Quarkonium suppression in Heavy Ion Collisions

and AdS/CFT

Hong Liu

Massachusetts Institute of Technology

HL, K. Rajagopal, U. A. Wiedemann hep-ph/0607062, hep-ph/0612168

Q. Ejaz, T. Faulkner, HL, K. Rajagopal, U. A. Wiedemann arXiv:0712.0590

T. Faulkner, HL, arXiv:0807.0063

Plan• Heavy ion collisions

• Quakonium suppressions

• Insights and predictions from string theory

Propagation of heavy quakonia in a hot medium

potentials of infinitely heavy quarks

breakup of heavy quakonia in a hot medium

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, ……

QCD Phase diagramSmooth crossover

Relativistic Heavy ion collisions

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

Quark-gluon fluid of RHIC

RHIC QGP:

RHIC Experiments :

thermalization, collective flow, jet quenching, J/ψ suppression, ………

exciting opportunities, but difficult challenges

many dynamical phenomena:

QGP has been formed

behaves very differently from a weakly coupled QGP gas

strongly coupled, liquid-like (nearly ideal )

(Perturbation theory: inadequate )

String theory to the rescue!

AdS/CFT techniques have potential to make important impacts !

2. Use strongly coupled N=4 SYM plasma as a benchmark for understanding the QCD QGP.

Can N=4 SYM plasma serve as an ``Ising model’’ for QCD QGP?

finite temperature helps!

1. Find gravity duals for gauge theories close to QCD

Heavy ion collisions and AdS/CFTString theory techniques provide qualitative, and semi-quantitative insights and predictions regarding properties of strongly interacting quark-gluon plasma:

• Shear viscosity• Jet quenching

• Quarkonium suppression

Things work better than expected !?

• heavy quark diffusion

• Thermodynamic properties

……………

Many mysteries remain!

Quarkonium suppression: some predictions for LHC or RHIC

Heavy Quarkonia

Charm:

11))((~ QCDSH dmd , 1)( , S HQCDH mm

, 3.0)( GeV, 3.1 S cc mm fm 5.0d

The radii of charmonium (J/ψ, ψ′, ...) and bottomonium (ϒ, ϒ’, ...) families provide a unique set of decreasing length scales in QCD.

Heavy quarkonia are good probes of QGP

1. The potential between the quark and anti-quark in the bound state is weakened by the color screening of the plasma.

Due to their small sizes, heavy quakonia like J/ψ could survive the deconfinement transition.

A quarkonium in QGP:

shallower bound state or no bound state et al

2. The bound state can be broken apart by collisions with gluons and quarks in the plasma.

medium-induced width

Dissociation temperature

/ (c c)J

(b b)

: Tdiss ~ 2 TC

: Tdiss ~ 3 TC

Asakawa, Hatsuda;Datta, Karsch, Petreczky, Wetzorke

• Dissociation temperature Td

d: size of a meson

• Lattice estimate:

)(~ dS TLd

LS (T): screening length (decreases with T)

Their excited states already dissociate ~ 1.1 TC

• Color screening in a medium can be characterized by :

Quarkonium suppression

J/ψHeavy ion collisions: color screening in the produced medium

J/ψ suppression Matsui and Satz (1987)

One of the most important probes of the QGP.

Basic theoretical questions

How does the screening effect depend on the velocity ?

To understand the pT dependence:

Velocity dependence of the dissociation temperature Td ?

Lattice: Hard

How does QGP affects the propagation of J/ψ ? momentum-dependence of the width ?

Not known in QCD

)collisions p pin p of observed J/ of (#NcollisionsAu Au in p of observed J/ of #)(

Tcoll

TJ/

TAA pR

Strategy: see what happens in our ``Ising model’’

Insights and predictions from string theory

• Speed limit for heavy quakonia in a hot medium

• from potentials of infinitely heavy quarks

• break-up of heavy quakonia in a hot medium from string worldsheet instantons

A qualitative predicition

Static quark potentialGauge theory description:

gluon flux linesString theory description:

0z

Our (3+1)-dim world,

String lives in one extradimension Gravity approximation: finding

minimal energy string shape

Maldacena; Rey, Yee

Screening of quarks in a QGP

0.277 /SL T

(3+1)-dim world at temperature T,

event horizon

Quarks are screened

Ls

N=4 : , QCD (2 flavor): ~ 0.5 /SL T(lattice)

Rey, Theisen Yee;Brandhuber, Itzhaki, Sonnenschein Yankielowicz ……..

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 Td :

d: size of a meson

this suggests:

TLL SS

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

)(~ dS TLd

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

Does the scaling apply to QCD?

A simple argument

2 1/ 41

2 4

1 1(v) ~ (1 v ) ~(1 v )

SL TT

In a rest frame of quark pair, the medium is boosted:

44/124

2

2

2

2)v1(~

v11~)0(

v11~v)( TT

4~)0( T

If similar kind of scaling does apply to QCD, any implication?

Should be used as a basic theoretical input in any phenomenological modeling of J/ψ suppression

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

zero velocity : (lattice)

J/ψRHIC

LHC?

Data to come

RHIC: low statistics on J/psi with 2 < PT < 5 GeV, very low statistics for PT> 5GeV

Reach in PT will extend to 10 GeV in coming years at RHIC.

LHC will reach even wider range.

Beyond quark potential

( ) ( )2ik k

Next step: genuine heavy-quark mesons

So far: crude extrapolation from infinitely heavy quark potential

Want to understand:

Adding flavors in AdS/CFTKarch,Katz

N=4 SYM theory does not contain dynamical quarks.

Add NF hypermultiplets in fundamental representation to N=4 SYM N=2 theory with flavors

On gravity side, this can be achieved by adding NF D7-branes to the AdS5 x S5 geometry.

mq

Mesons: open string excitations on D7-branes.

small T/mq

Aharony, Fayyazuddin, Maldacena,

Meson Spectrum

mq

Meson spectrum can be found by solving linearized Laplace equations for small fluctuations on the D7-brane.

Bare quark mass: qm Meson masses: qmM ~,

Babington, Erdmenger, Evans, Guralnik, Kirsch; Kruczenski, Mateos, Myers, Winters;

One finds a discrete spectrum of mesons:

Very tightly bound:

λ: ‘t Hooft coupling

qBE mE 2

Meson “Dissociation”Mateos, Myers and Thomson, Hoyos, Landsteiner, Montero

Meson dissociation:

q

d

mMT ~~

Babington, Erdmenger, Evans, Guralnik, Kirsch

Gravity approximation:

Mesons are stable at T < Td.

completely disappear for T > Td

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 ,

As v > vC(T), quark and anti-quark get completely screened.

vC: speed of Light at the tip

Speed limit at a generic temperature

Stable Mesons

vC(T)

“Td(v)’’

Inference from infinitely heavy quark potential remarkably accurate.

Large k behavior of the dispersions relation of mesons are controlled by the screening behavior.

Width of mesons?Gravity approximation:

Mesons are stable for T < Td, no width

completely disappear for T > Td

mq

Open strings on D7-brane sees a geometry which is smoothly capped off.

In fact mesons are stable to all orders in perturbative α’ expansion.

However, bound states should always have a nonzero width in a finite temperature medium.

Field theory considerationsOn the field theory side, meson widths receive contributions from:

• Mesons -> glue balls , lighter mesons, or other gauge singlets

(1/Nc suppressed, present at zero temperature)

• Breakup by high energy gluons:

• Breakup by collisions with thermal medium quarks

Non-perturbative in α’, worldsheet instantons

Worldsheet instantons

Gauge theory interpretation

Medium modified quark mass: '2

)(

mT

qrm

Instanton action:

μ: chemical potential for quark number

D: worldsheet determinant

1m instantons A Boltzmann gas of thermal quarks

Meson widths

Open strings can tunnelinto the black hole through the disk instantons

Mesons become unstable and obtain a nonzero width.

Gauge theory:

Meson widthsFaulkner, HL

Do these features exist in QCD?

• Velocity scaling of screening length

• Speed limit for heavy quark mesons

• Velocity scaling of dissociation temperature

Dramatic slowdown near Td

All of them are rather qualitative features, which may not depend on the precise details of the underlying theory.

Far from being obvious in perturbation theory !

• Dramatic increase of meson widths at large momenta

Conclusion

String theory has immediate testable predictions for experiments after all …….