Peter Steinberg Bulk Dynamics
Bulk Dynamics in Bulk Dynamics in
Heavy Ion Heavy Ion CollisionsCollisions
Peter SteinbergPeter SteinbergBrookhaven National LaboratoryBrookhaven National Laboratory
INPC2004INPC2004June 27-July 2, 2004June 27-July 2, 2004
Göteborg, SwedenGöteborg, Sweden
Peter Steinberg Bulk Dynamics
Strongly-Interacting Matter
On the lattice, onlyreach 75-80% of
Stefan-Boltzmann limit
In context of N=4 SUSY QCDthis is the signature of
a strongly-interacting plasma(Klebanov et al, 1996)
Shift of paradigm:QCD does not predict weakly interacting QGP for accessible T
Can we study strongly-interacting matter in A+A collisions?
Peter Steinberg Bulk Dynamics
The Bulk of Particles: dN/d
Comprehensive study of particle production in A+A• Energy• Centrality• Rapidity
dN
/d
19.6 GeV 130 GeV 200 GeV
Most Central
PHOBOS
Participant
Spectator
Peter Steinberg Bulk Dynamics
The Bulk of Particles: dN/dpT
STAR
Peter Steinberg Bulk Dynamics
Dynamical ModelsNuclear Geometry
Parton distributionsNuclear shadowing
Parton production& reinteraction
Chemical Freezeout &Quark Recombination
Jet FragmentationFunctions
Hadron Rescattering
Thermal Freezeout &Hadron decays
Independent stages: Bulk physics integrates time history
0 fm/c
2 fm/c
7 fm/c
>7 fm/c
Peter Steinberg Bulk Dynamics
Dynamical Models vs. Data
HIJINGHard + Soft
Hadron Transport
RHIC Data
pp Data
ParticleDensity
near y=0
2 1/3
3~5/
TAA
F
m dNA
dyAR
GeVfm
Large variation inpredictions
Peter Steinberg Bulk Dynamics
The Big Surprise
Contrary to popular belief…
Bulk observables are “simple”
…just not necessarily at =0!
Peter Steinberg Bulk Dynamics
Participant Scaling
Participant scaling = Long-range rapidity correlations
Peter Steinberg Bulk Dynamics
“Limiting Fragmentation” in A+A
Yield depends on ’-ybeam
Logarithmic increase at =0 centrality-dependent “universal curve”
peripheral central
log log /
~ '
beamy yTF
beam F T
beam
mx e
My y x m M
y
2.4beamy
Peter Steinberg Bulk Dynamics
Difference between p+p vs. A+A
/ 2s
In a head-on p+p collision…
…half of energy emerges as “leading particles” flat in xF
In a typical A+A collision…
…“leading particles” can be struck again!
May make sense to consider A+A as havingall the available energy for particle production
/ 2part NNN s
NA49
Peter Steinberg Bulk Dynamics
Universality of Total Multiplicity
A+A per participant pair ~ p+p @ s/2 ~ e+e- @ sA real surprise at RHIC – not predicted by SPS extrapolations
LEP200 GeV
Peter Steinberg Bulk Dynamics
Essential Features of A+A
1.Npart scaling• Factorization of Energy & Geometry
2.Universal multiplicity / Npart/2• Connections between e+e- & p+p
3.“Limiting fragmentation”
How can we understand this in a simple way?
Dynamical models have too many independent stages
Peter Steinberg Bulk Dynamics
Hydrodynamic Evolution
Strongly-interacting 6Li released from an asymmetric trapO’Hara, et al, Science 298 2179 (2002)
A new canonical image for heavy-ion physics
Hydro useful for strongly interacting matter:
buildup of pressure gradients due to geometry
How does it work for A+A?
Peter Steinberg Bulk Dynamics
Longitudinal Dynamics
1. Early thermalization
2. Blackbody EOS
3. Multiplicity formula:
4. Npart scaling
5. Gaussian dN/dy
z
y
Landau
Assumes matterstops briefly and
explodes longitudinally
Ultra-high energy densityRapid thermalization 2
2
1ln
2
s
m
1/ 4chN Ks
ch partN N
/ 3p
/ 0E V t
Peter Steinberg Bulk Dynamics
Universal Multiplicity Formula
Multiplicity formula impliesp=/3 in early times
Nch=2.2s1/4
Npart scaling impliesEntropy~Volume
Peter Steinberg Bulk Dynamics
dN/dy: Longitudinal Dynamics
2
exp ln2 2 p
dN y sL
dy L m
M. Murray, BRAHMS
dN/dy may be consequence of hydrodynamic evolutionof Lorentz contracted early stage = DYNAMICS
Peter Steinberg Bulk Dynamics
Limiting Fragmentation
20s GeV
60s GeV
130s GeV
200s GeV
y-yy-yTT
21/ 4/ 2
2
y LdN se
dy L
Approximate scalingin y’
Peter Steinberg Bulk Dynamics
Transverse Dynamics1. Assume boost-
invariance
2. dN/dy is initial condition
3. Non-trivial EOS
4. Pressure gradients Radial & elliptic flow
5. Cooper-Frye Freezeout
dN
dy
y
Peter Steinberg Bulk Dynamics
Radial Flow
20eff TT T m
A clear mass effect on top of “thermal” spectrum
Kolb & Rapp 20% normalizationat 2 GeV
Subm. to PRLnucl-ex/0401006
Au+Au 200 GeVAu+Au 200 GeV
Peter Steinberg Bulk Dynamics
Elliptic Flow vs. Geometry
2~ 1 2 cos 2 R
dNv
d
Hydrodynamic limit
STAR
PHOBOS
Hydrodynamic limit
STAR
PHOBOS
Compilation and Figure from M. Kaneta
Peripheral collisions show “elliptic flow”
Reasonable agreement with hydro
Peter Steinberg Bulk Dynamics
pT Dependence
2 ~ Tv p
“fine structure” (mass dependence) Described by hydro (and hydro-inspired) fits
STAR
Peter Steinberg Bulk Dynamics
Pseudorapidity Dependence
Limiting fragmentation works almost too well for v2()(Is there really a hydro “limit”?)
Challenge even for 3D hydro calculations, even ifrule sounds simple!
T. Hirano - CGC+HydroT. Hirano - CGC+Hydro
T. Hirano, Nov ‘03
PHOBOS19.6, 62,130,200 GeV
PHOBOS130 GeV
Peter Steinberg Bulk Dynamics
Hydro approach appears to bewarranted by a wide range of data
(but no single model gets everything right!)
Joining longitudinal & tranverse
stages is arbitrary for now(when does evolution begin?)
Serious conceptual issues regardingapplicability of hydro to small
systems…
Peter Steinberg Bulk Dynamics
More similarities: AA & e+e-
Similar “longitudinaldynamics”?
Similar “energy density”?
Peter Steinberg Bulk Dynamics
Limiting FragmentationDELPHI PLB 459 (1999)
p+p e+e-
Peter Steinberg Bulk Dynamics
Similar Freezeout Properties
e+e-
A+A
From Braun-Munzinger, Stachel, Redlich (2003)
Becattini (1995)
Relative particle yields described using
thermal-statistical modelsin both e+e- and A+A
Peter Steinberg Bulk Dynamics
Radial Expansion in p+p?
R. Witt, STAR Collaboration
Peter Steinberg Bulk Dynamics
Radial Expansion in p+p?
HBT radii have similar relativemomentum dependence:
Similar “expansion dynamics”?
A A T
A A Tp p T
R mC f m
R m
Rout / Rout(pp) Rside / Rside(pp)
Rlong / Rlong(pp)
START. Gutierrez, QM04
Peter Steinberg Bulk Dynamics
Soft Physics = Difficult Physics?
Dynamical models have few constraintsalthough global constraints seem to matter
Peter Steinberg Bulk Dynamics
Incoming nuclei:Npart, Lorentz contraction
Rapid thermalization:Entropy production
1D expansion stage:Rapidity distributions
3D expansion stage:Elliptic & radial flow
Freezeout into hadrons:Statistical phenomenology
t = 0.0 fm/c
t = 0.1 fm/c
t < 0.6 fm/c
t = 0.6 fm/c
t = 6-10 fm/c
Soft Physics = Hydrodynamics?
0T
3 cp T T
3p B
cT T
System is strongly interacting throughout(conserving entropy the whole time!)
Peter Steinberg Bulk Dynamics
Paths to Progress How do we understand differences and similarities
between A+A and p+p, e+e-?• Is hydrodynamics in conflict with Color Glass Condensate?
How does this system thermalize so rapidly?• Which degrees of freedom thermalize and when?• Partons, hadrons, or something else (G. Brown)?
How can we integrate the longitudinal and transverse physics?• For now, study systematics of initial state, EOS, final state• Ultimately, need 3D hydrodynamic calculations starting at the
earliest times no parameters!
Data over a broad rapidity range with PID is essential• Soft physics is global physics: y = 0 may not be special
Peter Steinberg Bulk Dynamics
Extra Slides
Peter Steinberg Bulk Dynamics
Longitudinal Transverse
z
y~
mz O
s
x
y
~z O R
pz
pTLongitudinal dynamics provide initial conditions
for transverse dynamics
Peter Steinberg Bulk Dynamics
Energy Density
2
3~ 0.4
Tpp
F
mdN
dy R
GeV
fm
2 1/3
1/3
TAA
F
TAApp
Tpp
m dNA
dyAR
mA
m
3~ 5 /
~ 10AA
pp
GeV fm
Energy densityrelated to
energy creatednear =0
Peter Steinberg Bulk Dynamics
Centrality Dependence
200/19.6
200/130
0
Changes in one rapidity region are correlatedwith particles in distant regions
Evolution of particle density with centrality is energy-independent
Peter Steinberg Bulk Dynamics
Available Energy
BRAHMS data suggests only75% “available energy”
Contradiction? Possibly.
SLD: Leading K± inss jets ~1.5 units fromend of rapidity range
Do we consider this to NOT bepart of the jet?
Peter Steinberg Bulk Dynamics
Even More Similarities: p+p, e+e-
Limiting fragmentation is a general feature of strong radiation
May explain similarity of multiplicity & energy dependence
ln 1/ ~ beamx y y
Peter Steinberg Bulk Dynamics
Sizes & ShapesHBT correlations in A+Ashow similar information
at all beam energies
Rs ~ Ro ~ 6 fmReaction
plane studiesshow elliptical
shape
STARnucl-ex/0312009
PRL in press
Peter Steinberg Bulk Dynamics
Expansion Dynamics
kT(mT)-dependence probesradial expansion
Difficult for boost-invarianthydrodynamic calculations
Rs
Ro
Peter Steinberg Bulk Dynamics
Total Multiplicity vs. Models
Peter Steinberg Bulk Dynamics
Peter Steinberg Bulk Dynamics
Peter Steinberg Bulk Dynamics
Total Multiplicity in A+A
Peter Steinberg Bulk Dynamics
Coalescence at Moderate pT
Molnar
Peter Steinberg Bulk Dynamics
Two-Particle Correlations
200 GeV Au-Au data
STAR preliminary
peripheral
central
pt 0.15-2 GeV/c
pT correlations “Neck Formation” from minijets:Coupling of “hard” with “soft”, perhaps via energy loss
Trainor
Peter Steinberg Bulk Dynamics
Is the QGP Strongly Interacting?
McLerran
Peter Steinberg Bulk Dynamics
T h e y t r y t o d e m o n s t r a t e t h a t t h e s a m e r e s u l t s o f t h e s t a t i s t i c a lT h e y t r y t o d e m o n s t r a t e t h a t t h e s a m e r e s u l t s o f t h e s t a t i s t i c a lm o d e l c a n b e o b t a i n e d s t a r t i n g f r o m d i f f e r e n t a s s u m p t i o n sm o d e l c a n b e o b t a i n e d s t a r t i n g f r o m d i f f e r e n t a s s u m p t i o n s
I s s t a t i s t i c a l p o p u l a t i o n t r i v i a l ?I s s t a t i s t i c a l p o p u l a t i o n t r i v i a l ?
,,,,, 21 3
21 2
22
21 mmmm
N
iiif
N
N
j j
Nj
NN pPMpdpd
N
JBR
j
j1
423
1
13
3 22!
)12(
)2(
1
,,,,,, 312121 IIII II
J . H o r m u z d i a r e t a l . , I n t . J . M o d . P h y s . E ( 2 0 0 3 ) 6 4 9 , n u c lJ . H o r m u z d i a r e t a l . , I n t . J . M o d . P h y s . E ( 2 0 0 3 ) 6 4 9 , n u c l -- t h 0 0 0 1 0 4 4t h 0 0 0 1 0 4 4 D . R i s c h k e , N u c l . P h y s . A 6 9 8 ( 2 0 0 1 ) 1 5 3 , t a l k a t Q M 2 0 0 1D . R i s c h k e , N u c l . P h y s . A 6 9 8 ( 2 0 0 1 ) 1 5 3 , t a l k a t Q M 2 0 0 1 V . K o c h , N u c l . P h y s . A 7 1 5 ( 2 0 0 3 ) 1 0 8 , n u c lV . K o c h , N u c l . P h y s . A 7 1 5 ( 2 0 0 3 ) 1 0 8 , n u c l -- t h 0 2 1 0 0 7 0 , t a l k g i v e n a t Q M 2 0 0 2t h 0 2 1 0 0 7 0 , t a l k g i v e n a t Q M 2 0 0 2
R e l a t i v i s t i c i n v a r i a n t : d e p e n d s o nR e l a t i v i s t i c i n v a r i a n t : d e p e n d s o na s w e l l a s o n a s w e l l a s o n
C o r r e c t , b u t n o t t r i v i a lC o r r e c t , b u t n o t t r i v i a l
Becattini
Peter Steinberg Bulk Dynamics
T h e p e c u lia r p re d ic t io n o f th e s ta tis t ic a l m o d e lT h e p e c u lia r p re d ic t io n o f th e s ta tis t ic a l m o d e l
w h ic h c a n b e e a s ily s p o ile d b y m o s t w h ic h c a n b e e a s ily s p o ile d b y m o s t |M|M ifif || 22 if c h a n n e l if c h a n n e l c o n s ta n ts d e p e n d o n p a r t ic le c o n te n tc o n s ta n ts d e p e n d o n p a r t ic le c o n te n t
jM
jN
j
j
Ω
Ω
BR
BR
M
N
E x a m p leE x a m p le
Q u ite re s tr ic t iv e : o n ly a s in g le s c a le Q u ite re s tr ic t iv e : o n ly a s in g le s c a le a n d fa c to r iz a t io na n d fa c to r iz a t io n
N
iii
Nif IhmfMMM
1
342)()()(
jM
jN
j
j
Ω
Ω
BR
BR
M
N
Becattini
Peter Steinberg Bulk Dynamics
Transport & Coalescence
Molnar
Peter Steinberg Bulk Dynamics
Global Fits to Heavy Ion Data
T (GeV)
(fm/c)Even simple modelscan be extended to cover
a large variety of data
Renk
Peter Steinberg Bulk Dynamics
Hydro & Boost Invariance
Renk
Peter Steinberg Bulk Dynamics
Importance of Viscosity
41
3s
T s
Viscous effects do notsubstantially modify
ideal hydro
Teaney
Peter Steinberg Bulk Dynamics
Can We Observe A Phase Transition?
McLerran
Peter Steinberg Bulk Dynamics
Phase Transitions with v2
Particle Density + Hydro + EOS = Prediction for v2Hadronic cascades insufficient High-mass resonances?
P. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C. C62 054909 (2000).
Peter Steinberg Bulk Dynamics
Marek’s Horn & Step
Clear value to the role of energy scan in pushingour understanding of central heavy ion collisions
Is this a smoking gun for a QCD phase transition?
Peter Steinberg Bulk Dynamics
Marek’s Kink
Are pions the only carriersof entropy?
PHOBOS “approach”:Trade in p+p for e+e-
Baryon density affectsglobal particle production
P. Steinberg, WW04
Peter Steinberg Bulk Dynamics
Klebanov: QCD vs. Gravity
String Theory in AdS
Stacked D-BranesOpen & Closed Strings
Black Holes GravitonsGravitinos
etc.
N=4 SYM lives on the surface
QuarksGluonsGluinos
Peter Steinberg Bulk Dynamics
Entropy Bound from AdS/CFT
AdS CFT
A calculationfor scattering
off a black hole…
…gives informationabout the dual
field theory
Peter Steinberg Bulk Dynamics
Gauge-String Duality & RHIC
Duality:
Strongly-Coupled QCD Weakly coupled strings
Weakly-Coupled QCD (pQCD) Strongly coupled strings
1000’s of papers working on strongly-coupled QCDs(unfortunately not “our” QCD)
Simple AdS equations Infinitely summed SYM diagrams
Will some general guides emerge?Possible way out of the paradoxes?
Peter Steinberg Bulk Dynamics
Limiting Fragmentation & CGC
Peter Steinberg Bulk Dynamics
Non-superposition
A+A is NOT a superposition of Npartx(p+p) collisions,or Npart blast waves… Need longer-range correlations
Peter Steinberg Bulk Dynamics
Dynamical Transport Models
UrQMD: Marcus Bleicher and Horst Stocker,arXiv:hep-ph/0006147
Snellings
Peter Steinberg Bulk Dynamics
Coincidence?: Shifted Gaussians in p+A?
Raw dN/dyRaw dN/dy dN/dydN/dyNNpartpart/2/2
dN/dy’dN/dy’NNpartpart/2/2
' lny y ln / 2s m
NA5 DeMarzo et al. (1984)NA5 DeMarzo et al. (1984)
PredictionPredictionFitFit
NormalizedNormalized
Peter Steinberg Bulk Dynamics
Thermal Yields in e+e- & A+A
Peter Steinberg Bulk Dynamics
RHIC Experiments (to scale)
Two BIG Spectrometers:100’s-1000’s particles event
Particle ID, photons & leptons
Two small detectors:Forward particles,Particle multiplicity
PHENIX
STAR
BRAHMS
PHOBOS
Peter Steinberg Bulk Dynamics
dN/dy Gaussians & WidthsE895 E895 E8953.0 GeV
Au+Au
BRAHMS
prel.
NA49 NA49
3.6 GeV Au+Au
4.1 GeV Au+Au
8.8 GeV Pb+Pb
17.3 GeV Pb+Pb 200 GeV Au+Au
In central events, pion rapidity distributions are Gaussian!No boost invariance in any region of phase space
Peter Steinberg Bulk Dynamics
Entropy in Strong Interactions
We believe we are making thermalized matterin heavy ion collisions
Energy in a Volume + EOS Entropy
N SCounting particles is accounting for entropy
New degrees of freedom should lead to“additional” particle production
/s T
S sV
Peter Steinberg Bulk Dynamics
Energy & Geometry “Factorize”
62 GeV200 GeV
Peter Steinberg Bulk Dynamics
What Controls v2?
Particle density appears to be a control variable
Is there really a “hydro limit”?
NA49Phys.Rev. C68
(2003) 034903