Bulk Dynamics in Heavy Ion Collisions

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


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?


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


The Bulk of Particles: dN/dpT

STAR


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


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


The Big Surprise

Contrary to popular belief…

Bulk observables are “simple”

…just not necessarily at =0!


Participant Scaling

Participant scaling = Long-range rapidity correlations


“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


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


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


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


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?


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


Universal Multiplicity Formula

Multiplicity formula impliesp=/3 in early times

Nch=2.2s1/4

Npart scaling impliesEntropy~Volume


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


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’


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


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


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


pT Dependence

2 ~ Tv p

“fine structure” (mass dependence) Described by hydro (and hydro-inspired) fits

STAR


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


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…


More similarities: AA & e+e-

Similar “longitudinaldynamics”?

Similar “energy density”?


Limiting FragmentationDELPHI PLB 459 (1999)

p+p e+e-


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


Radial Expansion in p+p?

R. Witt, STAR Collaboration


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


Soft Physics = Difficult Physics?

Dynamical models have few constraintsalthough global constraints seem to matter


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!)


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


Extra Slides


Longitudinal Transverse

z

y~

mz O

s

x

y

~z O R

pz

pTLongitudinal dynamics provide initial conditions

for transverse 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


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


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?

qq


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


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


Expansion Dynamics

kT(mT)-dependence probesradial expansion

Difficult for boost-invarianthydrodynamic calculations

Rs

Ro


Total Multiplicity vs. Models




Total Multiplicity in A+A


Coalescence at Moderate pT

Molnar


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


Is the QGP Strongly Interacting?

McLerran


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


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


Transport & Coalescence

Molnar


Global Fits to Heavy Ion Data

T (GeV)

(fm/c)Even simple modelscan be extended to cover

a large variety of data

Renk


Hydro & Boost Invariance

Renk


Importance of Viscosity

41

3s

T s

Viscous effects do notsubstantially modify

ideal hydro

Teaney


Can We Observe A Phase Transition?

McLerran


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).


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?


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


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


Entropy Bound from AdS/CFT

AdS CFT

A calculationfor scattering

off a black hole…

…gives informationabout the dual

field theory


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?


Limiting Fragmentation & CGC


Non-superposition

A+A is NOT a superposition of Npartx(p+p) collisions,or Npart blast waves… Need longer-range correlations


Dynamical Transport Models

UrQMD: Marcus Bleicher and Horst Stocker,arXiv:hep-ph/0006147

Snellings


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


Thermal Yields in e+e- & A+A


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


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


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


Energy & Geometry “Factorize”

62 GeV200 GeV


What Controls v2?

Particle density appears to be a control variable

Is there really a “hydro limit”?

NA49Phys.Rev. C68

(2003) 034903

Documents

Bulk Dynamics in Heavy Ion Collisions