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Transport properties of strongly coupled Quark-Gluon Plasma (sQGP)

Transport properties of strongly coupled Quark-Gluon Plasma (sQGP). Edward Shuryak Department of Physics and Astronomy State University of New York Stony Brook NY 11794 USA. Two types of transport particles <=> momentum (diffusion <=> viscosity). as coupling strength goes up

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Transport properties of strongly coupled Quark-Gluon Plasma (sQGP)

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  1. Transport properties ofstrongly coupled Quark-Gluon Plasma (sQGP) Edward Shuryak Department of Physics and Astronomy State University of New York Stony Brook NY 11794 USA

  2. Two types of transportparticles <=> momentum(diffusion <=> viscosity) as coupling strength goes up in MD, inAdS/CFT In gases both are proportional to the same collision cross section, but Viscosity only decreases for a while, And then other means of momentum Trasfer -- via collective modes -- appears And viscosity is again large in glasses and solids at very strong coupling Diffusion constant indefinitely decreases <= Particles ``get stuck” and cannot move Related to drag force By Einstein relation Dp/dx \sim 1/D

  3. Viscosity-diffusion summary plot ^ Better liquid AdS/CFT eta/s: Kovtun,Son, Starinets,hep-th/0405231 Dc:Casalderrey, Teaney, PRD 74,085012 (06) Colored lines: Classical MD for a strongly Coupled plasma with Monopoles: Liao,ES hep-ph/0611131,v2 (and this fig, is from its) wCFT: eta:Huot et al hep-ph/0608062 Dc:Chesler and Vuirinen hep-ph/0607148 ==> particle gets less mobile Plasma coupled stronger

  4. Why do we think that QGP is strongly coupled at RHIC?I-RHIC phenomenology • 1a: hydro works => viscosity is very low: eta/s=.1-.2 << 1 (Teaney,ES) • 1b: Because parton cascade requires huge cross sections >> (pQCD predictions) (Molnar-Gyulassy) (a comment: they are not the same => a cascade makes no sense in a strongly coupled regime, while hydro only works better) • 1c: charm diffusion: Dc << pQCD predicts (from R_AA and v2 of electrons at RHIC <= Moore+Teaney) • 1d: very strong jet quenching, including charm, again well beyond pQCD predictions • 1e: conical flow from quenched jets in Mach direction (Casalderrey-Teaney –ES) seem to be observed

  5. Wake effect or “sonic boom” Sonic boom from quenched jets Casalderrey,ES,Teaney, hep-ph/0410067; H.Stocker… • the energy deposited by jets into liquid-like strongly coupled QGP must go into conical shock waves • We solved relativistic hydrodynamics and got the flow picture • If there are start and end points, there are two spheres and a cone tangent to both

  6. PHENIX jet pair distribution Note: it is only projection of a cone to asymuth Note 2: more recent data on 3-body correlators, from both STAR/PHENIX are consistent with conical flow , not a deflected jet

  7. Why do we think that QGP is strongly coupled at RHIC?II-lattice+QM • 2a: ``New spectroscopy”: Interaction is strong enough to make multiple bound states (ES+Zahed, 03), s-wave n=1mesons, colored pairs like qg or non-singlet gg • 2b: Marginal states with small binding may lead to small m.f.p. <= (ES+Zahed, 03) a la Feshbach resonances for ultracold trapped atoms –charmed (Rapp, van Hees) • 2c: Baryons seem to survive till about 1.6Tc (Liao,ES) • 2d: large energy (up to 4 GeV) and entropy (up to 20)of a heavy dipole around Tc(Karsch et al,04) remains a mystery: huge number of states, many quasiparticles? Protostrings =>Polymeric “electric” chains of gluons barQ - g - g … Q(Liao,ES)

  8. Why do we think that QGP is strongly coupled at RHIC?III:AdS/CFTN=4 SUSY YM theory at strong coupling at finite T  sQGP at RHIC • 3a: p,e=O( N^2 T^4) even the famous coefficient .8 is better reproduced by the large-g (Klebanov…96) series (3/4+…) • 3b: viscosity is small: eta/s=1/4pi (Son et al,04) • 3c:Heavy quarkdrag and diffusion constant are OK (Yaffe et al, Casalderrey-Teaney)and conical flow is seen(Gubser et al) • 3d: a complete gravity dual to RHIC collisions =>departing black hole/ horizon=>ES,Sin+Zahed, Janik-Peschanski, Gubser… • 3e: quasiparticles are heavy M*=sqrt(lambda)T>>T and have huge number of bound states

  9. Why do we think that QGP is strongly coupled at RHIC?IV-Electric/Magnetic duality • N=2 SUSY YM (``Seiberg-Witten theory”) is a working example of confinement due to condenced monopoles • It teached us that monopoles must be very light and weakly interacting (in IR) near the critical point • This + Dirac condition => [(e g)/hbar c=1/2] => electric coupling must be large there • e/m equilibrium at (1.2-1.5)Tc: gluons and monopoles have comparable masses and couplings => • New picture: sQGP is a plasma of fighting electric and magnetic quasiparticles

  10. New (compactified) phase diagramdescribing an electric-vs-magnetic fight Dirac condition Thus at the e=g line Near deconfinement line g->0 in IR (Landau’s U(1) asymptotic freedom) => e-strong-coupling Why this diagram is better? => in allblue region There are e-flux tubes, not only in the confined phase! In fact, they are maximally enhanced at Tc,not below it.

  11. Entropy (and energy) associated with a static dipole gets huge at Tc (shown at large r only vs T/Tc ) • #(states) =exp(S)=e^16 • What those states may be? • string picture provides the answer • (Polyakov 78 => Klebanov,Maldacena,Thorn et al hep-th/0602255) • EQP language: electric polymers (Liao,ES hep-ph/0508035 Ads/CFT Minahan 98) Kaczmarec et al hep-lat/0510094

  12. are there e-flux tubes in QGP? • Dual superconductivity as a confinement mechanism (‘tHooft, Mandelstam 1980’s) => monopole condensation at T<Tc explains it => Meissner effect confines electric fluxes (dual to Abrikosov vortices) • But at T>Tc (uncondenced) MQPs do the same!Due toLorentz force they are reflected from a region with E field => compressing E into flux tubes, even in classical plasma!

  13. magnetic flux tubes at the Sun,(work without any superconductor!) where classical electrons rotate around it • B: about 1 kG, • Lifetime: few months

  14. Electric and magnetic screening masses E/M equilibrium • Dual Superconductor model works well • vacuum with monopole condensate • flux tube as Abrikosov vortex • Seiberg-Witten, a working example E dominated M- domi nated • Nakamura, et al, PRD69(2004)014506 • Approaching Tc from above: • E-screening mass decrease •  less E-charge •  E-charge getting heavier • M-screening mass increase •  more M-charge •  M-charge getting lighter G. S. Bali, hep-ph/9809351

  15. Classical strongly coupled plasmasAs Gamma= <|Epot|>/<Ekin> grows gas => liquid => solid Gelman,ES,Zahed,nucl-th/0601029 With a non-Abelian color => Wong eqn Gas, liquid solid

  16. MD simulation for plasma with monopoles (Liao,ES hep-ph/0611131)monopole admixture matters: 50-50 mixture makes the best liquiddiffusion decreases indefinitely, viscosity does not(1000 particles in a stable spherical drop) Diffusion can be stopped

  17. A flurry of recent papers on heavy quark dynamics in N=4 plasma • HKKKYhep-th/0605158 • J.Casalderrey and D.Teaney hep-ph/0605199 diffusion constant for heavy quark • Agree nicely via Einstein relation (very nontrivial in string setting) • Qualitatively agree with classical MD results!

  18. Now we compare Dc to weak and strong coupling predictions The cross is phenomenological range added by me, following Moore-Teaney R_AA, v2 ==> Range from MD With different EQPs/MQPs ratio ==> Strong: not very Diferent from MD Weak coupling Chester and Vuorinen, Hep-ph/0607148

  19. Floating matter destributionFriess et al, 0607022

  20. Subsonic emission => no cone(as in b-tagged jets – Antinori,ES, nucl-th/0507046) subsonic Supersonic Note how angle moves as v->cs

  21. Short history of developing``gravity dual” for RHICfrom basically 5dim GR • AdS+Black Hole: Hawking radiation from the horizon is used to mimic non-zero T(Witten,98) • receeding BH/horizon from collapsing matter =>cooling+expansion(ES,Sin,Zahed,05) • Stretching black hole => Large-time solution (Janik-Peschanski,05) reproduces Bjorken hydro, even withviscosity (Nakamura+Sin,06,Janik 06) • Falling objects produced in a collision form amembrane falling under its own weight => (Shu Lin and ES,hep-ph/0610168) <= Israel’s junction cond.1966 • nov.06 Gubser et al Departing point black hole solution => spherically expoding fireballl

  22. (Shu Lin and ES,hep-ph/0610168) departing 2 heavy ultrarelativistic quarks stretch a longitudinal string 5-dim Pythia model in which strings don’t break But fall instead into the 5th dimension AdS5 center Scaling solution (used in Euclidean appl. By Gross et al, Makeenko) is only stable if Y<.27 and exist if Y<.5 The non-scaling solution approach rectangular shape, small fragmentation region and rapidity-independent bulk AdS5 center

  23. All objects – massless, massive close strings, open strings => fall in AdS and form a massive membrane because they tend to the same trajectory at large time=> Observer at z=0 (r=infty) sees induced Tmn with hydro flow Strething black hole has approximately conserved horizon area => entropy Old AdS metric New metric, JP at late time (I disagree with Janik on singularity issue)

  24. Strongly coupled QGP has been produced at RHIC robust collective flows, even for charm Strong jet quenching leading to robust conical flow, now supported by 3-body correlators AdS/CFT => strongly coupled conformal regime not too close to Tc Heavy quark diffusion and quenching in the right ballpark conical flow seen hydro explosion can be derived from GR => Collapsing membrane, bh formation Conclusions • at (1-1.4)Tc dominated by magnetic QPs • postconfinementwith e-flux tubes • Classical MD is being done, smaller viscosity due to monopoles

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