Ad SCFT and Heavy Ion Collisions at RHIC

Ad. S/CFT and Heavy Ion Collisions at RHIC and LHC Hong Liu Massachusetts Institute of Technology

QCD has presented us many fascinating dynamical phenomena: Confinement, chiral symmetry breaking, asymptotic freedom, internal structure of nucleons …… largely guided by experiments, great challenges for theorists. Recently, heavy ion collision experiments opened new windows into probing dynamical phenomena in QCD: Many body physics, collective phenomena, ……. thermalization, finite temperature, ……

Small baryon density : Smooth crossover at

Relativistic heavy ion collisions RHIC (2000): Au+Au : center of mass energy per pair of nucleons Au: 197 nucleons; Total: 39. 4 Te. V Temperature (1 fm after collision) ~ 250 Me. V Baryon chemical potential ~ 27 Me. V Deconfinement crossover in QCD: TC ~ 170 Me. V LHC: Pb + Pb (2009)

QCD Phase diagram LHC RHIC

Quark-gluon liquid Experiments at RHIC suggest: At T ~ 1. 5 TC , the quark-gluon plasma (QGP) is so strongly coupled that it is better thought of as a liquid than a gas. A B Evolution well described by ideal hydrodynamics (very small viscosity)

according to perturbative QCD calculations Water

How to calculate properties of a strongly coupled QGP liquid? Lattice calculations: great for static (thermodynamic) properties dynamical quantities: scarce and indirect Perturbative QCD calculations: right theory, wrong approximation

String theory to the rescue!

Ad. S/CFT correspondence Maldacena (1997), Gubser, Klebanov, Polyakov; Witten (1998) Strongly coupled gauge theories Finite temperature QGP Classical gravity in a higher dimensional spacetime Black hole Infinite families of examples are known, including gauge theories which are: conformal or nonconformal confining or non-confining supersymmetric or non-supersymmetric

(3+1)-dim world, Finite Temperature Ad. S event horizon (black hole) Ad. S: anti-de Sitter spacetime (negative cosmological constant) Our (3+1)-dimensional world lies at the boundary of Ad. S.

However, it is NOT yet known what is the gravity description of QCD.

Strategy Understand QGP properties in other theories which are analyzable at strong coupling and compare with experiments. (wrong theory, right approximation) new discovery machine, look for universality “Ising model’’ for QCD QGP: N=4 Supersymmetric Yang-Mills at finite T two parameters: NC , scale invariant Large NC , large λ limit: “easy’’ to calculate

Purpose of the talk Describe some of the dynamical insights into properties of strongly coupled plasma obtained from Ad. S/CFT: • Thermodynamic properties • Shear viscosity • Jet quenching • heavy quark diffusion • Quarkonium suppression (a prediction from string theory)

Q 1: Thermodynamics N=4 SYM: Gubser, Klebanov, Peet Thermodynamics of very weakly and very strongly coupled plasmas can be similar. Infinite families of gauge theories (with different gauge groups and matter contents) share similar properties: Nishioka, Takayanagi

RHIC Karsch hep-lat/0106019 QCD: Weak dependence on T of in the range TC ~ 4 TC approximately scale invariant

Q 2: Shear viscosity For all known strongly coupled QGPs with a gravity description: Policastro, Son, and Starinets Kovtun, Son and Starinets Buchel, J. Liu Conformal or not, supersymmetric or not, chemical potential or not, confining at T=0 or not, having fundamentals or not with varying number of degrees of freedom QCD: The only other system which comes close: strongly coupled cold atomic gas

Universality ? We now know infinite classes of different QGPs: similar thermodynamical properties universality of shear viscosity Is QCD at T~ a few TC in this class? To what observables does the universality apply ?

Q 3: Jet Quenching 10 -20 Ge. V jet High energy partons lose energy quickly in the QGP ? ? an excess of low energy particles redistributed to rather large angles The dominant effect of the medium on a high energy parton is medium-induced Bremsstrahlung. : reflects the ability of the medium to “quench” jets. encodes all the soft physics (in the high energy limit )

Jet Quenching parameter Experimental estimate: : 5 -15 Ge. V 2/fm Perturbation theory: : <1 From N=4 SYM: Ge. V 2/fm HL, Rajagopal, Wiedemann is NOT proportional to the number of scattering centers.

Universality of ? A family of conformal field theories (CFT) with a gravity dual: (large N and strong coupling) HL, Rajagopal Wiedemann, s. CFT : entropy density Estimate for QCD:

Q 4: Heavy quarks moving in a QGP Considering a very heavy quark moving in a QGP, is it more like an electron moving in the water (point-like, bremsstrahlung) or a bullet moving in the water (described by hydrodynamics) not known in QCD

A moving quark in a strongly coupled N=4 plasma Chesler , Yaffe, 0712. 0050 See also Gubser, Pufu and Yarom

A prediction from string theory

Heavy quarkonia as probes of QGP A hallmark of QGP is that it screens color objects. The potential between the quark and anti-quark in a quarkonium bound state is sensitive to the screening of the plasma. They dissociate at Td > TC Heavy ion collisions: color screening in the produced medium J/ψ suppression Matsui and Satz (1987)

Screening of heavy quarks in QCD Heavy quark potential for T > TC O. Kaczmarek, F. Karsch, P. Petreczky, F. Zantow, hep-lat/0309121 Screening length: Heavy ion collisions: Q and Qbar move relative to the plasma screening at finite velocity ? (not known)

Screening in N=4 SYM V(L): potential between a Q and Qbar LS(T) Similar to QCD above TC L

Finite velocity scaling HL, Rajagopal, Wiedemann Moving at a finite velocity v Finding string shape of minimal energy Event horizon Dissociation temperature: Chernicoff, Garcia, Guijosa Peeters, Sonnenschein, Zamaklar

I will now assume a similar scaling applies to QCD Dissociation temperature:

A prediction from string theory HL, Rajagopal, Wiedemann zero velocity : (lattice) Hatsuda; ~ 2. 1 TC Asakawa, Datta, Karsch, : Tdiss ~ 3. 6 TC Petreczky, Wetzorke RHIC ~1. 5 Tc LHC? Could lead to significant suppression at large PT. This effect may be tested at RHIC II or LHC J/ψ RHIC

Nuclear modification factor RAA • Double the p. T range to 10 Ge. V/c • Consistent with no suppression at high p. T: RAA(p. T>5 Ge. V/c) = 0. 89± 0. 20 • Indicates RAA increase from low p. T to high p. T • Different from expectation of most models: Ad. S/CFT: H. Liu, K. Rajagopal and U. A. Wiedemann, PRL 98, 182301(2007) and hep-ph/0607062 Two Component Approach: X. Zhao and R. Rapp, hep-ph/07122407 Quark Matter 2008, Jaipur, India, Feb. 4 -10, 2008 33 Zebo Tang, USTC/BNL

Propagation of mesons in QGP Does the screening affect the propagation of mesons in a QGP? Mateos, Myers and Thomson Speed limit : As Ejaz, Faulkner, HL, Rajagopal, Wiedemann , This could also lead to observable effects.

Heavy ion collisions and Ad. S/CFT String theory techniques provide qualitative, and semiquantitative insights and predictions regarding properties of strongly interacting quark-gluon plasma. Many other things I did not have time to discuss “Wrong theory, right approximation” appears to work much better than “right theory, wrong approximation” Universality? Thank You