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RHIC paradigms: Early Thermalization and Collectivity are they achieved in RHIC’s new state of matter ?
Rene Bellwied (Wayne State University)
Workshop on Critical Examination
of RHIC Paradigms
April 14–17, 2010
The Department of Physics
The University of Texas at Austin
Outline

Why is it important ?
2
What is based on the assumption of thermalization?
The phase diagram
The models
(transition,
critical point,
Phase properties)
(lattice QCD,
Hydrodynamics,
Statistical hadronization)
Basic thermodynamics
Energy:
dE = T dS – p dV + S m dN
Free energy: dF = -S dT – pdV + S mdN
thermal (or kinetic) equilibration: dT = 0
chemical equilibration: dN = 0
chemical equilibration at a fixed Tch and a fixed m
thermal equilibration at a fixed Tth (lower than Tch)
chem. freeze-out occurs when inelastic collisions cease
thermal freeze-out occurs when elastic collisions cease
Temperature progression:Tc > Tch> Tth
Measured yields and spectra will only tell us that the hadrons are
equilibrated. Basic thermal models are not dynamic, they tell you
nothing about the evolution of the system until freeze-out.
Statistical evolution of relativistic heavy ion collisions
Model:
lQCD
Effect:
hadronization
Freeze-out surface: Tcrit
Temperature (MeV): 190
Expansion velocity:
SHM
Blastwave
chemical f.o.
Tch
165
kinetic f.o.
Tkin(X,W)
160
b=0.45
Tkin(p,k,p,L)
80
b=0.6
Hydro condition ?
partons
time:
hadrons
~4 fm/c
~4 fm/c
(nucl-ex/0604019)
Fast equilibration measurements:
strangeness enhancement & v2
References:
Lattice QCD:
hep-lat/0608013
arXiv:0903.4155
Statistical Hadronization:
hep-ph/0511094
nucl-th/0511071
Blastwave:
nucl-ex/0307024
arXiv:0808.2041
Famous example: Assessing the Initial Energy Density
Bjorken-Formula for Energy Density:
PRD 27, 140 (1983) – watch out for typo (factor 2)
 Bj 
1 1 dET
p R 2  0 dy
dET
3 dN ch
 mT
dy
2 dy
dN ch 
m
 1
dy  mT
2


2


at y 0
1
2
dN ch
d
and hence
1 1
3 
m 2 
 Bj  2 mT 1
p R 0
2  mT 2 
Bj~ 23.0 GeV/fm3
1
2
dN ch
d
Central Au+Au (Pb+Pb) Collisions:
17 GeV: BJ 3.2 GeV/fm3
130 GeV: BJ 4.6 GeV/fm3
200 GeV: BJ 5.0 GeV/fm3
Bj~ 4.6 GeV/fm3
Lattice c
Can it thermalize that fast ?

Not through collisions. That takes at
least 5 fm/c (big problem)

Alternate ideas:
◦ Plasma instabilities (start off with fields
instead of particles)
◦ Hawking radiation (start off with extremely
high gluon densities)
◦ System born into thermal state ?
7
What is the alternative to
thermalization ?
A system that is not equilibrated, a system that
is governed by a non-thermal fragmentation
process (jets in pp, overlapping mini-jets in AA)
Jets that populate
the bulk part of the
spectrum
something that generates correlated emission
other than decays or HBT
Hadronization in QCD
(the factorization theorem)
Jet: A localized collection of hadrons which come from
hadrons
a fragmenting parton
c
a
Parton Distribution Functions
Hard-scattering cross-section
Fragmentation Function
b
d
hadrons
leading
particle
High
~ pT (> 2.0 GeV/c) hadron production in pp collisions:
h
d pp
0
D
d

2
2
h/c

K
dx
dx
f
(
x
,
Q
)
f
(
x
,
Q
)
(
ab

cd
)

a
b a
a
b
b
2

dyd pT
dtö
pzc
abcd
“Collinear factorization”
High pT Particle Production in A+A
h
dN AB
2
2

ABK
dx
dx
d
k
d
kb

a
b
a
2

dyd pT
abcd
 f a / A ( xa , Q 2 ) f b / B ( xb , Q 2 )
 g (k a ) g (k b )
Intrinsic kT, Cronin Effect
 S A ( xa , Qa2 ) S B ( xb , Qb2 )
d

(ab  cd )
dtö
1
zc*
  dP( )
0
zc
0
h/c
*
c
2
c
D (z ,Q )

pzc
Parton Distribution Functions
Shadowing, EMC Effect
Hard-scattering cross-section
c
Partonic Energy Loss
a
b
d
Fragmentation Function
hadrons
leading particle
suppressed
General Comment:
fragmentation does not do well with identified
particle production or kinematics.
It gets the charged particle distributions sort of
correct, but any attempt to determine kinematic
observables (pt or v2) or even yield for specific
particle species correctly have failed until now.
This is important because much of the evidence
for equilibration (chemical or thermal) relies on
the reproduction of exact patterns of identified
particle properties. Thermal and chemical patterns
are very sensitive to mass and flavor.
The basic RHIC paradigms

Paradigm 1: Chemical equilibration at the partonic level
◦ Evidence: yields at chemical freeze-out (hadronic), strangeness/charm enhancement

Paradigm 2: Kinetic equilibration (thermalization) at the partonic level
◦ Evidence: spectra at thermal freeze-out, validity of hydrodynamics, radial expansion

Paradigm 3: Strong partonic collectivity in agreement with near ideal
hydrodynamics
◦ Evidence: spectra, v2, HBT

Paradigm 4: Hadronization is not dominated by fragmentation even at
high pT
◦ Evidence: B/M ratios, quark scaling for v2 and energy loss

Paradigm 5: Energy loss is purely partonic
◦ Evidence: lack of color or mass dependence in RAA

Paradigm 6: Particle correlations map initial conditions in a thermally
expanding partonic system
◦ Evidence: pt and centrality evolution of properties of same-side structure.

‘Anti’ Paradigm: pp is a small AA system
◦ Evidence: momentum conservation corrected spectra and HBT
Paradigm 1

Chemical equilibration at the partonic level
◦ Evidence: yields at chemical freeze-out (hadronic),
strangeness/charm enhancement
Statistical Hadronization 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)
Particle production:
Statistical models do well
Ratios that constrain model parameters
Does it work in elementary collisions ?
Equilibration in Elementary Collisions ?
Is a process which leads to multiparticle production
equilibrated ?
 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
p+p
Ensemble of events constitutes a statistical ensemble.
Canonical description, i.e. local quantum number conservation
(e.g.strangeness) over small volume. T and µ are simply Lagrange
multipliers (“Phase Space Dominance”)
A+A
We can talk about p,T and µ.
Grand-canonical description, e.g. percolation
of strangeness over large volumes, most likely
in deconfined phase if chemical freeze-out is
close to phase boundary.
PBM et al., nucl-th/0112051)
RHIC flavor dependence of yield scaling
up, down
strange
charm

PYTHIA (e+e-):
◦ D / Ds = 7.3

Statistical Hadronization Model
(AuAu):
◦ D / Ds = 2.8

Measured (e+e-):
◦

D / Ds = 4.8 +- 0.8
Measured (AuAu, STAR prel.):
◦ D / Ds = 2.6 +- 0.9
•participant scaling for light quark hadrons (soft production)
•strangeness and charm described by SHM
The latest numbers from fitting particle
yields (Cleymans et al. SQM 2009)
Paradigm 2

Kinetic equilibration (thermalization) at the partonic
level
◦ Evidence: spectra at thermal freeze-out, validity of
hydrodynamics, radial expansion
Kinetic freeze-out distributions
(particle spectra)
N.B. Constituent quark recombination models yield exponential spectra with
partons following a pQCD power-law distribution. (Biro et al. hep-ph/0309052)
T is not related to actual “temperature” but reflects pQCD parameter p0 and n.
Alternate: thermal constituent quarks (Chen et al., arXiv:0801.2265)
“Thermal” Spectra
Invariant spectrum of particles radiated by a thermal source:
d 3N
dN
E

 Ee ( E m )/T
3
dp
dy mT dmT df
where: mT= (m2+pT2)½ is the transverse mass
m = bmb + sms is the grand canonical chem. potential
T = temperature of source
Neglect quantum statistics (small effect) and integrating over
rapidity gives:
dN
mT T
 mT K1 (mT /T ) 
 mT e mT /T
mT dmT
R. Hagedorn, Supplemento al NuovoCimento Vol. III, No.2 (1965)
At mid-rapidityE = mTcoshy = mTand hence:
dN
 mT e mT /T
mT dmT
“Boltzmann”
“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
• Common flow and temperature:
at a minimum T, bT
T
2
for
pT m
for pT  m (blue shift)
explosive
source
light
T,b
heavy
mT
1/mT dN/dmT
purely thermal
source
1/mT dN/dmT
Tth  m bT

Tmeasured  
1 bT
Tth
1 bT

light
heavy
mT
Identified Particle Spectra for Au-Au
@ 200 GeV
The spectral shape gives

us:
◦ Kinetic freeze-out
temperatures
◦ Transverse flow

BRAHMS: 10% central
PHOBOS: 10%
PHENIX: 5%
STAR: 5%
The stronger the flow the
less appropriate are simple
exponential fits:
◦ Hydrodynamic
models (e.g. Heinz et
al., Shuryak et al.)
◦ give evolution
◦ Hydro-like
parameters
(Blastwave fits e.g
E.Schnedermann et
al., PRC48 (1993)
2462
◦ give freeze-out
surface
Explains: spectra, flow & HBT
Blastwave toy model (Lisa et al.)
One gets a common freeze-out T
and a common expansion velocity
(firmly rooted in the hadronic phase)
Hydrodynamics in High-Density Scenarios



Kolb, Sollfrank
& Heinz,
hep-ph/0006129
Ideal hydro: 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
Many alternative fit functions

Alternative question: is it Tsallis or
Boltzmann statistics that describes
the bulk of the system ?

Non-extensive ansatz describes
particle spectra from lowest to
highest pt (based on correlation
length = convolution of mini-jets).
No thermalization.
Two-component model (soft =
Boltzmann, hard = power-law)
describes the spectra. Bulk is
thermal, fragmentation is not.
Very interesting question that
requires more data comparison
(other than spectra)

Takahashi et al., SQM 2009

Paradigm 3

Paradigm 3: Strong collectivity in agreement with
near ideal hydrodynamics
◦ Evidence: spectra, v2, HBT
Elliptic flow described by fluid dynamics
In hydro: Anisotropic flow needs to build up early
(80% partonic, 20% hadronic)
Hydro is not ideal…..

v2/ as a function of centrality
does not reach the ideal limit

If the system reaches local thermal
equilibrium, according to ideal
hydro dynamic calculation, v4/v22
approaches 0.5 at high pT region
Hydro
STAR preliminary limit
STAR preliminary
N. Borghini and J.-Y. Ollitraut,
Phys. Lett. B 642 227 (2006)
32
…but viscous hydro is doing well
/s ~ 0
/s = 1/4p
/s = 2 x 1/4p
/s = 3 x 1/4p
Collectivity at early times
• Strange quark particle have significantly lower hadronic
interaction cross section (early development of flow)
• Heavier particles have lower flow (hydro pattern)
Paradigm 4

Hadronization is not dominated by fragmentation
even at high pT
◦ Evidence: quark scaling for v2 and energy loss
1977:two distinctly different hadronization processes
More likely in vacuum ?
neither corresponds to parton/hadron duality…
More likely in medium ?
Evidence at RHIC:
B/M ratio in AA can be attributed to recombination
Recombination
in medium
Fragmentation
in vacuum
cartoon
baryon
STAR
@ SQM 2005
meson
#3:The medium consists of constituent quarks ?
(my group’s main contribution)
baryons
mesons
Nuclear Modification Factor Rcp
0-5%
40-60%
0-5%
√sNN=200
GeV
√sNN=200
GeV
60-80%
Strange RCP signals range of
recombination model relevance
Recombination scaling can be applied
to RCP as well as v2
Baryon and meson suppression
sets in at the same quark pT .
Paradigm 5
Energy loss is purely partonic
 Partons always hadronize (fragment) outside the
medium
◦ Evidence: lack of color or mass dependence in RAA

Formation Time of Hadrons in RHIC / LHC QGP
(C. Markert, RB, I.Vitev, 0807.1509)
RHIC
LHC
41
Nuclear suppression factors of identified particles
light quarks (u,d,s):
heavy quarks (c,b):
STAR
@ QM 2009
non-photonic electrons
= B- or D-mesons
High pt quenching differences between
particles could be due to early formation and
subsequent color transparency
(Brodsky et al., Vitev et al., Markert & RB)
Paradigm 6

Particle correlations map initial conditions of a
thermally expanding partonic system
◦ Evidence: pt and centrality evolution of properties
of same-side structure.
Correlations: don’t they tell me when
something is not thermalized ?
We know of specific processes that cause
correlations even in thermal systems (jet
fragmentation, resonance decay, HBT,
annihilation, v2).
But the development of strong correlations
across large sections of low-momentum
‘bulk’ particles should hint at nonequilibrium.
Lots of structure in RHIC emissions
(STAR preliminary)
Number correlations
in coordinate space
as a f(centrality)
pp
AA
A modification of the fragmentation process in pQCD ?
Initial conditions plus radial expansion
Hama, Grassi, Kodama,
Takahashi et. al.
NexSPheRio
(color ropes due to nuclear density profile)
Dumitru, Gelis, McLerran,
Gavin, Moschelli et al.
CGC &Glasma
(flux tubes due to initial gluon profile)
Correlations are unrelated to the propagation of a jet through the medium.
They are due to a collective push on fluctuating initial conditions
Initial condition model applied to STAR CuCu data
(f-width and amplitude of same-side structure)
centrality dependence
STAR preliminary
pt dependence
STAR preliminary


STAR preliminary
STAR preliminary

‘Anti’ Paradigm

pp is a small AA system
◦ Evidence: momentum conservation corrected
spectra and HBT
AA spectra corrected for energy and momentum conservation
pp spectra and HBT treated like AA spectra
Combined pp and AA fit
Summary and Conclusions





We have discovered a deconfined phase of nuclear matter
(quark scaling, quenching)
Although the evidence for the basic RHIC paradigms of early
thermalization and strong collectivity is circumstantial, it is
based on a variety of many particle identified measurements
(yield, spectra, quenching, flow) and is thus the simplest
consistent model applicable.
The resulting properties from very strong coupling to large
correlation structures are unexpected and not readily described
by pQCD.
This might be an intermediate phase of high collectivity just
prior to hadron formation which will subside at even higher
initial temperatures (pQCD limit potentially achieved at LHC).
Its properties are very relevant to hadron formation in the
medium and to structure formation out of the medium.
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