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Infrared Slavery Above and Hadronic Freedom Below Tc

@Nagoya. Infrared Slavery Above and Hadronic Freedom Below Tc. STAR rho^0/pi^- ratio. in collaboration mainly with G.E. Brown, Mannque Rho NPA 740 (2004) 171 (w/Shuryak) NPA 747 (2005) 530 nucl-th/0507073; PRC, accepted. Chang-Hwan Lee @. Our works on Exotic States in Hot & Dense Matter.

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Infrared Slavery Above and Hadronic Freedom Below Tc

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  1. @Nagoya Infrared Slavery Above and Hadronic Freedom Below Tc STAR rho^0/pi^- ratio in collaboration mainly with G.E. Brown, Mannque Rho NPA 740 (2004) 171 (w/Shuryak)NPA 747 (2005) 530nucl-th/0507073; PRC, accepted Chang-Hwan Lee @

  2. Our works on Exotic States in Hot & Dense Matter RHIC T Astrophysics Hadrons Neutron Star K bound system Black Hole Density

  3. Plan of Talk Below Tc : Chiral Symmetry Restoration Above Tc: colorless Mesonic Bound States • Brown/Rho Scaling • Vector Manifestation a la Harada/Yamawaki • What can we learn from lattice calculations ? • Implications for RHIC: STAR “rho^0/pi^-” ratio Scaling decay width & Delayed-decay of mesons

  4. Below Tc: Chiral Symmetry Restoration • Dropping Masses a la Brown/Rho Scaling • Harada/Yamawaki & Harada/Sasaki/Rho Vector Manifestation. Fixed Point of RG approach gives vanishing coupling, vanishing mass towards chiral symmetry restoration point. both mass & decay-width scale !

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

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

  8. 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

  9. below TcChiral Symmetry Restoration Vector Manifestation RG fixed point Vanishing coupling M r s RHIC p Tc Q) What happens above Tc ? Hadronization ?

  10. What RHIC found • RHIC data is consistent with ideal hydrodynamics. • Matter formed at RHIC is not weakly interacting quasi-particle gas. • It is the most perfect liquid known: viscosity/entropy (h/s) = 0.1 (much less than that of most liquids, e.g. h/s=1 for He4 at high pressure, 40 for water)

  11. Global Chemical Equilibrium with high temperature ! T=165 ±10 MeV, STAR White paper, 2005

  12. Ideal Hydro vs RHIC data [Teaney et al.]

  13. Flow

  14. Flow is consistent with ideal hydrodynamics

  15. Jet-quenching

  16. What happened at RHIC ? Hydrodynamical Expansion Elliptic Flow Hydrodynamical expansion of trapped Li6

  17. (h/s = 0) Ideal Hydrodynamics • QCD: h/s » 1 • RHIC : h/s ≈ 0.1 • AdS/CFT : h/s ≈ 0.08 (Policastro, Son, Starinets) • much less than that of most liquids h/s=1 for He4 at high pressureh/s=40 for water

  18. Question • Why does the matter formed at RHIC behaves as a nearly ideal fluid ? • What is the matter formed at RHIC ? • Because it’s in a very strong coupling regime • sQGP, Quark-Gluon-Liquid

  19. Mesonic bound states above Tc: • Hatsuda & Kunihiro, PRL 55 (1985) 158(para pion & sigma)Asakawa, Hatsuda, & Nakahara, NPA 715 (2003) 863cBrown, Lee, Rho, & Shuryak, NPA 740 (2004) 171Quark-antiquark bound states exists above Tc. - Kitazawa, Kunihiro, Nemoto

  20. Potential from Bielefeld Lattice Results cf) Wong, hep-ph/0408020; combination of V & F What is the binding energy if we take the potential extracted from lattice free energy ? Assumption: finite value of V1 at r=∞ is absorbed into the renormalized thermal mass of quarks.

  21. Above Tc: Running coupling at large diatance Strong coupling regime above Tc Lattice Calculation by F. Zantow et al. (Bielefeld)

  22. Heavy quark potential (renormalized) from Bielefeld lattice mq=1.4 GeV

  23. Mass of Bound States (with heavy quark potential) thermal quark mass Solid lines are just to guide you.

  24. Modification for light quarks in chiral limit color-magnetic effects (cf K-electron) a =velocity of particles (c=1 unit) With chirally restored u, d quarks (helicity eigenstates) 32 degrees of freedom (including plasmino) = lattice result 32 above Tc !

  25. Effective degrees of freedom [Karsch et al.] Idea gas limit staggered fermions Effective degrees of freedom is lower by 20% from ideal gas limit (massless limit). 32 istead of 37 (ideal gas limit)

  26. With modified potential (chiral limit)

  27. heavy quark potential chiral limit heavy quark potential chiral limit

  28. Unorthodox phase structure (Hypothesis) 2mq* a1 M r Mesons disappear qq s Ideal Liquid QGP p Tc Tzb • Masses of colorless pion, sigma-like modes above Tc go to zero at T = Tc;+

  29. Lattice Results from Miller: Gluon Condensate Soft glue Hard glue is responsible for ldeal liquid Hard glue

  30. Implications for RHIC Scaling decay width (nucl-th/0507073) Vector manifestation by Harada & Yamawaki No decay near Tc ! dominant decay is around & below T=120 MeV

  31. Braun-Munzinger, Stachel, Wetterich (2003) • Chemical freezeout temperature is close to Tc. • Equilibration in the chirally broken sector just below Tc. • Puzzle: “r/p” ratio was lower than STAR experiment roughly by a factor of 2 Our point of view Equilibrium of hadronic mode has to be already established above Tc at RHIC ! [ Below Tc, coupling vanishes ! ]

  32. STAR: Peripheral collisions: Tchemical freeze out = Tc PRL 92 (2004) 092301 Tc : chemical equilibrium Delayed decay of rho at T=120 MeV Equilibrium is already established above Tc at RHIC

  33. Rough counting 32 d.o.f. can produce roughly 60 p’s (including r, a1, s decay, etc) 19 p- With massless mesonic bound states at Tcthis ratio is governed mainly by degrees of freedom 3 (r0) = 0.15 20 (pi- from s & r, …)

  34. Peripheral collisions: Tchemical freeze out = Tc 4 x 10-4 with vacuum mass( Braun-Munzinger et al. ) With massless mesonic bound states at Tcthis ratio is governed mainly by degrees of freedom 3 (r0) = 0.16 19 (pi- from s & r, …) [ nucl-th/0507073, PRC, accepted]

  35. Conclusions • Our analysis (chiral symmetry restoration + Bielefeld Lattice Result) indicates masslessmesonic bound states at Tc;+. • mass & width (simultaneous scaling):delayed rho decay is consistent with rho/pi ratio in peripheral collisions in STAR. Thanks to Bielefeld Lattice Group (F. Zantow) for providing us their results.

  36. Lots to be done. • Problem of Hadronization through Tc :continuity of hadronic degrees of freedom • HBT puzzle • Clear signal of chiral symmetry restoration at RHIC? • …… Thanks !

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