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Page 1: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

A prediction from string theory,with strings attached

Hong Liu

Massachusetts Institute of Technology

HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062, hep-ph/0612168

Qudsia Ejaz, Thomas Faulkner, HL, Krishna Rajagopal, Urs Wiedemann

arXiv:0712.0590

Page 2: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Plan

• Heavy ion collisions and AdS/CFT

• J/ψ suppression

• A prediction from string theory

• Propagation for heavy quark mesons in a hot medium

Page 3: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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, ……

Page 4: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

QCD Phase diagram

Smooth crossover

Page 5: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Relativistic Heavy ion collisions

Page 6: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Relativistic heavy ion collisions

Deconfinement crossover in QCD: TC ~ 170 MeV

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

GeVsNN 17SPS (CERN):

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

Page 7: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

QCD Phase diagram

RH

IC

Page 8: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Quark-gluon fluid of RHIC

RHIC QGP: strongly coupled, nearly ideal fluid (sQGP)

Main theoretical tool for strong coupling: Lattice calculation

But information on dynamical quantities: scarce and indirect

RHIC Experiments revealed many dynamical phenomena:

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

Perturbation theory: inadequate

Many new challenges

Page 9: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

String theory to the rescue!

AdS/CFT techniques have potential to make important impact !

Page 10: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

It is NOT yet known what is the precise string theory description of QCD.

Page 11: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

• What are the commonalities and differences of quark-gluon plasmas in different gauge theories?

• Discovery machine: experiments

deeper understanding of both QCD and AdS/CFT

Perturbative Lattice Strongly coupled

theories from AdS/CFTexperiments

AdS/CFT

Page 12: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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:

• Shear viscosity

• Jet quenching

• Quarkonium suppression

Things work better than expected !?

• heavy quark diffusion

• Thermodynamic properties

……………

Many mysteries remain!

Page 13: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Quarkonium suppression: a prediction for LHC or RHIC

Page 14: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Heavy Quarkonia

Charm:

J/ψ ( ) : BNL and SLAC (1974, November revolution)cc

11))((~ QCDSH dmd

1)( , S HQCDH mm

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

Heavy quakonia like J/ψ could survive deconfinement transition.

Page 15: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Heavy quarkonia are good 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.

more unstable

Page 16: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Quarkonium suppression

J/ψ

Heavy ion collisions: color screening in the produced medium

J/ψ suppression Matsui and Satz (1987)

)collisions p pin p of observed J/ of (#N

collisionsAu Au in p of observed J/ of #)(

Tcoll

TJ/

TAA pR

Page 17: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Screening of heavy quarks in the Quark gluon plasma

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

Heavy quark potential for T > TC

Screening length: TLS /5.0~

Page 18: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Quarkonia above TC

/ (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

Charmonium spectra at different temperatures

Satz, hep-ph/0512217

• Lattice estimate:

)(~ dS TLd

Page 19: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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

Propagation of J/ψ in a QGP.

Not known in QCD

)collisions p pin p of observed J/ of (#N

collisionsAu Au in p of observed J/ of #)(

Tcoll

TJ/

TAA pR

Try to gain insight from string theory by studying relatives of QCD.

Page 20: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Static quark potential

Gauge 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

Page 21: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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 ……..

Page 22: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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

Page 23: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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?

Page 24: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

A simple argument

2 1/ 41

2 4

1 1(v) ~ (1 v ) ~

(1 v )SL T

T

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

44/124

2

2

2

2)v1(~

v1

1~)0(

v1

1~v)( TT

4~)0( T

Page 25: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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

Page 26: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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

Could lead to significant suppression at large PT.

J/psi

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

RHIC has not reached Td for J/ψ.

Page 27: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,
Page 28: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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

28Zebo 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

Page 29: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Charmonium Spectral functions

( ) ( )2

ik k

( )k

Study of genuine quarkonia requires understanding behaviorof spectral functions.

J/ψ : poles in the complex plane.

Velocity effect:

Can AdS/CFT help?

Need genuine mesons.

So far: crude extrapolation from infinite heavy quark potential.

Satz

( )k,

Page 30: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Adding flavors in AdS/CFTKarch,Katz

N=4 SYM theory does 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: excitations on D7-branes.

small T/mq

Aharony, Fayyazuddin, Maldacena,

Page 31: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Meson masses

Size of a meson:

Bare quark mass: qm

Meson masses: qmM ~

qmMd

~

1~

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

Page 32: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Meson Dissociation

Mateos, Myers and Thomson, Hoyos, Landsteiner, Montero

Gravity approximation: Mesons are stable at low temperature.

Meson dissociation:

We would like to understand how the screening effect is reflected in the meson spectrum.

q

d

mMT ~~

Babington, Erdmenger, Evans, Guralnik, Kirsch

Page 33: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Dispersion relation

, Cv k k

0.88 for 0.65 C dv T T

0.35 for 0.98 C dv T T

V0: speed of lightat the tip

Mateos, Myers and Thomson

In the hot medium, mesons travel at a velocity smaller than the vacuum speed of light !

Page 34: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

General results

In the large k limit: (exact analytic result)

v0 is precisely given by the local speed of light at the tip.

Ejaz, Faulkner, HL, Rajagopal, Wiedemann

Page 35: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Embedding of the brane and fluctuations

Embedding of D7-brane:

Action for fluctuations: (scalar mesons)

(can only be solved numerically)

Solving the Laplace equations: discrete spectrum, dispersion relations

Page 36: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Large k limit

In the large k limit, the wave equations for mesons become

that of a four-dimensional spherical harmonic oscillator localized near the tip of the brane and thus be solved exactly.

Wave function

Page 37: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Group Velocity

T2

T1

T3

T3 > T2 > T1

maximum

Page 38: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Speed limit at a generic temperature

Stable Mesons

v0(T)

“Td(v)’’

Near Td, v0 (T) 0, for arbitrary large k.

Inference from infinitely heavy quark potential remarkably accurate.

Page 39: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Size of a meson

Semi-classical analysis:

TLS

1)v1(~v)( 4/12

This gives maximal meson size at a given v and T

Td

1)v1(~ 4/12

max

D7-brane story: from IR/UV connection,

Tr

r

r

R

r

Rd

tiptip

1)v1(~~

~ 4/120

0

22

max

Page 40: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

why the wave function of a large k meson is localized at tip?

Increasing k, the meson becomes more loosely bounded, and its size should increase, eventually to the maximally possible size allowed by the v0 (T).

From IR/UV connection, its wave function should more and more localized to the tip.

Page 41: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Summary

(Real part) of the dispersions relation and wave function of hologrpahic mesons match very well with (in some sense are controlled by) the screening behavior.

In order to understand the ``dissociation’’, one needs to understand the momentum dependence of the imaginary part of dispersion relation.

HL, Faulkner, in progress

Fast mesons: good probes of the geometry near the horizon

Page 42: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

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.

Local speed of light in the bulk

Far from being obvious in perturbation theory !

Page 43: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Is the modified dispersion relation observable?

v>v0

Will J/ψ break apart?

Or will it slow down and survive the medium

What happens when medium disappears?

Time delay?

J/ψ suppression

………………

Page 44: A prediction from string theory, with strings attached Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs. Wiedemann hep-ph/0607062,

Conclusion

String theorists have a lot to learn from experiments.

String theorists also have a lot to offer for experiments.