Masayasu Harada (Nagoya Univ.)

1. Dilepton Production from Dropping Rho in the Vector Manifestation Masayasu Harada(Nagoya Univ.) at Chiral 07 (Osaka, November 14, 2007) based on M.H. and C.Sasaki, Phys.Rev.D74:114006,2006 see also M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003) 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. and C.Sasaki, Nucl. Phys. A 736, 300 (2004)

2. 1. Introduction ☆ ＱＣＤ in hot and dense matter T Quark-Gluon-Plasma phase Color-Superconducting phase Hadron phase μB

3. ☆ Melting of quark – anti-quark condensate 〈 q q 〉 Is there a signal ?

4. ☆ Brown-Rho scaling G.E.Brown and M.Rho, Phys. Rev. Lett. 66 2720 (1991) dropping r mass ⇔ chiral symmetry restoration Theoretical description of dropping r mass. ☆ Vector Manifestation M.H. and K.Yamawaki, Phys. Rev. Lett. 86, 757 (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). near chiral restoration point longitudinal r= Chiral partner of p Dropping r mass ・・・ signal of the chiral restoration based on the VM.

5. 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

6. ☆ Strong violation of the VD・・・ Prediction of the VM gives a substancial suppression ! G. E. Brown and M. Rho, arXiv:nucl-th/0509001; arXiv:nucl-th/0509002. ☆ Recent experiments exclude dropping ρ ? CERES : Talk given by P. Braun-Munzinger at KIAS-APCTP Workshop "Relativistic Heavy-Ion Collison : Present and Future" 2006-09 Heavy Ion Meeting (HIM 2006-09). NA60 Nucl.Phys.A774:715-718,2006. dropping ρ?? ☆ These analyses seem to assume the vector dominance (VD). Effect from the violation of the VD to the rate ?

7. Outline 1. Introduction 2. Hidden Local Symmetry and the Vector Dominance 3. Thermal Dilepton Spectra in the Vector Manifestation 4. Summary

8. 2. Hidden Local Symmetry and the Vector Dominance ◎ Hidden Local Symmetry ・・・ EFT for r and pbased on chiral symmetry of QCD 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) r = gauge boson of the HLS massive through the Higgs mechanism ◎ Systematic low-energy expansion including dynamical r 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) loop expansion ⇔ derivative expansion

9. † U=e= ξ ξ L R 2iπ/ F π F , F・・・ Decay constants of π and σ π σ 2 m = ag F 2 2 π ρ h ∈ ［SU(N ) ］ f V local ◎ 3 parameters at the leading order g ∈ ［SU(N ) ］ Fp・・・ pion decay constant g・・・ gauge coupling of the HLS a = (Fs/Fp)2 ⇔ validity of the vector dominance f L,R global L,R ☆ Hidden Local Symmetry ・ 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. ◎ HLS analysis[M.H. and K.Yamawaki, Phys. Rept. 381, 1 (2003)] ・ a = 4/3 in the large Nc limit ・ a = 2 including 1/Nc corrections cf: AdS/QCD anlysis by Sakai-Sugimoto, PTP143,843 (2005) see also AdS/QCD analysis by M.H., M.Matsuzaki and K.Yamawaki, PRD74, 076004 (2006). r dominance is accidental only for Nc = 3 (and T = 0) ☆ Vector dominance (r dominance) at T = 0 e+ e- a/2 1 – a/2 a = 2 ⇒ vector dominance long standing problem not clearly explained in QCD !

11. e+ e- ☆ r dominance at T > 0 ? a/2 1 – a/2 0 → 1 1 → 1/2 ◎ a = 2 kept fixed in several analyses (No T-dependence on a) ◎ Parameters of hadronic Lagrangians depend on T. ・・・Intrinsic temperature dependence signature of internal structure of hadrons (Hadrons are constructed from quarks and gluons.) ・ VM predicts a(T) → 1whenmr(T) → 0forT → Tc Strong violation of r dominance in the VM Strong suppression of r contribution to the dilepton spectrum

12. ☆ Intrinsic temperature dependence of parameters ・・・ obtained by integrating out heavier hadrons ・ Effects of heavy hadrons are negligible ? ・・・ Not True near the critical temperature e.g., Hagedon temperature based on string model large Nc QCD each contribution from hadrons is suppressed by 1/Nc phase transition is driven by infinite number of hadrons ・ Infinite number of hadrons contribute near Tc in real-life QCD Integrating out infinite number of hadrons near Tc → a large T dependence of the parameters for effective models for light hadrons (e.g., π and ρ in the HLS)

13. ☆ 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

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

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

16. ☆ T-dependences of physical parameters ・・・ intrinsic T dependence + hadronic temperature effects from thermal π and ρ intrinsic T dependence for T > Tf = 0.7 Tc ρ mass mρ → 0 ρ width Γρ → 0 a Tf/Tc Tf/Tc ◎ Intrinsic T dependence ・・・ basic ingredient for the Vector Manifestation (VM) ◎ VM predicts ; dropping r ; strong violation of the vector dominance

17. ◎ Vector dominance ? direct γππ coupling ： 1 – a/2 Tf/Tc strong violation of the VD VD is good ・ Strong violation of the VD occurs near Tc due to the intrinsic effect.

18. 3. Thermal Dilepton Spectra in the VM M.H. and C.Sasaki, Phys.Rev.D74:114006,2006

19. T = 0.4 Tc No much difference ! ☆ Effect of violation of the vector dominance VM (forT → Tc) a(T) → 1 whenmr(T) → 0 VM with VD a(T) = 2 kept fixed whenmr(T) → 0 v.s.

20. T = 0.8 Tc vacuum ρ< VM < VM with VD T = 0.85 Tc vacuum ρ≪ VM ≪ VM with VD!! Signal of the VM Violation of VD is very important ◎ Near Tc T = 0.75 Tc VM with VD vacuum ρ VM < vacuum ρ< VM with VD!! VM

21. ◎ Hidden Local Symmetry Theory・・・ EFT for r and p Systematic chiral perturbation including dynamical r ◎ Vector dominance in the HLS ・ a = 4/3 in the large Nc limit ・ a = 2 including 1/Nc corrections ◎ Vector Manifestationin hot matter ・・・ mρ → 0 for T → Tc ⇒ mρ→ 0・・・ signal of the chiral symmetry restoration ! 4. Summary ・ strong violation of the VD ・・・ important for the dilepton rate ◎ future direction ・ Effects of collisional broadening including A1, … ・・・ work in progress (M.H., C.Sasaki and W.Weise)

22. The End