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
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.
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