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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
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Phases of Nuclear Matter
Phase Transition: Tc = 170 ± 15% MeV e ~ 0.6 GeV/fm3
TTc
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
colorsNWeak coupling
limit Strong 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 Su
persymmetr
y
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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
ee
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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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trans
vers
e m
omen
tum
pt
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 2 cos 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
( )e e
PHENIXHuovinen et al
detailed hydro calculations (QGP+mixed+RG, zero viscosity) 0 ~ 0.6 -1.0 fm/c e~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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cos4 BRHIC
Vis ityEntropy Density k
sQGP – the most perfect fluid?
lowest viscositypossible?
4s
helium waternitrogen
viscosity bound?
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cos4 BRHIC
Vis ityEntropy 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?
4s
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
0 suppressed by 5!
AuAu 200 GeV
RAA
Direct γ
π0
η0.2
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 q0.3 GeV 4.5 GeV2/fm0.4 GeV 10.60.5 GeV 20.7
t
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 0.15DTT
, 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-likeFind 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 wakesSTAR
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]
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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
SS
Plugging in numbers
3/ 2
1 (3)1 15 ...4s
0.5 (0.35)
4 ~ 19 (13)1 0.05 (0.08)
sQGPS
Supersymcolors SN
1st order correction 20%
1st order correction 3%
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Energy Density
R2
2c
2
1 1 22
TBj
dER c dy
e
PHENIX: Central Au-Au yields
GeVddET 2503
0
Energy density far above transition value predicted by lattice.
3~ 15 @ 0.6 / ( )GeV fm c thermalizationfm
e
R~7fm
Lattice: TC~190 MeV (eC ~ 1 GeV/fm3)Phase transition- fast cross overto experimentalist: 1st order