Understanding the Quark-Gluon Plasma via String Theory Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs A. Wiedemann hep-ph/ , hep-ph/ , hep-ph/ Qudsia Ejaz, Thomas Faulkner, HL, Krishna Rajagopal, Urs Wiedemann to appear

Plan Heavy ion collisions Jet quenching J/ψ suppression: a prediction Shear viscosity (a quick overview) N =4 SYM v.s. QCD

Quark-Gluon Plasma At room temperature, quarks and gluons are always confined inside colorless objects (hadrons): protons, neutrons, pions, …..  Quark-gluon plasma (QGP) Very high temperature (asymptotic freedom):  Interactions become weak  quarks and gluons deconfined Infinitely high temperature: QGP behaves like an ideal gas.

Is there a deconfinement phase transition separating the hadronic and QGP phases? Can one create quark-gluon plasma in the lab?

QCD Phase diagram (2006) Smooth crossover at

Relativistic Heavy ion collisions

Relativistic Heavy Ion Collider (RHIC) RHIC: Au+Au LHC: Pb + Pb (2009) : center of mass energy per pair of nucleons Au: 197 nucleons; Total: 39.4 TeV Energy density (peak) > 5 GeV/fm 3 Temperature (peak) ~ 300 MeV

Creating a little Big Bang

Experimental probes of the QGP ? QGP at RHIC exists for about sec (5 fm), making it impossible to study it using any external probes. Some basic questions: Has the QGP been formed? Has the created hot matter reached thermal equilibrium? If yes, when? Properties: weakly or strongly coupled? equation of state? Viscosity? opacity? What are its signatures?

Quark-gluon fluid of RHIC Collective behavior of the observed final-state hadrons (elliptic flow) Interaction of produced hard probes with the medium (jet quenching, J/Ψ suppression) Nearly ideal, strongly coupled fluid (sQGP) But information on dynamical quantities: scarce and indirect Main theoretical tool for strong coupling: Lattice calculation New theoretical tools are needed. But information on dynamical quantities: scarce and indirect New theoretical tools are needed!

String theory to the rescue!

Collective motion and shear viscosity of sQGP

Collective motion If lots of p+p collisions plus free streaming: final state momenta uniformly distributed in azimuth angle. If interaction  equilibration  pressure  pressure gradients  collective motion  anisotropy of momenta distribution in. x y

Elliptic flow Rough agreement with hydrodynamic models based on perfect liquid. Near-perfect fluid discovered Created hot matter equilibrates very early: before 1fm. likely strongly interacting ! Strong signal ! Shear viscosity should be small!

Universality of Shear viscosity Policastro, Son, and Starinets (2001) N =4 SYM: The value turned out to be universal for all strongly coupled QGPs with a gravity description. RHIC: Teaney (2003) Kovton, Son and Starinets (2003) Buchel, J. Liu Lattice: Meyer (2007) Water

AdS/CFT and Jet quenching

Hard probes Hard scatterings in p+p collisions produce: back-to-back high energy quarks ("jets“). The presence of hot matter modifies the properties of jets.

Jet Quenching 1.The number of high energy particles observed should be much smaller than expected from p+p collisions : 2. monojets: sometimes they never make out. Only 20% ! QGP They lose energy! QGP

Parton energy loss in QGP Baier, Dokshitzer, Mueller, Peigne, Schiff (1996): : reflects the ability of the medium to “quench” jets. The dominant effect of the medium on a high energy parton is medium-induced Bremsstrahlung.

Toward understanding Opacity : 5-15 GeV 2 /fm Perturbation theory: Experimental estimate: Strongly coupled QGP? : < 1 GeV 2 /fm Hadronic gas: : < 0.1 GeV 2 /fm Theoretical challenge: non-perturbative calculation of for QCD QGP slightly above T C.

Need a non-perturbative definition of Compute in SYM theory using AdS/CFT Strategy:

: a non-perturbative formulation : multiple rescatterings of hard particles with the medium Hard: weakly coupled Soft: likely strongly coupled Assume: E >> ω >> k┴ >>T

Soft scatterings Amplitude for a particle propagating in the medium Soft scatterings are captured by Light like Wilson lines. Zakharov (1997); Wiedemann (2000) High energy limit (eikonal approximation):

A non-perturbative definition of Assuming: Thermal average (Hard to calculate using lattice) Nonperturbative definition of Wiedemann HL, Rajagopal, Wiedemann L : conjugate to the p T Light-like Wilson loop: : length of the medium

Wilson loop from AdS/CFT Black hole in AdS spacetime: radial coordinate r, horizon: r=r 0 constant r surface: (3+1)-dim Minkowski spacetime horizon Recipe: Maldacena (1998); Rey and Yee (1998) Our (3+1)-dim world, Wilson loop C in our world : area of string worldsheet with boundary C

Extremal configuration r=r 0 extremal string configuration: string touches the horizon. two disjoint strings Interactions between the quark and the medium Interaction of the string with the horizon of a black hole.

Wilson loop The corresponding BDMPS transport coefficient reads With

of N =4 SYM theory It is not proportional to number of scattering centers Experimental estimates: 5-15 GeV 2 /fm BDMPS transport coefficient reads: Take:

and number of degrees of freedom General conformal field theories (CFT) with a gravity dual: (large N and strong coupling) s CFT : entropy density an estimate for QCD: HL,Rajagopal Wiedemann, For non-conformal theories, it may decrease with RG flow.

Summary In QGP of QCD, the energy loss of a high energy parton can be described perturbatively up to a non-perturbative jet-quenching parameter. We calculate the parameter in N =4 SYM (not necessarily full energy loss of SYM) It appears to be close to the experimental value.

Quarkonium suppression: a prediction for LHC or RHIC II

Heavy quarkonium in a QGP Above T C, light-quark mesons no longer exist due to deconfinement. : T diss = 2.1 T C : T diss = 3.6 T C while their excited states already dissociate above 1.2 T C. Heavy quarkonia are bound by short-distance Coulomb interaction: may still exist above T C. In a QGP, interactions between a quark and an anti-quark are screened by the plasma. A heavy quark meson will dissociate when the screening length becomes of order the bound state size.

Quarkonium suppression Quarkonium suppression is a sensitive probe of QGP. Matsui and Satz (1987) J/ψ

Heavy quark mesons produced in heavy ion collisions could move very fast relative to the hot medium: How does the screening effect depend on the velocity? (not known in QCD) Velocity dependence of the T diss ? Connecting lattice QCD directly to heavy ion phenomenology is difficult:

Static quark potential in N =4 SYM probe brane event horizon quarks are screened LsLs Finding string shape of minimal energy In the large N C and large limit:, quark potential = energy of open string connecting the pair Maldacena; Rey, Yee; Rey, Theisen Yee; Brandhuber, Itzhaki, Sonnenschein Yankielowicz ……..

Quark potential at finite velocity Finding string shape of minimal energy Event horizon Moving at a finite velocity v In a rest frame of quark pair, the medium is boosted: HL, Rajagopal Wiedemann

Velocity dependence of dissociation temperature Dissociation temperature T d : d: size of a meson What would happen if QCD also has similar velocity scaling? Given: this suggests:

Has RHIC reached T d for J/ψ ? Lattice: J/ψ may survive up to 2T C Similarity of the magnitude of J/ψ suppression at RHIC and SPS RHIC has not reached T diss for J/ψ. Karsch, Kharzeev, Satz,

Quarkonium suppression: a prediction via string theory Heavy quark mesons with larger velocity dissociate at a lower temperature. HL,Rajagopal,Wiedemann This effect may be significant and tested at RHIC II or LHC Expect significant suppression at large P T. J/psi

Data to come RHIC: low statistics on J/ψ with 2 < P T < 5 GeV, no data for P T > 5GeV Reach in P T will extend to 10 GeV in coming years at RHIC. LHC will reach even wider range.

N =4 SYM versus QCD

Conformal no asymptotic freedom, no confinement supersymmetric no chiral condensate no dynamical quarks, 6 scalar and 4 Weyl fermionic fields in the adjoint representation. Physics near vacuum and at very high energy is very different from that of QCD N =4 SYM theory

conformal no asymptotic freedom, no confinement supersymmetric (badly broken ) no chiral condensate no dynamical quarks, 6 scalars and 4 fermions in the adjoint representation. N =4 SYM at finite T QCD at T ~T C -3 T C N =4 SYM versus QCD (continued) near conformal (lattice) not intrinsic properties of sQGP not present may be taken care of by proper normalization

N =4 SYM versus QCD Strongly coupled N =4 SYM at finite T Ideal gas (T= infinity QCD) T=0 QCD confinement

It is likely that QCD has a string dual in the large N limit. Finite-T QCD in a strongly coupled regime could be described by a black hole in this string theory. N =4 SYM versus QCD Universality of black hole (horizon physics) Universality between QCD and N =4 SYM for observables probing intrinsic properties of the medium.

Summary String theory techniques provide qualitative, and semi-quantitative insights and predictions regarding properties of strongly interacting quark-gluon plasma: Shear viscosity Jet quenching parameter Quarkonium suppression (a prediction) Expect many more chapters to be written for the marriage between string theory and physics of QCD in extreme conditions.

Energy and entropy density QCD: N =4 SYM: Karsch:hep-lat/ Gubser, Klebanov,Peet (1998)

Speed of sound Karsch, hep-ph/

Jet quenching: monojet phenomenon STAR collaboration: nucl-ex/

Jet quenching: data (II)