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Testing Gauge-String Duality* with Nuclear

Collision Data from RHICRichard Seto

University of California, Riverside

2010 APS April Meeting Thurgood Marshall East

Feb 13, 2010

*aka AdS5/CFT

experimentalist

10:45 am

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Some thoughts about what we are looking for

Introduction to heavy ions and RHIC Several Topics

◦ Elliptic flow /s◦ Jet (quark) energy loss ◦ Heavy quark diff coefficient◦ τ0 (thermalization time) and Tinit

◦ Mention others Summarize (Scorecard) and conclude

Outline

q̂

3

Phases of Nuclear Matter

Phase Transition: Tc = 170 ± 15% MeV e ~ 0.6 GeV/fm3

T

Tc

4

Collide Au + Au ions for maximum volumes = 200 GeV/nucleon pair, p+p and d+A to compare

BNL-RHIC Facility

STAR

Soon to Come – the LHC

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Old paradigm◦ RHIC – “weakly”

interacting gas- Quark gluon plasma Everything “easy” to

calculate using pQCD and stat mech.

What we found◦ Strongly interacting fluid-

the sQGP

A bit of history

Strong elliptic flow

Jet quenching

Everything “hard” to calculate

Naïve expectations

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Right Theory Wrong

approx

String Theory to the rescue ?

αS

pQCD

'

4

t Hooft

colorsN

Weak coupling

limitStrong couplinglimit

Gauge String duality aka AdS5/CFT

sQGP

Wrong Theory “Right” approx

But we Model ~ala condensed matter

Capture essential features

Gauge –String Duality

=4 S

upersy

mm

etry

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Why do we think AdS/CFT will work? Problems: conformal theory

(no running coupling)◦ BUT!

◦ RHIC in a region T>Tc where αs is ~constant (T is only scale)

What about the coupling size?◦ expansion on the strong coupling side is in 1/λ

RHIC αS ~ ½ 1/λ ~ 1/20 λ=4Ncolorsαs (NC=3~LARGE!)

What about all those extra super-symmetric particles, the fact that there are no quarks…◦ Find universal features

◦ Pick parameters insensitive to differences

◦ Make modifications to the simplest theory (=4) to make it look more like QCD

Ultimately find a dual to QCD

~ 0.8SB

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The Task

RHIC data

field theory e.g. =4 Supersymmetry a “model”

ParametersParameters

Fits to dataHydro/QCD based model

CompareAnd learn

Gravity String Theory

QCD

Gauge- String Duality aka AdS5/CFT

More modelingrescaling

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transv

ers

e m

om

entu

m p

t

time

Relativistic Heavy Ion Collisions Lorenz contracted pancakes Pre-equilibrium < ~1fm/c ?? QGP and hydrodynamic

expansion ~ few fm/c ??

Stages of the Collision

Tc ~ 190 MeV

T

time

Tinit=?PuresQGP

τ0

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Flow: A collective effect 2 2

2 2 2cos 2x y

x y

p pv

p p

dn/d ~ 1 + 2 v2(pT) cos (2 ) + ...Initial spatial anisotropy converted into momentum anisotropy. Efficiency of conversion depends on the properties of the medium.

x

yz

Coordinate space: initial asymmetry

pressure

py

px

Momentum space: final asymmetry

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Hydrodynamic Equations

Energy-momentum conservation

Charge conservations (baryon, strangeness, etc…)

For perfect fluids (neglecting viscosity!),

Energy density Pressure 4-velocity

Within ideal hydrodynamics, pressure gradient dP/dx is the drivingforce of collective flow.

Hydrodynamicsa critical tool to extract information from data

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Strong flow Implies early thermalization

If system free streams◦ spatial anisotropy is lost◦ v2 is not developed

0 /fm c

0

max

( )

PHENIXHuovinen et al

detailed hydro calculations (QGP+mixed+RG, zero viscosity) 0 ~ 0.6 -1.0 fm/c ~15-25GeV/fm3

(ref: cold matter 0.16 GeV/fm3)

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ViscosityStrongly Coupled fluids have small

viscosity!

                       

Anisotropic Flow Conversion of spatial anisotropy to

momentum anisotropy depends on viscosity Same phenomena observed in gases of

strongly interacting atoms (Li6)

weakly coupledfinite

viscosity

strongly coupled

viscosity=0

The RHIC fluid behaves like this,

that is, viscocity~0

M. Gehm, et alScience 298 2179 (2002)

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the low-brow sheer force(stress) is:

Calculating the viscosity

energy momentum stress tensor

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using gauge-string duality

σ(0)=area of horizon

“The key observation… is that the right hand side of the Kubo formula is known to be proportional to the classical absorption cross section of gravitons by black three-branes.”

8 G

dualGravity=4 SYM“QCD”strong coupling

Policastro, Son, Starinets hep-th 0104066=4 SupersymmetryGravity

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finishing it up Entropy black hole “branes” Entropy

=4 SYM“QCD”Entropy

black hole Bekenstetein, Hawking

= Area of black hole horizon

SYM " "

black hole area

4GQCDs 136 104 B

Kss k

Kovtun, Son, Starinets hep-th 0405231

=σ(0)

k=8.6 E -5 eV/K

This is believed to be a universal lower bound for a wide class ofGauge theories with a gravity dual

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What does the data say? Data from STAR

◦ Note – “non-flow contribution subtraction (resonances, jets…)

Use Relativistic-Viscous hydrodynamics

Fit data to extract ◦ Will depend on initial

conditions

Task was completed recently by Paul Romatschke after non-flow Subtraction was done on the data

STAR “non-flow” subtracted data

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Extracting /s

Best fit is to /s ~0.08 = 1/4◦ With glauber initial

conditions Using CGC

(saturated gluon) initial conditions /s ~0.16

Note: Demir and Bass◦ hadronic stages of the

collision do not change the fact that the origin of the low viscosity matter is in the partonic phase (arXiv:0812.22422)

STAR “non-flow” subtracted

Phys.Rev.C78:034915 (2008) 

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cos

4 BRHIC

Vis ity

Entropy Density k

sQGP – the most perfect fluid?

lowest viscositypossible?

4

s

helium waternitrogen

viscosity bound?

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cos

4 BRHIC

Vis ity

Entropy Density k

viscocity~0, i.e. A Perfect Fluid?

See “A Viscosity Bound Conjecture”, P. Kovtun, D.T. Son, A.O. Starinets, hep-th/0405231

◦ THE SHEAR VISCOSITY OF STRONGLY COUPLED N=4 SUPERSYMMETRIC YANG-MILLS PLASMA., G. Policastro, D.T. Son , A.O. Starinets, Phys.Rev.Lett.87:081601,2001 hep-th/0104066

lowest viscositypossible?

4

s

helium waternitrogen

viscosity bound?

Meyer Lattice: /s = 0.134 (33)

RHICarXiv:0704.1801

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Jet quenching

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Centrality and RAA :the suppression factor

“Spectators”

“Spectators”

“Participants”

Impact Parameter

Hard interactions ~ Ncollisions

Use a Glauber model

Centrality def’n head on – central glancing - peripheral

Participant

BinaryCollisions

AuAucoll

AA

ppcoll

AuAu yieldN

Rpp yieldN

1000

1

AuAucoll

ppcoll

N

N

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What is the energy density? “Jet quenching”

direct photons scale as Ncoll

p0 suppressed by 5!

AuAu 200 GeV

RAA

Direct γ

π0

η

0.2

Direct γ

0

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Hard probes in QCD- the jet quenching parameter

=4 SYM- no running of coupling no hard probes (a quark would not form a jet- just a soft glow of gluons)

Various schemes◦ Introduce heavy quark ◦ Start with jet as an initial state◦ Formulate the problem in pQCD

Non perturbative coupling to medium is embodied in one constant (<pT

2>/length)

=4 SYM (Liu, Rajagopal, Wiedemann)

q̂

0 QCD – hard probes

(jets) Assumption - Quark

energy loss by radiation of gluons

q̂

q̂

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Hard probes in QCD- the jet quenching parameter

=4 SYM- no running of coupling no hard probes (a quark would not form a jet- just a soft glow of gluons)

Various schemes◦ Introduce heavy quark ◦ Start with jet as an initial state◦ Formulate the problem is pQCD

Non perturbative coupling to medium is embodied in one constant (<pT

2>/length)

=4 SYM (Liu, Rajagopal, Wiedemann)

q̂

0

q̂

q̂

Formulate in terms ofWilson loop and calculateIn N=4 SYM using Ads/CFT

3/ 2

3

34ˆ

54

SYMq T

hep-ph/0605178 

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solution was for static medium at temperature T

But the temperature is falling at RHIC as a function of time.

Plugging in numbers

T q

0.3 GeV 4.5 GeV2/fm

0.4 GeV 10.6

0.5 GeV 20.7t

T

2ˆ ( ) 5 15 /q AdS GeV fm

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Use PQM model (parton quenching model)◦ Realistic model of energy loss (BDMPS)◦ Realistic geometry

What do the experiments get?

2.1 6.33.1 5.2ˆ 13.2 2q

2ˆcf 5 15 /q GeV fm

q̂

arXiv:0801.1665

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heavy quark diffusion

throw a pebble in the stream

see if it moves

mu~3 MeVmd~5 MeVms~100 MeVmc~1,300 MeVmb~4,700 MeV

ΛQCD~200 MeV

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Non photonic electrons (aka charm+bottom)

PRL 98, 172301 (2007)

high pT non-photonic e± suppression increases with centrality

similar to light hadron suppression at high pT

non-photonic e± Flowcharm suppressed and

thermalizes

Can we describe this in the context of the sQGP?

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Make modification to =4◦ Add heavy quark (adding a D7 Brane )

Drag a heavy quark at a constant velocity and see how much force is needed – calculate a drag coefficient Mμ=f/v D=T/μM

Rescale to QCD

◦ Herzog:

Gubser: alternate set of parameters (λ=5.5, 3 ¼TSYM=TQCD)

DHQ (AdS)=0.6/T

AdS: DHQ the diffusion coefficient

2 0.15D

TT

, 0.5 , 0, 19

, 0 , 0 , 0

~ ~ 4s s

s

QCD QCDSYM

QCD SYM SYM

D DDWhere

D D D

hep-th/0605158, hep-th/0605191

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Rapp and vanHees model has “non-

pertubative” features◦ resonant scattering

fits flow and RAA

DHQ =4-6/2T =

0.6-0.9/T

Getting DHQ from data

PRL 98, 172301 (2007)Cf D(AdS)=0.6/T

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Equilibration and temperature

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Equilibration time (τ0) from AdS

Temperature and τ0

modelRapidly expandingSpherical plasma Ball

Black hole in AdS5

τe-fold =1/8.6Tmax

dual

Perturb it

Study rate of equilibrationto hydrodynamical description

~ hydro-like modes~non hydro-like

Find rate of decayOf non hydo-likemodes

τ0 (AdS)= 4 τe-foldarXiv:hep-th/0611005

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Make a measure of low pT photons (black body radiation)

Use a model of time dependence and fit data

Thermal photons - Temperature from the data

t

T

pQCD

See special symposium

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Models follow same trend depend on τ0

Thermal photons

5 e-fold4 e-fold

3 e-fold

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J/psihigh pt

Liu, Rajagopal, Wiedermann“Hot Wind” +Hydro

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Mach cones and diffusion wakes

STAR

Δϕ

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SCORECARDquantity units Theory Exper

imentdata method Collab comment

s/sSB [1] 0.77 ~0.8 Lattice 1st order correction

/s [2] 0.1 ~0.08 Charged flow

Viscous hydro[9]

STAR Universal?1st order

[3]

GeV2

/fm5-15 13 R_AA

(pion)Fit to PQM [10]

PHENIX

Average over time

DHQ (τHQ) @T=0.300 GeV [4]

0.6/T 0.6-0.9/T

HQ decay e-

Fit to[11] Rapp, vanHees

PHENIX

Rescaledtheory

T(τ0 =3fm) [5]

GeV 0.300 (4-efold)

0.380 Fit to[12] models

PHENIX

τ0 [6] fm 0.3 0.6 Fit to flow [13]

STAR/ PHENIX

Init cond needed

J/ψ [7] stronger suppression pt>5 Some inconsistency between experiments

wait for more data [14]

Mach cones, [8] diffusion wakes

exists Something is there Need more studies [15]

q̂

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There are complications and assumptions that I skipped over e.g.◦ for Hydro need to use Israel-Stewart as not to violate causality need EOS (from lattice – at the moment various ones

are used for the fits)◦ The electrons from experiment are actually ~½ B

mesons at high pT. For the AdS side we (I) typically assumed m=1.4

And the list goes on

A word of caution

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The Gauge-String Duality (AdS/CFT) is a powerful new tool

The various theoretical together are giving us a deeper understanding of the sQGP◦ Can work hand in hand to with the

experimentalists pQCD, Gauge String Dualities, Lattice,

Viscous Hydrodynamics, Cascade simulations, … ◦ Bring different strengths and weakness◦ ALL are needed and must work together

Conclusion

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[1]hep-th/9805156 [2]hep-th 0405231 [3]hep-ph/0605178 [4]hep-th/0605158, hep-th/0605191 [5]arXiv:hep-th/0611005 [6]arXiv:0705.1234 [7]hep-ph/0607062 [8]arXiv:0706.4307 [9]Phys.Rev.C78:034915 (2008)  [10]arXiv:0801.1665 [11]Phys. Rev. Lett. 98, 172301 (2007) [12]arXiv:0804.4168 [13]nucl-th/0407067 [14]Phys. Rev. C 80 (2009) 41902 [15]arXiv:0805.0622

References for scorecard

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3/ 2

3 15 (3)1 ...

4 8SB

S

S

Plugging in numbers

3/ 2

1 (3)1 15 ...

4s

0.5 (0.35)

4 ~ 19 (13)

10.05 (0.08)

sQGPS

Supersymcolors SN

1st order correction 20%

1st order correction 3%

q̂

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Energy Density

pR2

2ct

2

1 12

2T

Bj

dE

R c dy

PHENIX: Central Au-Au yields

GeVd

dET 25030

Energy density far above transition value predicted by lattice.

3~ 15 @ 0.6 / ( )

GeVfm c thermalization

fm

R~7fm

Lattice: TC~190 MeV (C ~ 1 GeV/fm3)

Phase transition- fast cross overto experimentalist: 1st order