field Method ρ ◎ In HLS with Rξ- like gauge fixing ・・・ well-defined limit of m → 0 ρ ? gauge invariance ・・・ guaranteed by the gauge invariance in the HLS

  14. ☆ Order Counting ・・・ same as ordinary ChPT loop expansion = low-energy expansion ☆ Expansion Parameter in the ChPT with HLS ☆ Validity of the expansion O.K. in the large Nc QCD O.K. in the HLS

  15. ・ 4-quark state → σ does not exist in the large Nc QCD ・ 2-quark state → mσ = ma0 = 980 MeV > mρ in the large Nc QCD σ is not needed in the large Nc QCD ? ☆ Effect of scalar meson ? ◎ σ(600) (Γσ = 370 MeV) mσ= 560 MeV < mρ = 770 MeV see e.g., M.H., F.Sannino and J.Schechter, PRD 54, 1991 (1996)

  16. ◎ No need of scalar meson in large Nc QCD Unitarity in pp scattering is satisfied without scalar meson up untillE ≦ 4pFp for Nc ≧ 6 M.H., F.Sannino, J.Schechter, PRD69, 034005 (2004) real part of S-wave amplitude Nc=3 Nc=4 Nc=5 0.5 (Fp)2～ Nc g2～ 1/Nc a = 2 (fixed) Nc=7 Nc=6 0 0

  17. ◎ 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) based on chiral symmetry of QCD ρ ・・・ gauge boson of the HLS ◎ Chiral Perturbation Theory with HLS H.Georgi, PRL 63, 1917 (1989); NPB 331, 311 (1990): M.H. and K.Yamawaki, PLB297, 151 (1992) M.Tanabashi, PLB 316, 534 (1993): M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) Systematic low-energy expansion including dynamical r loop expansion ⇔ derivative expansion ☆ many parameters ! ・・・ not determined by the chiral symmetry should be detemined from QCD more experimental data are available

  18. matching integrate out ~ 1 GeV Bare theory bare parameters Quantum effects Quantum theory physical quantities ☆ Wilsonian matching between EFT and QCD M.H. and K.Yamawaki, PRD 64, 014023 (2001) high energy QCD quarks and gluons (perturbative treatment) Both (perturbative) QCD and EFT are applicable Λ EFT for hadrons low energy

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

  20. ☆ Inclusion of the effect of current quark masses bare parameters π + quantum corrections improved by RGEs K ρ + + ・・・ ρ + + ・・・ very good agreement ! M.H., T.Fujimori and C.Sasaki, in preparation

  21. 3. Vector Manifestation of Chiral Symmetry M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001) M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003) Note : work in the chiral limit (mq = 0)

  22. ☆ Vector Manifestation M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (2001) ・・・ Wigner realization of chiral symmetry longitudinalρ ＝ chiral partner of π c.f. conventional linear-sigma model manifestation scalar meson = chiral partner of π

  23. Quark Structure and Chiral representation (S. Weinberg, 69’) coupling to currents and densities longitudinal components

  24. Chiral Restoration vector manifestation linear sigma model mρ → 0 is necessary ・・・ support BR scaling

  25. 4. Formulation of the Vector Manifestation in Hot Matter M.H. and C.Sasaki, Phys. Lett. B 537, 280 (2002) M.H. and C.Sasaki, Nucl. Phys. A 736, 300 (2004)

  26. ◎ Assumptions ・ Relevant d.o.f until near Tc-ε ・・・ only π and ρ ・ Other mesons (A1, σ, ...) ・・・ still heavy ・ Partial chiral restoration already at Tc-ε ☆ View of the VM in Hot Matter

  27. ・・・ Bare parameters have temperature dependences. Wilsonian matching condition at T = 0 ☆ Application of the Wilsonian matching at T > 0 high energy QCD quarks and gluons (perturbative treatment : OPE) Λ matching integrate out quarks and gluons in hot matter Bare HLS forrandp Extension of WM condition to T > 0 low energy ◎ Intrinsic temperature dependence signature of internal structure of hadrons (Hadrons are constructed from quarks and gluons.)

  28. ☆ Wilsonian matching at T → Tc - e • current correlators in the OPE ☆ Can we satisfy GV → GA in the HLS ?

  29. ☆ Yes ! ◎VM Conditionsin hot matterfor T → Tc ☆ Can we satisfy GV → GA for T → Tc in the HLS ? ◎ current correlators in the bare HLS

  30. VM conditions quantum effect through RGEs hadronic thermal effects π ρ ・・・ fixed point of RGE ρ π ☆ ρ pole mass for T → Tc bare theory → 0 Vector Manifestation

  31. mρ→ 0・・・ signal of the chiral symmetry restoration ! G.E.Brown and M.Rho, PRL 66, 2720 (1991) ☆ Is mr(T) → 0 related to the chiral symmetry restoration ? ◎ Wilsonian matching near Tc add the quantum and hadronic thermal corrections ◎ Quantum theory

  32. ◎ Hidden Local Symmetry Theory・・・ EFT for r and p Systematic low-energy expansion including dynamical r loop expansion ⇔ derivative expansion ◎ Wilsonian matching between the HLS and QCD Matching of axial-vector and vector current correlators → Determination of the bare parameters + quantum corrections improved by Wilsonian RGEs Physical predictions ・・・ very good agreement ! ◎ Vector Manifestation in hot matter ・・・ mρ → 0 for T → Tc ⇒ mρ→ 0・・・ signal of the chiral symmetry restoration ! 5. Summary

  33. ・ Pion velocity near Tc for T → Tc ・ Vector and axial-vector susceptibilities at Tc determined by the intrinsic thermal effects • M.H., Y.Kim, M.Rho and C.Sasaki, Nucl. Phys. A 727, 437 (2003) M.H., Y.Kim, M.Rho and C.Sasaki, Nucl. Phys. A 730, 379 (2004) ⇔ Prediction in the non-linear σ model vp(Tc) → 0 for T → Tc D.T.Son and M.A.Stephanov, PRL88, 202302 ・ Large violation of vector dominance of electromagnetic form factor of pion at Tc • M.H. and C.Sasaki, Nucl. Phys. A 736, 300 (2004) ◎ Predictions of the VM in hot matter

  34. The End

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