AdS/CFT and Heavy Ion Collisions at RHIC and LHC

Hong Liu

Massachusetts Institute of Technology

QCDQCD has presented us many fascinating dynamical phenomena:

Recently, heavy ion collision experiments opened new windows into probing dynamical phenomena in QCD:

Confinement, chiral symmetry breaking, asymptotic freedom,internal structure of nucleons……

largely guided by experiments, great challenges for theorists.

Many body physics, collective phenomena, …….

thermalization, finite temperature, ……

Smooth crossover at MeV 170~CTSmall baryon density :

Relativistic heavy ion collisions

Deconfinement crossover in QCD: TC ~ 170 MeV

LHC: Pb + Pb (2009) GeVsNN 500,5

RHIC (2000): Au+Au GeVsNN 200

NNs : center of mass energy per pair of nucleons

Au: 197 nucleons; Total: 39.4 TeV

Temperature (1 fm after collision) ~ 250 MeV

Baryon chemical potential ~ 27 MeV

QCD Phase diagram

RH

IC

LHC

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 ofas a liquid than a gas.

A B

Evolution well described by ideal hydrodynamics

(very small viscosity)

)1.0(densityentropy

osityshear viscO

s

)1(~ Os

according to perturbative QCD calculations

~ 10s

Water

How to calculate properties of a strongly coupled QGP liquid?

dynamical quantities: scarce and indirect

Lattice calculations:

great for static (thermodynamic) properties

Perturbative QCD calculations:

right theory, wrong approximation

String theory to the rescue!

AdS/CFT correspondenceMaldacena (1997), Gubser, Klebanov,Polyakov; Witten (1998)

Strongly coupledgauge theories

Classical gravity in a higher dimensional spacetime

Finite temperature

QGPBlack hole

Infinite families of examples are known, including gauge theories which are:

conformal or nonconformalconfining or non-confining supersymmetric or non-supersymmetric

0z

(3+1)-dim world,

Our (3+1)-dimensional world lies at the boundary of AdS.

AdS z

AdS: anti-de Sitter spacetime (negative cosmological constant)

Finite Temperature

event horizon (black hole)

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

However,

StrategyUnderstand QGP properties in other theories which are analyzable at strong coupling and compare with experiments.

(wrong theory, right approximation)

new discovery machine,

“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

look for universality

Purpose of the talk

Describe some of the dynamical insights into properties of strongly coupled plasma obtained from AdS/CFT:

• Shear viscosity

• Jet quenching

• heavy quark diffusion

• Thermodynamic properties

• Quarkonium suppression (a prediction from string theory)

Q1: ThermodynamicsN=4 SYM:

4

3

000

P

P

S

S

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:

2.1.89 ,4

3

0

ffS

S

Gubser, Klebanov, Peet

Nishioka, Takayanagi

RHIC

QCD: 06.14

38.0

)(

) few a(

CT

Weak dependence on T of in the range TC ~ 4 TC 4/T

approximately scale invariant

Karschhep-lat/0106019

Q2: Shear viscosityFor all known strongly coupled QGPs with a gravity description:

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

)1.0(Os

QCD:

The only other system which comes close: strongly coupled cold atomic gas

Policastro, Son, and Starinets

Kovtun, Son and Starinets Buchel, J. Liu

08.04

1

s

Universality ?

We now know infinite classes of different QGPs:

similar thermodynamical properties

universality of shear viscosity

To what observables does the universality apply ?

Is QCD at T~ a few TC in this class?

Q3:Jet Quenching10-20 GeV jet

????

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.

High energy partons lose energy quickly in the QGP

q̂ : reflects the ability of the medium to “quench” jets.

encodes all the soft physics (in the high energy limit )

Jet Quenching parameter

: 5-15 GeV2/fmq̂

Perturbation theory:

Experimental estimate:

: < 1 GeV2/fmq̂

q̂

From

is NOT proportional to the number of scattering centers. q̂

N=4 SYM:

33

45

432/3

69.26ˆ TNTq cSYMSYM

/fm.GeV 4.5ˆ 2SYMq MeV TC

N s 300 ,2

1 ,3

HL, Rajagopal, Wiedemann

Universality of ?

A family of conformal field theories (CFT) with a gravity dual: (large N and strong coupling)

ˆ

ˆ

44

N

CFT

N

CFT

s

s

q

qsCFT : entropy density

63.0120

5.47

ˆ

ˆ

44

N

QCD

N

QCD

s

s

q

q

Estimate for QCD:

HL,RajagopalWiedemann,

q̂

Q4: Heavy quarks moving in a QGP

Considering a very heavy quark moving in a QGP,

an electron moving in the water

a bullet moving in the water

(point-like, bremsstrahlung)

or

(described by hydrodynamics)

is it more like

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

The potential between the quark and anti-quark in a quarkonium bound state is sensitive to the screening of the plasma.

A hallmark of QGP is that it screens color objects.

Heavy ion collisions: color screening in the produced medium

Matsui and Satz (1987)

J/ψ suppression

They dissociate at Td > TC

Screening of heavy quarks in QCD

O.Kaczmarek, F. Karsch, P.Petreczky,F. Zantow, hep-lat/0309121

Heavy quark potential for T > TC

Screening length:

TLS /5.0~

Heavy ion collisions: Q and Qbar move relative to the plasma

screening at finite velocity ? (not known)

Screening in N=4 SYM

L

V(L): potential between a Q and Qbar

LLVT

1~)( :0

TTLS

277.0)(

LS(T)

Similar to QCD above TC

Finite velocity scaling

Finding string shapeof minimal energy

Event horizon

Moving at a finite velocity v

TLL SS

1)v1(~)v1)(0(~v)( 4/124/12

HL,Rajagopal,Wiedemann

Chernicoff, Garcia, Guijosa

Peeters, Sonnenschein, Zamaklar

Dissociation temperature:

)0()v-(1~v)( 4/12dd TT

I will now assume a similar scaling applies to QCD

TLL SS

1)v1(~)v1)(0(~v)( 4/124/12

Dissociation temperature:

)0()v-(1~v)( 4/12dd TT

A prediction from string theoryHL,Rajagopal,Wiedemann

This effect may be tested at RHIC II or LHC

Could lead to significant suppression at large PT.

RHIC ~1.5 Tc

)0()v-(1~v)( 4/12dd TT

/ (c c)J

(b b)

: Tdiss ~ 2.1 TC

: Tdiss ~ 3.6 TC

Asakawa, Hatsuda;Datta, Karsch, Petreczky, Wetzorke

zero velocity : (lattice)

J/ψRHIC

LHC?

Quark Matter 2008, Jaipur, India, Feb. 4-10,

200833Zebo Tang, USTC/BNL

Nuclear modification factor RAA

• Double the pT range to 10GeV/c

• Consistent with no suppression at high pT: RAA(pT>5 GeV/c) = 0.89±0.20

• Indicates RAA increase from low pT to high pT

• Different from expectation of most models: AdS/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

Propagation of mesons in QGP

Does the screening affect the propagation of mesons in a QGP?

, Cv k k

0.88 for 0.65 C dv T T

Speed limit :

0.35 for 0.98 C dv T T

Mateos, Myers and Thomson

Ejaz, Faulkner, HL, Rajagopal, Wiedemann

1Cv

dTT 0CvAs ,

This could also lead to observable effects.

Heavy ion collisions and AdS/CFT

String theory techniques provide qualitative, and semi-quantitative insights and predictions regarding properties of strongly interacting quark-gluon plasma.

“Wrong theory, right approximation” appears to work much better than “right theory, wrong approximation”

Universality?

Thank You

Many other things I did not have time to discuss