peter steinberg cipanp 2003 dynamics of soft particle production in heavy ion collisions peter...

Peter Steinberg CIPANP 2003

Dynamics of Soft Particle Production in Heavy Ion Collisions

Peter SteinbergBrookhaven National Laboratory

Visiting Fulbright Professor at University of Cape Town, South Africa

CIPANP May 19-24 2003New York City, NY USA


1. Can we understand the early dynamics?2. Is the initial state modified before freezeout?3. Can simple regularities in the data teach us how to

disentangle energy & geometry?

Statistical Mechanic

sHydrodynamic

s Geometry QCDPartonsaturation

BjorkenHydro

GlauberModel

Statistical/ThermalModelsstopping multiplicity

spectraRadial flowElliptic

flow

Strangeness

HBT

EnergyDensity

A Briefer History of Time


Question 1

Where does the entropy come from?

What are the degrees of freedom ofa Au+Au collision at RHIC?


Energy & Geometry

3/4

121

part

N

icoll NNpart

4ib

Participant

BinaryCollisions

“Glauber Model”

sNN/2

sNN/2

Nucleon-Nucleon

CMS Energy

Short distance,Incoherent

Long distance,Coherent


Nucleon Structure & Nuclear Collisions• With increasing energy: quarks partons

• Nuclei act as overlapping layers of nucleons increased density

Proton Quark Model High Energy

Et /~ “snapshot”of vacuumfluctuations

High EnergyProton

High EnergyProton in a

Nucleus

Figures from H. Satz, QM2002


Parton Saturation2 2

2 2

( , ) ( ) 1xG x Q QR Q

22 2

2

2

1 / 3

( , )( )

1~

ss s

xG x QQ Q A

R

fmA

• Density (thickness) momentum scale Qs

• Below Qs, target is “black”, cross section saturates• Theoretical approach: “Color Glass Condensate”

• Weak coupling Strong fields! 2 2, ~ 1/s sxG x Q Q

“Packing Factor”

Lipatov, Levin, Ryskin, McLerran, Venugopalan, Mueller, Iancu, Jalilian-Marian, Dumitru, etc.


Saturation Phenomenology• Qs controls low-x physics: applies to HERA & RHIC

• Golec-Biernat-Wusthoff energy scaling of p cross section

• Rapidity (geometric scaling)

• Centrality – Npart scaling (sources) modified by thickness

• McLerran-VenugopalanMuellerKharzeev/Nardi

2 20

0s

xQ x Qx

2

22

, A spart s

s s

S QdN cN xG x Qdy Q

2sQ W

Geometry QCDInitialFinal

~ .25 3 20 ~ 2

@130 ( )Q GeV

GeV RHIC

2 ~ /s s part coll partQ xG N N


LPHD: How do we “see” saturation?• Saturation calculations

depend on hypothesis:

• “Local parton hadron duality” tested in e+e-• Dokshitzer, Mueller, Khoze,

Ochs, etc.• pQCD mysteriously “works”

at low p

• Hadronization is “soft”• No modification of parton

spectrum and yield

~1chadrons partonsN cN


•Initial state LPHD Final state!

• limiting fragmentation (1-x)4

•Shape seems be found in pp (& e+e-) as well…

Saturation vs. Multiplicity Data• Kharzeev, Levin, Nardi

4

22 2

1 /,

ln / ,TT s

x xx k

k Q W x

3

22 21 23 , ,T s T T

d NE dk x k x p kdp

“Quark counting” at high-x (Phenomenology!)

PHOBOS200 GeV

130 GeV

19.6 GeV

/ / / 2partdN d N


Saturation vs. Spectra• Low-x *p physics

controlled by dimensionless quantity

• RHIC data shows evidence of simliar “geometric scaling”:

• Further evidence that one scale may control much of the observed physics

2

20 0x

Q xQ

3

3 ~ ~ 1T Ts

s s

m md NE fdp p p

n

Schaffner-Bielich, McLerran,Venugopalan, Kharzeev


Implications for Initial State• Initial state Final State

• Coherence lower entropy than pQCD• Qs determines initial physics

• Momentum, Density, Formation Time

• Early formation time large energy densities

0 ~ .2s

fmQ

2 30

/~ ~ 5 18 20TdE dy GeVR fm

PHENIX


Critical remarks• Saturation approach is appealing

• Unifies many features of data with one scale• Trying to reconcile pQCD & unitarity• Qualitative connection to many aspects of data

• However, not a complete physical picture• Phenomenological factors need justification• LPHD is still a hypothesis! – needs testing


Question 2• What happens between the initial state and

final state?

• Can a hydrodynamic description make sense?• Thermalization• Dynamics (EOS)• Observables


Thermal Model Calculations

3

3 ( ) /

112

i

i

Si i s E T

d pN gVe

“StrangenessSuppression”

iSiQiBi SQB

(Cleymans,Redlich, Braun-

Munziger, Stachel,Magestro, Kaneta, Xu…)Grand

CanonicalEnsemble

Chemical FreezeoutTemperature

Baryon ChemicalPotential

Fireball Volume/ 20

B Q fixedS

Excellent fit to RHIC data

Equilibration mechanism?

Conservation laws obeyed globally,not locally!


Thermal Model Systematics

• A+A looks like thermalized hadron gas• So do elementary systems not a hadronic effect• Consensus: “born into” equilibrium well before freezeout

Kaneta & Xu

/ ~ 1E N GeV

LEP

Cleymans & Redlich


Hydrodynamic Approach• Landau (1953)

• Strongly interacting degrees of freedom• Short mean-free path

• Specify initial conditions, and then conserve:• Energy-momentum & “charges” (e.g. baryon #)

• Two basic approaches developed:

Landau (1953):Complete Stopping1D 3D expansiondN/dy ~ Gaussian

Bjorken (1983):Boost

InvariancedN/dy ~ const

ISR data (now RHIC data) seemed to prefer Bjorken…


The Hydro “Machine”

0T

0n x

0p

3

3 ,ii

d NE f x p p ddp

Energy-MomentumConservation

Baryon NumberConservation

Equation ofState (EOS)

Freezeout Hypersurface (x,t)Velocity field u(x,t)

Cooper-Frye Formula

Boost Invariant Initial Conditions

( , ) ( , )s x y or e x y

x

u x

Ideal gas

Lauret, Shuryak, Teaney


Hydro Initial Conditions• Glauber Matching to

final state multiplicity

WN WN

BC BC

e sWN e sBC e s

, (1 ) WN BCs x y x s xs (Kolb/Heinz)

Heinz/Kolb

, WNs x y s (Lauret, Shuryak, Teaney) 30

3

.6 ~ 25 /

~ 100 /~ 350

e fm GeV fm

s fmT MeV

Typical values:

Allows study of centralitydependence of initial state

(WoundedNucleons)

(BinaryCollisions)


Particle Spectra• Centrality dependence radial velocity

• NB: ~ T4 -> (T=120 MeV) << (T~165 MeV)

Pion ‘excess’ reduced by attentionto chemical freezeout conditions

P. Kolb & R. RappHeinz/Kolb

20T T m


Equation of State• EOS encodes all of the bulk dynamics

• 1st order phase transition (a la lattice) leads to softening of EOS: cs0

/ 3p B

/ 3p

~ / 6p

2s

dp cd

(Landau 1953:ideal, massless)

B

(resonance gas,much softer)

(QGP)

(Speed ofsound)

Heinz/Kolb


Elliptic Flow

21 2 cos 2dN vd

PHOBOS data

2 2

22 2

Y X

Y X

MomentumSpace

Glauber relates b to

Solutions to Hydro Equations:

CoordinateSpace


• v2 results have differing sensitivity to EOS

• Heavy particles sensitive to EOS• Less affected by thermal smearing

• Current results prefer 1st order PT!

Elliptic Flow Results

R. Snellings, STAR preliminary


Trouble Down the Hill?

• Trouble for hydro in the longitudinal direction• HBT: Rlong has problems (M. Lisa)• Elliptic flow away from 90o (T. Hirano)

• Where is the problem: initial state or freezeout?• 3D modeling? Viscosity (Teaney)?

• Is boost invariance justified, even at y=0?

T. HiranoHeinz/Kolb


Hydro vs. Saturation• If hydro is truly applicable then

• cf. Saturation + LPHD (parton-hadron duality)

• Interesting that numbers from saturation are not incompatible w/ hydro!• “Bottom up” (BMSS), Eskola, et al

(U.Heinz)

Initial State Final State

Initial State Final State


Critical Remarks• Ambiguities:

• Initial state• Need additional input beyond 2D Glauber

• Which EOS is required • Consistency with broad range of data

• Freezeout conditions • Many variations, incl. “Blast wave” (M. Lisa)

• Assumption of boost-invariance• Hiding important dynamics?

• Systematic studies are crucial!


Question 3• How much does simple “scaling” behavior

in the data teach us?

• What drives the physics?• Energy• Geometry


Simple Behavior of Nch• PHOBOS observes that e+e- sets multiplicity scale

• The rest is linear participant scaling (soft)• Simple argument: reduced leading particle effect

/ 2ch e e eff partN N s N

PHOBOS, QM2002

Nch /

e+ e

- fit

Is this “scaling”?

Au+Aue++e-

p+p


Scaling of Thermal Parameters

Thermal parameters: rapid change “saturation”

1.27 , 4.3165 , ~o o p

a GeV b GeVT MeV m 1 /B

ab s

JC, PBM, KR, etc.


Entropy & Chemistry• Thermodynamics B supresses s

• Increasing energy lowers BPAS, Cleymans, et al

AGS SPS RHIC

B Be p nsT

“Scaling”0B

Additional energy justmakes a “bigger” system:

LHC ~ RHIC

(entropy density)


Strangeness Enhancements

1

0.6

0.4

0.2

0.8

0 100 200 300 400Npart

J. Cleymans, B. Kaempfer, PAS, S. Wheaton, nucl-th/0212335

PHENIX

2s

ssuu dd

J. Cleymans

Energy: B 0, AA is “different”

Geometry: fraction of multiply-struck participantsdrives system towards full chemical equilibrium? NA49, E910

2s f


What have we learned?• RHIC provides extensive systematics in energy,

geometry (& rapidity)!• Which variables control the physics!

• Energy Larger multiplicity, “Saturation” as B0

• Nuclear geometry multiple collisions• Leading particles attenuated (e+e-)• Chemical equilibrium (strangeness)

• Caveat: Beware of coincidences!• Strive for uniqueness, or broad applicability


What is “stopping”?• None of this was predicted we don’t understand

some basic features of the initial state!• Transfer of energy: longitudinal transverse

• 20 years after Busza&Goldhaber: what is stopping?• dE/dx? Or “destroying” nucleons completely!?

GRV-HO

Net

Bar

yon

Bass & Muller, nucl-th/0212103

p p


Status of Soft Dynamics• Saturation is a reasonable picture of initial state

• One scale to rule them all!• Phenomenology many assumptions need justification

• Hydro addresses dynamics after initial state• Final state Information moving beyond R>Rp • Results sensitive to arbitrary initial conditions, EOS, and final

state! Systematics are crucial.• Empirical scaling is a reality check

• Chemistry matters! Nuclear geometry matters!• Beware of accidents: distinguish cause from correlation

• Global dynamics matter!• Strongly interacting, conservative system• Longitudinal dynamics may be very important• Be careful about what we factorize away!


Scope of this talk• Dynamics

• With increasing time, energy scales decrease• Must consider range of dynamical scenarios since the

soft processes are omnipresent!

• Soft particle production• Bulk (99%) of produced particles• These will be the “freezeout” of the QGP• Momentum scales are < 2 GeV

• Heavy Ion Collisions• d+A data is just becoming available• Will be an important contribution


Multiplicity Scaling

WA98WA97/NA57

Phobos

NA49

E917/866

STAR(PRELIMINARY)

RESULTS

E877

PHENIX

BRAHMS

Phobos

• Does the particle density act as a scale?• Elliptic flow “scales” in the same way…

Z. Xu NA49 compilation

Charged Particle Densityat =0


Multiplicity & v2

2 /~ dN dyS

Empirically <pT> is also a function of multiplicity & mass:

Hydro or CGC?Both predict this sort of behavior

Schaffner-Bielich et al

ParticlesArea

v2 data from AGSRHICscales with local particle density

Challenge to hydro?

NA49

peter steinberg cipanp 2003 dynamics of soft particle production in heavy ion collisions peter...

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