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Modern Nuclear Physics with STAR @ RHIC: Recreating the Creation of the Universe. Rene Bellwied Wayne State University ( ) Lecture 1: Why and How ? Lecture 2: Bulk plasma matter ? (soft particle production) Lecture 3: Probing the plasma (via hard probes).

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modern nuclear physics with star @ rhic recreating the creation of the universe
Modern Nuclear Physics with STAR @ RHIC:Recreating the Creation of the Universe

Rene Bellwied

Wayne State University


  • Lecture 1: Why and How ?
  • Lecture 2: Bulk plasma matter ?

(soft particle production)

  • Lecture 3: Probing the plasma

(via hard probes)

what is our mission
What is our mission ?
  • Discover the QGP
    • Find transition behavior between an excited hadronic gas and another phase
  • Characterize the states of matter
  • Do we have a hot dense partonic phase and how long does it live ?
    • Characterize medium in terms of density, temperature and time
    • Is the medium equilibrated (thermal, chemical)
the idea of two phase transitions
The idea of two phase transitions


The quarks and gluons deconfine because energy or parton density gets too high

(best visualized in the bag model).

Chiral symmetry restoration

Massive hadrons in the hadron gas are massless partons in the plasma. Mass breaks chiral symmetry, therefore it has to be restored in the plasma

What is the mechanism of hadronization ?

How do hadrons obtain their mass ?

(link to LHC and HERA physics)

what do we measure in a collider experiment
What do we measure in a collider experiment ?
  • particles come from the vertex. They have to traverse certain detectors but should not change their properties when traversing the inner detectors
  • DETECT but don’t DEFLECT !!!
  • inner detectors have to be very thin (low radiation length): easy with gas (TPC), challenge with solid state materials (Silicon).
  • Measurements: - momentum and charge via high resolution tracking in SVT and TPC in magnetic field (and FTPC) - PID via dE/dx in SVT and TPC and time of flight in TOF and Cerenkov light in RICH - PID of decay particles via impact parameter from SVT and TPC
  • particles should stop in the outermost detector
  • Outer detector has to be thick and of high radiation length (e.g. Pb/Scint calorimeter)
  • Measurements: - deposited energy for event and specific particles - e/h separation via shower profile - photon via shower profile
what do we have to check
What do we have to check ?
  • If there was a transition to a different phase, then this phase could only last very shortly. The only evidence we have to check is the collision debris.
  • Check the make-up of the debris:
    • which particles have been formed ?
    • how many of them ?
    • are they emitted statistically (Boltzmann distribution) ?
    • what are their kinematics (speed, momentum, angular distributions) ?
    • are they correlated in coordinate or momentum space ?
    • do they move collectively ?
    • do some of them ‘melt’ ?
signatures of the qgp phase
Signatures of the QGP phase

For more detail see for example: J. Harris and B. Müller, Annu, Rev. Nucl. Part. Sci. 1996 46:71-107


Phase transitions are signaled thermodynamically by a ‘step function’ when plotting temperature vs. entropy (i.e. # of degrees of freedom).

The temperature (or energy) is used to increase the number of degrees of freedom rather than heat the existing form of matter.

In the simplest approximation the number of degrees of freedom should scale with the particle multiplicity.

At the step some signatures drop

and some signatures rise

evidence some particles are suppressed

Peripheral Au + Au

STAR Preliminary

Central Au + Au


Evidence: Some particles are suppressed

If things are produced in pairs then one might make it out and the other one not.

If things require the fusion of very heavy rare quarks they might be suppressed in a dense medium

  • If the phase is very dense (QGP) than certain particles get absorbed
evidence some particles are enhanced
Evidence: Some particles are enhanced
  • Remember dark matter ? Well, we didn’t find clumps of it yet, but we found increased production of strange quark particles
how do we know what happened
How do we know what happened ?
  • We have to compare to a system that did definitely not go through a phase transition (a reference collision)
  • Two options:
    • A proton-proton collision compared to a Gold-Gold collision does not generate a big enough volume to generate a plasma phase
    • A peripheral Gold-Gold collision compared to a central one does not generate enough energy and volume to generate a plasma phase
kinematic variables of choice





Rapidity y = ln (E+pz/E-pz)

= lorentz invariant ‘velocity’

Transverse momentum pt = sqrt (px2+py2)

Kinematic variables of choice

y = -6 0 +6

0.) Global observablesA.) particle productionB.) particle spectraC.) particle flowD.) particle correlations
lattice qcd
Quarks and gluons are studied on a discrete space-time lattice

Solves the problem of divergences in pQCD calculations (which arise due to loop diagrams)








Lattice Results

Tc(Nf=2)=1738 MeV

Tc(Nf=3)=1548 MeV


(F. Karsch, hep-lat/9909006)

  • There are two order parameters
Lattice QCD

T = 150-200 MeV

e ~ 0.6-1.8 GeV/fm3

assessing the initial energy density calorimetry
Assessing the Initial Energy Density: Calorimetry

Bjorken-Formula for Energy Density:

PRD 27, 140 (1983) – watch out for typo (factor 2)

Time it takes to thermalize system (t0 ~ 1 fm/c)

~6.5 fm


Central Au+Au (Pb+Pb) Collisions:

17 GeV: eBJ  3.2 GeV/fm3

130 GeV: eBJ 4.6 GeV/fm3

200 GeV: eBJ  5.0 GeV/fm3

Note: t0 (RHIC) < t0 (SPS)

commonly use 1 fm/c in both cases

assessing the initial energy density tracking
Assessing the Initial Energy Density: Tracking

Bjorken-Formula for Energy Density:

Gives interestingly always slightly smaller values than with calorimetry (~15% in NA49 and STAR).

the problem with e bj

eBj~ 23.0 GeV/fm3

eBj~ 4.6 GeV/fm3

Lattice ec

The Problem with eBJ
  • eBJ is not necessarily a “thermalized” energy density
    • no direct relation to lattice value
    • requires boost invariance
  • t0 is not well defined and model dependent
    • usually 1fm/c taken for SPS
    • 0.2 – 0.6 fm/c at RHIC ?
  • system performs work p·dV  ereal > eBJ
    • from simple thermodynamic assumptions

 roughly factor 2

so what is e now
So what is e now ?
  • At RHIC energies, central Au+Au collisions:
  • From Bjorken estimates via ET and Nch: e > 5 GeV/fm3
  • From energy loss of high-pT particles: e≈ 15 GeV/fm3
  • From Hydromodels with thermalization: ecenter≈ 25 GeV/fm3
  • All are rough estimates and model dependent (EOS, t0, ... ?) , no information about thermalization or deconfinement. Methods not completely comparable
  • But are without doubt good enough to support that e >> eC≈ 1 GeV/fm3
how do we use hadrons
How do we use hadrons ?
  • Discovery probes:
    • CERN: Strangeness enhancement/equilibration
    • RHIC: Elliptic flow
    • RHIC: Hadronic jet quenching
  • Characterization probes:
    • Chemical and kinetic properties
    • HBT and resonance production for timescales
    • Fluctuations for dynamic behavior
basic idea of statistical hadronic models
Basic Idea of Statistical Hadronic Models
  • Assume thermally (constant Tch) and chemically (constant ni) equilibrated system
  • Given Tch and  's (+ system size), ni's can be calculated in a grand canonical ensemble

Chemical freeze-out

(yields & ratios)

  • inelastic interactions cease
  • particle abundances fixed (except maybe resonances)

Thermal freeze-out

(shapes of pT,mT spectra):

  • elastic interactions cease
  • particle dynamics fixed
particle production s tatistical models do well
Particle production:Statistical models do well

We get a chemical freeze-out temperature and

a baryochemical potential out of the fit

statistical hadronic models misconceptions
Statistical Hadronic Models : Misconceptions
  • Model says nothing about how system reaches chemical equilibrium
  • Model says nothing about when system reaches chemical equilibrium
  • Model makes no predictions of dynamical quantities
  • Some models use a strangeness suppression factor,others not
  • Model does not make assumptions about a partonic phase; However the model findings can complement other studies of the phase diagram (e.g. Lattice-QCD)
thermalization in elementary collisions
Thermalization in Elementary Collisions ?

Seems to work rather well ?!

Beccatini, Heinz, Z.Phys. C76 (1997) 269

thermalization in elementary collisions1
Thermalization in Elementary Collisions ?
  • Is a process which leads to multiparticle production thermal?
  • Any mechanism for producing hadrons which evenly populates the free particle phase space will mimic a microcanonical ensemble.
  • Relative probability to find a given number of particles is given by the ratio of the phase-space volumes Pn/Pn’ = fn(E)/fn’(E)  given by statistics only. Difference between MCE and CE vanishes as the size of the system N increases.

This type of “thermal” behavior requires no rescattering and no interactions. The collisions simply serve as a mechanism to populate phase space without ever reaching thermal or chemical equilibrium

In RHI we are looking for large collective effects.

statistics thermodynamics
Statistics  Thermodynamics


Ensemble of events constitutes a statistical ensemble

T and µ are simply Lagrange multipliers

“Phase Space Dominance”


  • We can talk about pressure
  • T and µ are more than Lagrange multipliers
are thermal models boring
Are thermal models boring ?

Good success with thermal models in e+e-, pp, and AA collisions.

Thermal models generally make

tell us nothing about QGP, but

(e.g. PBM et al., nucl-th/0112051):

Elementary particle collisions: canonical description, i.e. local quantum number conservation (e.g.strangeness) over small volume.

Just Lagrange multipliers, not indicators of thermalization.

Heavy ion collisions:

grand-canonical description, i.e. percolation of strangeness over large volumes, most likely in deconfined phase if chemical freeze-out is close to phase boundary.

t systematics
T systematics
  • it looks like Hagedorn was right!
    • if the resonance mass spectrum grows exponentially (and this seems to be the case), there is a maximum possible temperature for a system of hadrons
    • indeed, we don’t seem to be able to get a system of hadrons with a temperature beyond Tmax ~ 170 MeV!

[Satz: Nucl.Phys. A715 (2003) 3c]

filled: AA

open: elementary

does the thermal model always work
Does the thermal model always work ?

Data – Fit (s) Ratio

  • Particle ratios well described by Tch = 16010 MeV, mB = 24 5 MeV
  • Resonance ratios change from pp to Au+Au  Hadronic Re-scatterings!
strange resonances in medium
Strange resonances in medium

Short life time [fm/c]

K* < *< (1520) < 

4 < 6 < 13 < 40

Rescattering vs.

Regeneration ?

Medium effects on resonance and their decay products before (inelastic) and after chemical freeze out (elastic).

Red: before chemical freeze out

Blue: after chemical freeze out


ResonanceProduction in p+p and Au+Au

Life time [fm/c] :

 (1020) = 40

L(1520) = 13

K(892) = 4

++ = 1.7

Thermal model [1]:

T = 177 MeV

mB = 29 MeV

UrQMD [2]

[1] P. Braun-Munzinger, PLB 518(2001) 41

D.Magestro, private communication

[2] Marcus Bleicher and Jörg Aichelin

Phys. Lett. B530 (2002) 81-87.

M. Bleicher, private communication

Rescattering and regeneration is needed !

resonance yields consistent with a hadronic re scattering stage
Resonance yields consistent with a hadronic re-scattering stage
  • Generation/suppression according to x-sections












More D


Chemical freeze-out


f Ok






Less K*





Less L*









strangeness two historic qgp predictions
Strangeness: Two historic QGP predictions
  • restoration of csymmetry -> increased production of s
    • mass of strange quark in QGP expected to go back to current value (mS ~ 150 MeV ~ Tc)
    • copious production of ss pairs, mostly by gg fusion

[Rafelski: Phys. Rep. 88 (1982) 331]

[Rafelski-Müller: P. R. Lett. 48 (1982) 1066]

  • deconfinement  stronger effect for multi-strange
    • by using uncorrelated s quarks produced in independent partonic reactions, faster and more copious than in hadronic phase
    • strangeness enhancement increasing with strangeness content

[Koch, Müller & Rafelski: Phys. Rep. 142 (1986) 167]

Strangeness production depends strongly on baryon density

(i.e. stopping vs. transparency, finite baryo-chemical potential)

strangeness enhancement in b b ratios
Strangeness enhancement in B/B ratios
  • Baryon over antibaryon production can be a QGP signature as long as the baryochemical potential is high (Rafelski & Koch, Z.Phys. 1988)
  • With diminishing baryochemical potential (increasing transparency) the ratios approach unity with or without QGP, and thus only probe the net baryon density at RHIC.
new rhic data of baryon ratios

STAR p+p 200 GeV



New RHIC data of baryon ratios
  • The ratios for pp and AA at 130 and 200 GeV are almost indistinguishable. The baryochemical potentials drop from SPS to RHIC by almost an order of magnitude to ~50 MeV at 130 GeV and ~20 MeV at 200 GeV.
strangeness enhancement wroblewski factor evolution

Lines of constant lS

I. Increase instrange/non-strangeparticle ratios

PBM et al., hep-ph/0106066


II. Maximum isreached


III. Ratios decrease

(Strange baryonsaffected more stronglythan strange mesons)

See P.Senger’s talk


hidden strangeness mesons

<E>/<N> = 1 GeV

Peaks at 30 A GeV in AA collisions due to strong mB dependence

Strangeness enhancement:Wroblewski factor evolution

Wroblewski factor

dependent on T and mB

dominated by Kaons

strangeness enhancement




Strangeness enhancement
  • K/p – the benchmark for abundant strangeness production:
the switch from canonical to grand canonical tounsi redlich hep ph 0111159 hep ph 0209284
The switch from canonical to grand-canonical(Tounsi,Redlich, hep-ph/0111159, hep-ph/0209284)

The strangeness enhancement factors at the SPS (WA97) can

be explained not as an enhancement in AA but a suppression in pp.

The pp phase space for particle production is small. The volume is small and the volume term will dominate the ensemble (canonical (local)). The grand-canonical approach works for central AA collisions, but because the enhancements are quoted relative to pp they are due to a canonical suppression of strangeness in pp.

strangeness enhancement factors at rhic



Strangeness enhancement factors at RHIC

No Npart-scaling in Au-Au at RHIC -> lack of Npart scaling = no thermalization ?

Alternatives: no strangeness saturation in peripheral collisions (gs = 1)

non-thermal jet contributions rise with centrality

identified particle spectra for au au @ 200 gev

BRAHMS: 10% central



STAR: 5%

Identified Particle Spectra for Au-Au @ 200 GeV
  • The spectral shape gives us:
    • Kinetic freeze-out temperatures
    • Transverse flow
  • The stronger the flow the less appropriate are simple exponential fits:
    • Hydrodynamic models (e.g. Heinz et al., Shuryak et al.)
    • Hydro-like parameters (Blastwave)
  • Blastwave parameterization e.g.:
    • Ref. : E.Schnedermann et al, PRC48 (1993) 2462

Explains: spectra, flow & HBT

thermal spectra
“Thermal” Spectra

Invariant spectrum of particles radiated by a thermal source:

where: mT= (m2+pT2)½transverse mass (Note: requires knowledge of mass)

m = b mb + s ms grand canonical chem. potential

T temperature of source

Neglect quantum statistics (small effect) and integrating over rapidity gives:

R. Hagedorn, Supplemento al Nuovo Cimento Vol. III, No.2 (1965)

At mid-rapidityE = mT cosh y = mTand hence:


thermal spectra flow aside
“Thermal” Spectra (flow aside)
  • Describes many spectra well over several orders of magnitude with almost uniform slope 1/T
  • usually fails at low-pT
  • ( flow)
  • most certainly will fail
  • at high-pT
  • ( power-law)

N.B. Constituent quark and parton recombination models yield exponential spectra with partons following a pQCD power-law distribution. (Biro, Müller, hep-ph/0309052)

 T is not related to actual “temperature” but reflects pQCD parameter p0 and n.

thermal spectra and radial expansion flow


1/mT dN/dmT






purely thermal



1/mT dN/dmT




“Thermal” spectra and radial expansion (flow)
  • Different spectral shapes for particles of differing mass strong collective radial flow
  • Spectral shape is determined by more than a simple T
  • at a minimum T, bT
thermal flow traditional approach
Thermal + Flow: “Traditional” Approach

Assume commonflow pattern and common

temperature Tth

1. Fit Data  T

2. Plot T(m) Tth, bT

  • is the transverse expansion velocity. With respect to T use kinetic energy term ½ m b2

This yields a common thermal freezeout temperature and a common b.

hydrodynamics in high density scenarios
Hydrodynamics in High-Density Scenarios
  • Assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles)
  • Equations given by continuity, conservation laws, and Equation of State (EOS)
  • EOS relates quantities like pressure, temperature, chemical potential, volume = direct access to underlying physics

Kolb, Sollfrank

& Heinz,


hydromodels can describe m t p t spectra
Hydromodels can describe mT (pT) spectra
  • Good agreement with hydrodynamic prediction at RHIC & SPS (2d only)
  • RHIC: Tth~ 100 MeV,  bT  ~ 0.55 c
blastwave a hydrodynamic inspired description of spectra
Blastwave: a hydrodynamic inspired description of spectra

Spectrum of longitudinal and transverse boosted thermal source:



Ref. : Schnedermann, Sollfrank & Heinz,

PRC48 (1993) 2462

Static Freeze-out picture,

No dynamical evolution to freezeout

the blastwave function
The Blastwave Function
  • Increasing T has similar effect on a spectrum as
  • increasing bs
  • Flow profile (n) matters at lower mT!
  • Need high quality data down to low-mT
blastwave fits
Blastwave fits
  • Source is assumed to be:
    • In local thermal equilibrium
    • Strongly boosted
  • , K, p: Common thermal freeze-out at T~90 MeV and <>~0.60 c
  • : Shows different thermal freeze-out behavior:
    • Higher temperature
    • Lower transverse flow
  • Probe earlier stage of the collision, one at which transverse flow has already developed
  • If created at an early partonic stage it must show significant elliptic flow (v2)

Au+Au sNN=200 GeV

STAR Preliminary

 68.3% CL

95.5% CL

99.7% CL

blastwave vs hydrodynamics

Tdec = 100 MeV

Kolb and Rapp,PRC 67 (2003) 044903.

Blastwave vs. Hydrodynamics

Mike Lisa (QM04): Use it don’t abuse it ! Only use a static

freeze-out parametrization when the dynamic model doesn’t work !!

collective radial expansion
Collective Radial Expansion

From fits to p, K, p spectra:

  • <r >
    • increases continuously
  • Tth
    • saturates around AGS energy
  • Strong collective radial expansion at RHIC
  • high pressure
  • high rescattering rate
  • Thermalization likely

Slightly model dependent


Blastwave model

elliptic flow in the transverse plane for a mid peripheral collision
Elliptic Flow(in the transverse plane)for a mid-peripheral collision









Dashed lines: hard

sphere radii of nuclei

Re-interactions  FLOW

Re-interactions among what? Hadrons, partons or both?

In other words, what equation of state?

v 2 measurements miklos favorite
v2 measurements (Miklos’ Favorite)

Multistrange v2 establishes partonic collectivity ?

lifetime and centrality dependence from 1520 and k 892 k

Blast wave fit of p,K,p (Tkin +b) + Tchem

  • Dt ~ 6 fm/c

Based on entropy: Dt ~ (Tch/Tkin – 1) R/bs

  • Dt does not change much with centrality
  • because slight DT reduction is compensated by slower expansion velocity b in peripheral collisions.


More resonance measurements are needed

to verify the model and lifetimes

Lifetime and centrality dependence from (1520) / and K(892)/K

G. Torrieri and J. Rafelski, Phys. Lett. B509 (2001) 239

Life time:

K(892) = 4 fm/c

L(1520) = 13 fm/c

  • Model includes:
  • Temperature at chemical freeze-out
  • Lifetime between chemical and thermal freeze-out
  • By comparing two particle ratios (no regeneration)
  • results between :
  • T= 160 MeV =>  > 4 fm/c(lower limit !!!)
  •  = 0 fm/c => T= 110-130 MeV

(1520)/ = 0.034  0.011  0.013

K*/K- = 0.20  0.03 at 0-10% most central Au+Au

time scales according to star data

hadronic phase

and freeze-out

QGP and

hydrodynamic expansion

initial state



Time scales according to STAR data

Balance function (require flow)

Resonance survival

Rout, Rside

Rlong (and HBT wrt reaction plane)



5 fm/c

1 fm/c

10 fm/c

20 fm/c

Chemical freeze out

Kinetic freeze out

summary global observables
Summary: global observables
  • Initial energy density high enough to produce a QGP
    • e 10 GeV/fm3

(model dependent)

    • High gluon density

dN/dy ~ 800-1200

    • Proof for high density matter but not for QGP
summary of particle identified observables
Summary of particle identified observables

Statistical thermal models appear to work well at SPS and RHIC

  • Chemical freeze-out is close to TC
  • Hadrons appear to be born

into equilibrium at RHIC (SPS)

  • Shows that what we observe is

consistent with thermalization

  • Thermal freeze-out is common

for all particles if radial flow

is taken into account.

T and bT are correlated

  • Fact that you derive T,bT is

no direct proof but it is consistent with thermalization

  • There is no “ “ in bulk matter properties
  • However:
    • So far all pieces point

indeed to QGP formation

- collective flow

& radial

- thermal behavior

- high energy density

- strange particle production enhancement