W.A. Zajc

Durham Workshop

Heavy Ion Physics“versus” AdS/CFT

Perils, Pitfalls, Progress, Prospects

W.A. ZajcPhysics Department

Columbia University, New York, NY

( this talk available at http://www.phenix.bnl.gov/phenix/WWW/publish/zajc/sp/presentations/Durham )

16-Apr-09

W.A. Zajc

AdS/CFT - Pro Gauge/gravity duality, G.T. Horowitz and J. Polchinski, gr-qc/0602037 )

“Hidden within every non-Abelian gauge theory, even within the weak and strong nuclear interactions, is a theory of quantum gravity.”

Stringscape, by Matthew Chalmers, in Particle World:

“Susskind says that by studying heavy-ion collisions you are also studying quantum gravity that is ‘blown up and slowed down by a factor of 1020 ’ ”

The Black Hole War, L. Susskind, ISBN 978-0-316-01640-7 :

“…the Holographic Principle is evolving from radical paradigm shift to everyday working tool of – surprisingly – nuclear physics.”

16-Apr-09

W.A. Zajc

AdS/CFT - Con P. Petreczsky, QM09: “AdS/CFT is consistently wrong. ”

16-Apr-09

W.A. Zajc

Hypothesis Reality may lie between these two extremes For discussion:

Hard physics Fragile predictions Robust extractions

Soft physics: Robust predictions Fragile extractions

Not covered:AdS/QCD

16-Apr-09

W.A. Zajc

What Worked?: Quantitative pQCD Systematic Comparison of Jet Energy-Loss Schemes in a

Realistic Hydrodynamic Medium, S.A. Bass et al., 0808.0908

A (valuable!) exercise in Procrustean reductionism.

Good news: “Bad” news:

16-Apr-09

W.A. Zajc

Comment Yes- to some extent this is an illustration

of the “fragility” of RAA More differential more sensitive IAA

RAA versus reaction plane

However- not the real issue (see B. Cole QM08)

Instead: consistent treatment of collisional + radiative terms, finite L, expanding medium, coupling constant, kinematic cut-offs, assumed scale hierarchies, …16-Apr-09

W.A. Zajc

Strings That Might Work AdS/CFT is a general correspondence

Most useful to QCD when

How to equate QCD N =4 SYM ?Naïve?Correct for different d.o.f. ?Equal energy densities ?Equivalent q-q potential ?

16-Apr-09

12

2

2

CYM

S

NgL

34 2 CSYM Ng

19-Nov-08 Michigan Colloquium

New Dimensions in Heavy Ion Physics

Our 4-d world

String theorist’s 5+5-d world

The stuff formerly known as QGP

Heavy quark moving through the medium

Energy loss from string drag

Jet modifications from wake field

“The stress tensor of a quark moving through N=4 thermal plasma”, J.J. Friess et al., hep-th/0607022

W.A. Zajc

Heavy Quark Energy Loss in AdS/CFT

(Infinitely) massive quark trailing string General agreement on exact parametric form:

Heavy quark diffusion in strongly coupled N = 4 Yang Mills, Casalderrey-Solana and Teaney, hep-ph/0605199

Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, Herzog et al., hep-th/0605158.

Drag force in AdS/CFT, Gubser, hep-th/0605182

Roughly consistent with observed single-electron suppression pattern: Heavy Quark Diffusion with Relativistic Langevin Dynamics in the

Quark-Gluon Fluid, Akamatsu, Hatsuda and Hirano, 0809.1499(next slide)

16-Apr-09

MeV200250~forfm32~

1

2

2

T

ppm

T

dt

dp

C

QQ

W.A. Zajc

Heavy Quark Drag vs Data

16-Apr-09

32~2

:AdS/CFT

2

pm

T

dt

dp

Q

AdS/CFT g ~ 2-3 within uncertainty band:

Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid, Akamatsu, Hatsuda and Hirano, 0809.1499

W.A. Zajc

Light Quark Energy Loss in AdS/CFT (1)

Not yet (AFAIK) embedded in realistic hydro code no direct comparison !

Lightlike Wilson loop formalism (Liu, Rajagopal, Wiedemann http://arxiv.org/abs/hep-ph/0605178 )

Find

for l = 6 p aS = 0.5

Energy loss not proportional to number d.o.f (!)

16-Apr-09

3232/3

MeV300fm

GeV5.4

)4/5(

)4/3(ˆ

SYMTTq

W.A. Zajc

Light Quark Energy Loss in AdS/CFT (2)

But- completely different results in alternative set-ups: Falling string

Light quark energy loss in strongly-coupled N = 4 supersymmetric Yang-Mills plasma, Chesler et al., 0810.1985

Gluon energy loss in the gauge-string duality, Gubser et al., 0803.1470

Parton branching in N=4 Jet evolution in the N=4 SYM plasma at strong coupling,

Hatta, Iancu and Mueller, 0803.2481

Each have regimes corresponding to very high values of “quenching parameter “ ~10-100 GeV2/fm

See talk by E. Iancu for much more detail16-Apr-09

W.A. Zajc

Q. What Worked ?

A. Ideal hydro: (Liu, Hirano, Werner, Zhu; QM09)

16-Apr-09

Assertion In these complicated events, we have

(a posteriori) control over the event geometry:Degree of overlap

Orientation with respect to overlapReaction

Plane

“Central” “Peripheral”

Implications of Assertion We have (a posteriori) control over the event geometry:

Two possible scenarios:

“Free” quarks and gluons

“Strongly-coupled” quarks and

gluons

19-Nov-08 Michigan Colloquium

Motion Is Hydrodynamic

x

yz

When does thermalization occur? Strong evidence that final state bulk behavior

reflects the initial state geometry Because the initial azimuthal asymmetry

persists in the final state dn/df ~ 1 + 2 v2(pT) cos (2 f) + ...

W.A. Zajc

(Minimal) AdS / CFT

16-Apr-09

Graviton with 5-momentum k in

bulk satisfies kk = 0

described by 4 numbers

Those 4 numbers describe virtual gauge

quanta on 4-d boundary

( Adopted from S. Brodsky figure )

4

1

s

W.A. Zajc16-Apr-09

A Long Time Ago (1985) Dissipative Phenomena in Quark-Gluon

Plasmas, P. Danielewicz and M. Gyulassy, Phys.Rev. D31, 53,1985.

Noted several restrictions on smallest allowed h :

Most restrictive: l > h/<p> h > ~ n / 3

But recall s = 3.6 n for the quanta they were considering

h/s > 1 / (3.6 x 3) ~ 1 / (4 p) !!

23-Oct-08 W.A. Zajc

Estimating h/s Damping (flow, fluctuations, heavy quark motion) ~

h/s Has the QCD Critical Point Been

Signaled by Observations at RHIC?, R. Lacey et al., Phys.Rev.Lett.98:092301,2007 (nucl-ex/0609025)

The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)

Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)

Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √sNN = 200 GeV (PHENIX Collaboration), A. Adare et al., to appear in Phys. Rev. Lett. (nucl-ex/0611018)

4

1)2.12.01.1(

s

4

1)8.30.1(

s

4

1)0.23.1(

s

4

1)5.29.1(

s

CHARM!

23-Oct-08 W.A. Zajc

Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)

Signature: FLUCTUATIONS Calculation:

Payoff Plot:

4

1)8.31(

fm20~,fm1~

114

14

0

,,

22

0

020

2

2

s

sT

sT

gsTt

CfPf

CfPfpc

f

f

Diffusion eq. for fluctuations g

Compare to STAR data on centrality dependence of rapidity width s of pT fluctuations

Difference in correlation widths for central and peripheral collisions

23-Oct-08 W.A. Zajc

Has the QCD Critical Point Been Signaled by Observations at RHIC?, R. Lacey et al., Phys.Rev.Lett.98:092301,2007 (nucl-ex/0609025)

Signature: FLOW Calculation:

Payoff Plot:

Fit v2 ~I1(w)/I0(w); w = mT/2T

On-shell transport model for gluons, Z. Xu and C. Greiner, hep-ph/0406278.

PHENIX v2/e data

(nucl-ex/0608033) compared to R.S. Bhalerao et al.

(nucl-th/0508009)

4

1)2.01.1(

fm03.03.0

05.035.0

MeV3165

~

2.11.1

s

c

T

cTs

f

s

sf

23-Oct-08 W.A. Zajc

The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)

Signature: FLOW Calculation:

Payoff Plot:

Knudsen number K

Fits to PHOBOS v2 data to

determine s for Glauber and CGC

initial conditions

Decrease in flow due to finite

size

4

1)5.29.1(

4,/264.1,31/,7.0

/1

1

)(111

0

0

22

s

nsTcK

KK

vv

cdy

dN

Ac

dy

dN

ARn

R

K

S

perfect

SS

23-Oct-08 W.A. Zajc

Moore and Teaney Phys.Rev.C71:064904,2005 (perturbative, argue ~valid non-perturbatively)

Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √sNN = 200 GeV (PHENIX Collaboration), A. Adare et al., Phys. Rev. Lett. 98:172301,2007 (nucl-ex/0611018)

Signature: FLOW, ENERGY LOSS Calculation:

Payoff Plot:

4

1)0.23.1(

3for6~)/(/

2)64(~

s

NPD

TD

fHQ

HQ

Rapp and van Hees Phys.Rev.C71:034907,2005, to fit both PHENIX v2(e) and RAA(e)

W.A. Zajc

Non-Ideal Hydrodynamics Simple in 1st order, but… :

Unknown Initial Conditions Eccentricity fluctuations Unknown equation of state Instabilities, acausal effects

in relativistic viscous hydro Hadronic rescattering effects Bulk viscosity Numerical viscosity Finite size, core/corona effects

16-Apr-09

W.A. Zajc

Implementing and Testing Examples

P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99:172301, 2007

H. Song and U. Heinz, Phys. Rev. C78, 024902, 2008

M. Luzum and P. Romatschke hys.Rev.C78:034915,2008.

16-Apr-09

1 fm/c

3 fm/c

7 fm/c

W.A. Zajc

BNL, April 2008: Workshop on Viscous Hydrodynamics and Transport Models in Heavy Ion Collisions Workshop Summary

Concordance

16-Apr-09

M. Luzum and P. Romtschke Phys.Rev.C78:034915,2008. 

W.A. Zajc16-Apr-09

4/)8.30.1(/ s

S. Gavin and M. Abdel-Aziz: PRL 97:162302, 2006

pTfluctuations STAR

Comparison of Estimates

4/)2.12.01.1(/ s

R. Lacey et al.: PRL 98:092301, 2007

v2 PHENIX & STAR

4/)4.24.1(/ s

H.-J. Drescher et al.: arXiv:0704.3553

v2 PHOBOS

conjectured quantum limit

Various 2nd orderhydro calculations

A. Adare et al, PRL 98:172301, 2007

4/)0.23.1(/ sHeavy flavor drag, flow;

PHENIX

W.A. Zajc

Beyond ‘t Hooft Limit ? (1) A foolish consistency is the hobgoblin of little minds… Hydro direct photon results (Liu, Hirano, Werner, Zhu; QM09)

use

33.025.0~8

log)233(

6)(

Cf

S

TT

N

T

W.A. Zajc

Beyond ‘t Hooft Limit ? (2) Use this range for aS ~0.25-0.33 in result from

Myers, Paulos and Sinha (http://arxiv.org/abs/0806.2156)

® (Using most naïve as= gYM2/4p )

Compare this to compilation of h/s estimates:

!

4

1)73.154.1(~

16

5)3(151

4

12

2/1

2/3

sNs C

W.A. Zajc

Beyond ‘t Hooft Limit ? (3) Consistency check: Use same range aS ~0.25-0.33

In ‘ancient’ result from Gubser, Klebanov and Tseytlin (

http://arxiv.org/abs/hep-th/9805156)

® (Using most naïve as= gYM2/4p )

Check if this correspondsto ‘sensible’ temperaturerange using lattice resultsfor s(T)/sSB :

81.078.0~32

)3(45

4

32/3

SBSB s

s

s

s

W.A. Zajc

Preliminary

Knowing Knudsen Experimental fit of Knudsen number K = lmfp/R

on way to h/s estimate:

16-Apr-09

0

22

/1

1

KK

vv

Ideal

Still to do- Understand systematics ! Assumed T Assumed s Boltzmann transport

W.A. Zajc16-Apr-09

4/)8.30.1(/ s

S. Gavin and M. Abdel-Aziz: PRL 97:162302, 2006

pTfluctuations STAR

Comparison of Estimates

4/)2.12.01.1(/ s

R. Lacey et al.: PRL 98:092301, 2007

v2 PHENIX & STAR

4/)4.24.1(/ s

H.-J. Drescher et al.: arXiv:0704.3553

v2 PHOBOS

conjectured quantum limit

Various 2nd orderhydro calculations

A. Adare et al, PRL 98:172301, 2007

4/)0.23.1(/ sHeavy flavor drag, flow;

PHENIX

W.A. Zajc

Why I Think Knudsen Kneeds Work… Because you Kneed Kneither s nor cS: Starting point is always de Groot result:

Then assumed finite-size scaling Directly gives you K l , resulting in

This is (AFAIK) the sole physical content of this “formalism”, and you would probably “tune” it with hydro anyway…

16-Apr-09

Tn

T

ns

T

3.0316.04

264.1

0

22

/1

1

KK

vv

perfect

)/(

)/(2.03.0

2

2

2

22

0

v

vTR

v

vv

RTKs

perfect

W.A. Zajc

What About LQCD ? Transport coefficients are challenging: Nf=2+1 on 16 x 483 lattice estimated at

O(10) days on Exaflop machine(!) H. Meyer, QM09 Nonetheless:

16-Apr-09

W.A. Zajc

Perspective

16-Apr-09

Keep in mind the neglected:

Bulk viscosity(=0 in CFT)

Hadronic viscosity(potentially large )

( compilation from Aihong Tang, QM09)

W.A. Zajc

Beyond ‘t Hooft Limit ? (Caveats) The range for aS is very sensitive to the value for h/s :

® (Using most naïve as= gYM2/4p )

Compare this to compilation (Aihong Tang, QM09)

of h/s estimates:

!1.04

15~

16

5)3(151

4

12

2/1

2/3

S

C sNs

The Flow Knows Quarks The “fine structure” v2(pT) for different mass particles shows

good agreement with ideal (“perfect fluid”) hydrodynamics

Scaling flow parameters by quark content nq resolves meson-baryon separation of final state hadrons

baryons

mesons22

TT pmKE

W.A. Zajc

Recombination Recombination works:

® Deal with it Miklos Gyulassy: “One of the most remarkable

‘I don’t understand’ phenomena”16-Apr-09

W.A. Zajc

Implications for D.O.F While tempting to identify the coalescence patterns

with “underlying quark degrees of freedom”… Much work still needed to reconcile with ‘absence’ of

quasiparticles when h/s near quantum bound Quasi-Particle Degrees of Freedom versus the Perfect Fluid

as Descriptors of the Quark-Gluon Plasma, L.A. Levy et al., Phys.Rev.C78:044905,2008. 0709.3105

Quantum Criticality and Black Holes, S. Sachdev and M. Mueller, 0810.3005 :®“The theory of the quantum critical region shows that the transport

coefficients, and the relaxation time to local equilibrium, are not proportional to a mean free scattering time between excitations, as is the case in the Boltzmann theory of quasiparticles

16-Apr-09

09-Mar-09 Harvard Colloquium

Why AdS/CFT Matters… All the thermal parts are built upon

Bekenstein and Hawking’s (unproven) assertion that black holes have entropy:

Black holes have a temperature Black holes can radiate Black holes don’t lose information

Important to test these very underpinnings

244P

BHL

A

G

AS

W.A. Zajc

Calculating Multiplicity = Entropy Off-center collisions in AdS5 with applications to multiplicity estimates in

heavy-ion collisions, Gubser, Pufu and Yarom ( 0902.4062 ) FAILS !

But- AdS/CFT can’t separate “participants” from “spectators”, so… Fix this by hand (restrict E in shock by fractional overlap)

16-Apr-09

W.A. Zajc

A ‘Better” Adjustment

16-Apr-09

Make AdS/CFT more QCD-like by restricting 5th dimension zIR > z > zUV :Pro:

More ‘realistic’ predictions for LHC

Con: Breaks again…

W.A. Zajc

Summary

AdS/CFT has produced qualitatively new insights into the dynamics of heavy ion collisions.

The hard sector is hard. The soft sector is “firm”. Much ongoing activity to turn

qualitative insights into quantitative results.

16-Apr-09

W.A. Zajc

Thank you !

16-Apr-09

W.A. Zajc

The Charm Puzzle Conserved ! Loses energy:

PHENIX and STARRAA ~ consistent

RAA ~ unchangedin region whereb’s should dominate

• Flows Again,

little evidence fordecoupling of b’s

16-Apr-09

W.A. Zajc

Ongoing Work on QP’s Hadronic modes and quark properties in the quark-

gluon plasma, M. Mannarelli and R. Rapp,hep-ph/0505080

Quasi-particle model for lattice QCD: Quark-gluon plasma in heavy ion collisions, V. Chandra and V. Ravishankar, 0812.1430

Parton transport and hadronization from the dynamical quasiparticle point of view, W. Cassing and E.L. Bratkovskaya, 0808.0022

The Hot non-perturbative gluon plasma is an almost ideal colored liquid, A. Peshier and W. Cassing, hep-ph/0502138

16-Apr-09

W.A. Zajc

Beyond h/s = 1/4p, A. Buchel, R.C. Meyers and A. Sinha, 0812.2521

16-Apr-09

W.A. Zajc

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

1 .4

1 .6

-6 -4 -2 0 2 4 6

y

Speaking of Cartoons

What is this thing ??

Surely not the space-time development:

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

1 .4

1 .6

-6 -4 -2 0 2 4 6

y

?

16-Apr-09

W.A. Zajc

Restating the “Obvious”

A reminder:All nuclei are finiteMost nuclei are round

No nuclei areInfiniteCylindricalSharp spheres….

16-Apr-09

W.A. Zajc

Lesson

16-Apr-09

Details matter.