Infrared Slavery Above and Hadronic Freedom Below Tc

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Presentation transcript:

Infrared Slavery Above and Hadronic Freedom Below Tc HIM@APCTP The Ideal Liquid Discovered by RHIC Infrared Slavery Above and Hadronic Freedom Below Tc in collaboration with G.E. Brown, M. Rho, (partly, H.-J. Park, E. Shuryak) NPA 740 (2004) 171; 747 (2005) 530 hep-ph/0503016 nucl-th/0507011; nucl-th/0507073 Chang-Hwan Lee @

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: Scaling decay width & Delayed-decay of mesons

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 !

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

Above Tc: Ideal Liquid at RHIC (Shuryak’s talk) Matter formed at RHIC is not weakly interacting quasi-particle gas. Question Can hadronic modes survive after phase transition ? How can these modes connected with chiral symmetry restoration below Tc ?

Mesonic bound states above Tc: Hatsuda & Kunihiro, PRL 55 (1985) 158 (para pion & sigma) Asakawa, Hatsuda, & Nakahara, NPA 715 (2003) 863c Brown, Lee, Rho, & Shuryak, NPA 740 (2004) 171 Quark-antiquark bound states exists above Tc. QM2005 - Poster by Kitazawa (with Kunihiro, Nemoto) hep-ph/0505070, … - talk by Mannarelli (with Rapp)

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.

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

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

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

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

With modified potential (chiral limit)

heavy quark potential chiral limit heavy quark potential chiral limit

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;+

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

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

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

nucl-th/0507073 : 0.14 ≤ (rho0/pi-) ≤ 0.21 Peripheral collisions: Tchemical freeze out = Tc 4 x 10-4 with vacuum mass ( Braun-Munzinger et al. ) With massless mesonic bound states at Tc this ratio is governed mainly by degrees of freedom 3 (rho0) = 0.14 21 (pi- from rho, …) nucl-th/0507073 : 0.14 ≤ (rho0/pi-) ≤ 0.21

Conclusions Our analysis (chiral symmetry restoration + Bielefeld Lattice Result) indicates massless mesonic 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.

NA60 Comparison of data to RW, BR and Vacuum  pT dependence

Too early to rule out BR scaling. Comments on NA60 vs BR BR: done by Rapp. No consideration on scaling decay width. Q) What is bump around 0.5 GeV ?