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9. Vector Manifestation in Hot and/or Dense Matter

9. Vector Manifestation in Hot and/or Dense Matter. 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. and C.Sasaki, hep-ph/0304282.

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9. Vector Manifestation in Hot and/or Dense Matter

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  1. 9. Vector Manifestation in Hot and/or Dense Matter • 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. and C.Sasaki, hep-ph/0304282

  2. 9.1 Why VM in Hot and/or Dense QCD ?

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

  4. 他の極限 ？ QCD のさらなる解明への手がかり

  5. T μ B ☆ 有限温度・有限密度ＱＣＤ • 相構造の変化 • ハドロンの性質の変化 宇宙の進化 クォーク・グルーオン・プラズマ相 相 転 移 カラー超伝導相 ハドロン相 コンパクト天体 （中性子星・クォーク星） 通常の核物質

  6. J-PARC (原研 + KEK) • GSI ◎ 有限温度・有限密度ＱＣＤに関する実験 温度 これまでの実験・稼動中の実験 • SIS (GSI; Germany) • AGS (Brookhaven; USA) • SPS (CERN;Swintzerland) • RHIC (Brookhaven; USA) クォーク・グルーオン・プラズマ相 実験計画 • LHC (CERN) ハドロン相 密度

  7. QCDの情報 • 有限温度・有限密度でのハドロンの性質 • QGP相でのクォーク・グルーオンの性質 • 終状態のハドロン（π, P等）の観測 ◎ レプトン対のエネルギースペクトルの観測 ・・・

  8. ☆ 有限温度・有限密度ではハドロンの性質は真空中とは異なる ！ 分布 真空中と同じ分布関数 では説明できない レプトン対のエネルギー

  9. ☆ 実験を説明するシナリオ 1. ドロッピング ρ・・・ m (T, μ ) → 小 , Γ(T, μ ) → 小 for T, μ → 大 ρ ρ B B B 2. コリジョン・ブロードニング ・・・ Γ → 大, m～ ほぼ一定 for T, μ → 大 ρ ρ B コリジョン・ブロードニング ドロッピング ρ

  10. VM predicts dropping rho meson mass. Other predictions of VM ?

  11. Outline of Section 9 9.1 Why VM in hot and/or dense QCD ? 9.2 Vector manifestation in terms of chiral representation 9.3 Intrinsic temperature and/or density dependence 9.4 VM conditions at Tc and μc 9.5 Vector meson mass in the VM at Tc 9.6 Pion decay constants and pion velocity at Tc 9.7 Determination of the critical temperature 9.8 Vector and axial-vector susceptibilities at Tc 9.9 Violation of vector dominance at Tc 9.10 Vector manifestation in dense matter

  12. 9.2 Vector Manifestation in terms of Chiral Representation

  13. ☆ Vector Manifestation ・・・ Wigner realization of chiral symmetry ρ ＝ chiral partner of π c.f. conventional linear-sigma model manifestation scalar meson = chiral partner of π

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

  15. Chiral Restoration vector manifestation linear sigma model

  16. 9.3 Intrinsic Temperature and/or Density Dependence

  17. ☆ Application of Wilsonian matching at T > 0 and/or μ> 0 high energy QCD quarks and gluons Λ matching HLS ρ, π (and quasiquark) Intrinsic temperature and/or density dependence of bare parameters of the HLS hadronic thermal loop effects dense loop effects low energy Quantum effects physical quantities

  18. 9.4 VM Conditions at Tc and/or μc

  19. How do we realize Π → Π in hadronic picture ? V A • assumption ・・・ 2ndor weak 1st order phase transition for T → Tc and/or μ→μc ◎ Chiral symmetry restoration is characterized by

  20. ☆ Bare Parametes ・・・Intrinsic T and/or m dependences ◎ VM conditions for T → T and/or c ◎ current correlators in the bare HLS

  21. 9.5 Vector meson mass in the VM at the critical temperature

  22. 9.6 Pion decay constants and pion velocity at the ctrical temperature

  23. ☆ Temporal and spatial pion decay constants ; ; hadronic thermal correction parametric pion decay constant renormalized in the low-energy limit (Quantum corrections are included.)

  24. ・ VM condition : ☆ VM at Tc ◎ Pion velocity at Tc ・ Pion velocity becomes speed of light ⇔ cf: Vπ = 0 in the pion only theory (D.T.Son and M.Stephnov, PRL 88, 202302)

  25. 9.7 Determination of the critical temperature

  26. ・ RGE at Tc ・ Wilsonian matching

  27. 9.8 Vector and Axial-vector Susceptibilities at Critical Temperature M.H. Y.Kim, M.Rho and C.Sasaki, Nucl. Phys. A 727, 437 (2003)

  28. ☆ Vector and Axial-vector Susceptibilities at : vector current : axialvector current must be satisfied at Chiral Restoration M.H. Y.Kim, M.Rho and C.Sasaki, Nucl. Phys. A 727, 437 (2003)

  29. 9.9 Violation of vector dominance at the critical temperature M.H. and C.Sasaki, hep-ph/0304282

  30. Vector Dominance ☆ Pion EM form factor (tree level at T = 0)

  31. ☆ parametera at T>0 ・ VM condition : ; ◎ near Tc・・・ intrinsic thermal effect becomes important Large violation of vector dominance !

  32. 9.10 Vector Manifestation in Dense Matter M.H., Y.Kim and M.Rho, Phys. Rev. D 66, 016003 (2002)

  33. Please note that, in this subsection, I use μ ・・・baryon chemical potential M・・・ renormalization scale

  34. ☆ Inclusion of quasiquark near the critical point near the critical point G.E.Brown and M.Rho, Phys. Rept. 363, 85 (2002) Lagrangian

  35. ☆ Bare Parametes ・・・Intrinsic density dependences ◎ VM conditions for μ → μ c ◎ current correlators in the bare HLS

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