Hot Matter and Cool
Results from
RHIC
Helen Caines - Yale University
Every sentence I utter must be understood
not as an affirmation, but as a question.
- Niels Bohr (1885-1962)
QCD at the Interface between
Particle and Nuclear Physics
April 2003
QCD For Beginners
Quarks confined within hadrons via strong force
v(r) = a/r + s*r
At large r -second term dominates
At small r -Coulomb-like part dominates
However a function of q( mtm transfer) and a -> 0 faster
than q (or 1/r) -> infinity (called asymptotic freedom)
This concept of asymptotic freedom among closely packed
coloured objects (q and g) has led to one of the most exciting
predictions of QCD !!
The formation of a new phase of matter where the colour
degrees of freedom are liberated. Quarks and gluons are no
longer confined within colour singlets.
Helen Caines - Yale
The Quark-Gluon
Plasma!
APS – April 2003
2
Lattice QCD at Finite Temperature
Recently extended to mB> 0, order still unclear (2nd, crossover ?)
q q
q
q
q
q qq
q q
q q
q
q
q q q q
q
q q qq
q
q qq q q
q q
q q q q
q
q q q q
q
qq
qq
q
qq
q
q
qq
q
qq
q
F. Karsch, hep-ph/0103314
Critical energy density:
Ideal gas (StefanBoltzmann limit)
 C  (6  2)TC4
Tc ~ 150-170 MeV
c ~ 1 GeV/fm3
Helen Caines - Yale
APS – April 2003
3
(QCD) Phase Diagram of Nuclear Matter
TWO different phase transitions at
work!
Deconfinement transition
– Particles roam freely over
a large volume
Chiral transition
– Masses change
Calculations show that these occur
at approximately the same point
Two sets of conditions:
High Temperature
High Baryon Density
Helen Caines - Yale
APS – April 2003
4
Time Scales of a Relativistic Heavy Ion Collisions
soft physics
regime
e.m. probes (l+l-, g)
hard (high-pT) probes
Chemical freezeout (Tch  Tc) : inelastic scattering stops
Kinetic freeze-out (Tfo  Tch): elastic scattering stops
Helen Caines - Yale
APS – April 2003
5
RHIC @ Brookhaven National Laboratory
Relativistic
Heavy
Ion
Collider
h
• 2 concentric rings of 1740
superconducting magnets
• 3.8 km circumference
• counter-rotating beams of ions from
p to Au
Helen Caines - Yale
• 2000 run:
• Au+Au @ sNN=130 GeV
• 2001 run:
• Au+Au @ sNN=200 GeV
• polarized p+p @ s=200 GeV (P ~15%)
APS – April 2003
6
Geometry of Heavy Ion Collisions
spectators
Particle production scales
with increasing centrality
peripheral
(grazing shot)
Preliminary sNN = 200 GeV
participants
central (head-on) collision
Uncorrected
Number participants (Npart): number of nucleons in overlap region
Number binary collisions (Nbin): number of equivalent inelastic
nucleon-nucleon collisions
Helen Caines - Yale
APS – April 2003
Nbin ≥ Npart
7
Au-Au Central Events at RHIC
STAR
Helen Caines - Yale
APS – April 2003
8
dNch/dh
Charged Particle Multiplicity
19.6 GeV
200 GeV
130 GeV
PHOBOS Preliminary
Central
Peripheral
h
Central at 130 GeV:
4200 charged particles !
Total multiplicity
per participant pair
scales with Npart
Not just a superposition of pp
Helen Caines - Yale
APS – April 2003
9
B/B Ratios
RHIC Preliminary Au-Au 130 GeV
B - all from pair production
B - pair production +
transported
B/B ratio =1 - Transparent
collision
B/B ratio ~ 0 - Full stopping,
little pair
production
All data:
• mid-rapidity
• ratios from raw yields
Helen Caines - Yale
~2/3 of proton from pair production
First time pair production dominates
Still some baryons from beam
APS – April 2003
10
Do We Reach the Critical Energy Density?
Bjorken formula for thermalized energy
density:
 Bj
PHENIX
EMCAL
1 1 dET

p R 2 t 0 dy
time to thermalize the
system (t0 ~ 1 fm/c)
~6.5 fm
130 GeV
pR2
~30 times normal nuclear density
~ 5 times above critical from lattice QCD
dz  t 0 dy
For Central Events:
Bjorken ~ 4.5 GeV/fm3
Helen Caines - Yale
APS – April 2003
11
Is There Collective Motion?
Look at “Elliptic” Flow
y 2 - x 2 
 2
2
y + x 
Almond shape overlap region in
coordinate space
SPS, RHIC
AGS
Interactions
Anisotropy in
momentum space
v2: 2nd harmonic Fourier coefficient in dN/d with respect to the reaction plane

d 3N
1 d 2N 

E 3 
1 +  2vn cosn - r 
d p 2p pt dpt dy  n 1

Helen Caines - Yale
APS – April 2003
v2  cos2
  atan
py
px
12
Hydro Calculation of Elliptic Flow
Equal Energy Density lines
V2
A pressure build up -> Explosion
zero for central events
self quenching
Hydrodynamic model
Elliptic flow observable sensitive to
early evolution of system
Collective
motion + large energy density
SPS
->Hydrodynamics
AGS matter with
Assumes continuum
local
equilibrium, “thermalization”
PRL 86 (2001) 402
P. Kolb, J. Sollfrank,
and U. Heinz
Large v2 is an indication of early
thermalization
Nch/Nmax
Heavy-Ion Collisions create a system which approaches hydrodynamic limit
Helen Caines - Yale
APS – April 2003
13
Identified Particle V2
v2 of identified hadrons
hydro model including the1st order
phase transition with Tf=120MeV (*)
pion
proton
v2
V2
v2
Au+Au at sqrt(sNN)=200Ge
min. bias r.p. |h|=3~4
(*) P.Huovinen,
P.F.Kolb, U.W.Heinz,
P.V.Ruuskanen and S.A.Voloshin,
Phys. Lett. B503, 58 (2001)
STAR PRL87 (2001)182301
Negatives
Positives
pi-&K-,pbar
pi+&K+,p
STAR Preliminary
Au-Au 200 GeV
PHENIX Preliminary
pT (GeV/c)
PHENIX Preliminary
1
pT (GeV/c)
Hydro-inspired model also predicts mass dependence well
Helen Caines - Yale
APS – April 2003
14
Want to look at how energy
distributed in system.
purely thermal
source
Look in transverse direction
so not confused by
longitudinal expansion
T
dN/dmt a e-(mt/T)
dN/dmt- Shape depends on
mass and size of flow
Helen Caines - Yale
APS – April 2003
heavy
mT
Slope = 1/T
explosive
source
T,b
If there is radial flow
light
1/mT dN/dmT
Look at pt or mt = (pt2 + m2 )
distribution
A thermal distribution gives a
linear distribution
1/mT dN/dmT
Kinetic Freeze-Out and Radial Flow
light
heavy
mT
Heavier particles show curvature
15
Radial Flow and Hydrodynamical Model
PHENIX
Preliminary
STAR Preliminary
Models differ slightly in details but same concept
PHENIX:
Tfo ~ 104  21 MeV, < bt > ~ 0.5  0.1c
STAR
– April 2003
Tfo -~Yale
107  8 MeV, < bAPS
Helen Caines
t > ~ 0.55  0.1c
16
Tfo and <br> vs √s
<br >

increases continously

saturates around AGS
energy
Tfo
Slightly model dependent
here: blastwave model
(Kaneta/Xu)
Helen Caines - Yale
Strong collective radial
expansion at RHIC
 high pressure
 high rescattering rate
 Thermalization likely
APS – April 2003
17
Models to Evaluate Tch and mB
Statistical Thermal Model
Particle density of each particle:
F. Becattini; P. Braun-Munzinger, J. Stachel, D. Magestro
J.Rafelski PLB(1991)333; J.Sollfrank et al. PRC59(1999)1637
Assume:
• Ideal hadron resonance gas
• thermally and chemically
equilibrated fireball at hadrochemical freeze-out
Recipe:
• grand canonical ensemble to
describe partition function

density of particles of species i
• fixed by constraints: Volume V, ,
strangeness chemical potential
mS, isospin
• input: measured particle ratios
• output: temperature T and
baryo-chemical potential mB
Helen Caines - Yale
Qi
: 1 for u and d, -1 for u and d
: 1 for s, -1 for s
gi
: spin-isospin freedom
mi : particle mass
Tch : Chemical freeze-out
temperature
mq : light-quark chemical potential
ms : strangeness chemical potential
gs : strangeness saturation factor
si
Compare
APS particle
– April 2003 ratios to experimental data18
Beautiful Agreement Between Model & Data
Does the success of the model tell us we are dealing indeed with locally
chemically equilibrated systems?
This + flow measurements… If you ask me Yes!
Helen Caines - Yale
APS – April 2003
19
Phase Diagram from AGS to RHIC
Tch [MeV]
mB [MeV]
AGS s = 2-4 GeV
125
540
SPS s = 17 GeV
165
250
RHIC s = 130-200 GeV
175
30
Again slight variations in the models
early universe
Chemical Temperature Tch [MeV]
250
RHIC
200
quark-gluon plasma
Lattice QCD
SPS
150
AGS
deconfinement
chiral restauration
Remember:
Measure hadrons not
partons so can’t measure T>
Tc with this method
100
SIS
hadron
gas
50
atomic nuclei
0
0
200
Helen Caines - Yale
400
600
800
1000
QCD on Lattice
Tc = 173±8 MeV, Nf=2
Tc = 154±8 MeV, Nf=3
1200
neutron stars
Baryonic Potential mB [MeV]
APS – April 2003
20
Summary on “Soft” (pT < 2 GeV/c) Physics

Particle production is large



close to net baryon-free but not quite
lattice phase transition ~1 GeV/fm3, cold matter ~ 0.16 GeV/fm3
System exhibits collective behavior (radial + elliptic flow)



~ 20 in p+p

~2.5 in p+p
Energy density is high  4-5 GeV/fm3 (model dependent)



Vanishing anti-baryon/baryon ratio (0.7-0.8)


Total Nch ~ 5000 (Au+Au s = 200 GeV)
Nch/Nparticipant-pair ~ 4 (central region)
strong internal pressure that builds up very early
explosive expansion
Particles ratios suggest chemical equilibrium

Tch170 MeV, mb<50 MeV  near lattice phase boundary
Overall picture: System appears to be in equilibrium but
explodes and hadronizes rapidly
Helen Caines - Yale
APS – April 2003
21
High-pT Hadrons at RHIC
Now even have own
pp measurements so
detector effects
“cancel”
All 4 experiments
have an
impressive array of
data out to
high pT
Helen Caines - Yale
APS – April 2003
22
Why study high pT physics at RHIC ?
Early production in parton-parton scatterings with large Q2.
Direct probes of partonic phases of the reaction
New penetrating probe at RHIC




attenuation or absorption of jets
“jet quenching”
suppression of high pT hadrons
modification of angular
correlation
changes of particle composition
jet schematic
productionview
in quark
matter
of jet
production
hadrons
hadrons
q
APS – April 2003
q
qq
leading
particle
Helen Caines - Yale
leading
leading
particle
particle
hadrons
23
Nuclear Modification Factor
“Hard” Physics -
Scales with Nbin: Number of binary collisions
number of equivalent inelastic nucleon-nucleon collisions
Nuclear
d 2 N AA / dpT dh
Modification RAA ( pT ) 
2 NN
T
d
s / dpT dh
AA
Factor:
N-N cross section
<Nbinary>/sinelp+p
If no “effects”:
R < 1 in regime of soft physics
R = 1 at high-pt where hard
scattering dominates
Helen Caines - Yale
APS – April 2003
24
Hadron Suppression: Au+Au at 200 GeV
charged hadrons:
p0:
PHENIX preliminary
Suppression of central yields persists up to pT=10 GeV/c
Helen Caines - Yale
APS – April 2003
25
Hadron Suppresion for Identified Particles
L and p show different
behaviour to Ks and p
p
Suppression of L sets in at
higher pT
p0
L
K0
STAR Prelimimary
Helen Caines - Yale
APS – April 2003
s
Seem to come together at
~6GeV/c - “standard”
fragmentation?
Is this a mass effect or
a baryon/meson effect ?
26
Azimuthal Anisotropy (v2)of Particle Emission
low pT
high pT
Bulk (Hydrodynamic) Matter
Jet Propagation
y
y
x
x
Pressure gradient
converts position space
anisotropy to momentum
space anisotropy
Helen Caines - Yale
Energy loss results in anisotropy
due to different “length” of
matter passed through by parton
depending on location of hard
scattering
APS – April 2003
27
Elliptic “Flow” at High-pT
Jet propagation through anisotropic matter (non-central collisions)
STAR @ 200 GeV
• Finite v2: high pT hadron correlated with reaction plane from
“soft” part of event (pT<2 GeV/c)
• Finite asymmetry at high pT
 Significant in-medium interactions even at 10 GeV/c
Helen Caines - Yale
APS – April 2003
28
Jets in Heavy Ion Collisions
e+e-  q q
(OPAL@LEP)
pp jet+jet
(STAR@RHIC)
Au+Au ???
(STAR@RHIC)
Jets in Au-Au hopeless Task?
No, but a bit tricky…
Helen Caines - Yale
APS – April 2003
29
Leading Particle Correlations
Leading Particle
•Trigger on high pT leading particle
•Jet core: D × Dh ~ 0.5 × 0.5
incoming partons
•
 study near-side correlations
(Df~0) of high pT hadron pairs
• Complication: elliptic flow  high pT
hadrons correlated with the reaction
plane (~v22)
associated h
Dh < 0.5
Dh > 0.5
• Solution: compare azimuthal
correlation functions for
Dh<0.5 short range) 
particles in jet cone +
background
Dh>0.5 (long range) 
background only
Near-side correlation shows jet-like signal in central Au+Au
Helen Caines - Yale
APS – April 2003
30
Back-to-Back Jets?
• away-side (back-to-back) jet can be “anywhere” Dh~2.5 -
can’t use large Dh subtraction “trick“
PHENIX Preliminary
• Ansatz: correlation function:
high pT-triggered Au+Au event =
high pT-triggered p+p event
+
elliptic flow
+
background
pp
sNN  200 GeV
2-4 GeV
C2 ( Au + Au)  C2 ( p + p) + A  (1 + 2v22 cos(2D ))
A: from fit to “non-jet”
region D~p/2
Helen Caines - Yale
•black = real
•green = mixed event
•purple = black-green
v2 from reaction plane analysis
APS – April 2003
31
Away Side Jets are Suppressed
Peripheral Au + Au
C2 ( Au + Au)  C2 ( p + p) + A  (1 + 2v22 cos(2D ))
• Near-side well-described
• Away-side suppression in central
collisions
STAR Preliminary
near side
Central Au + Au
STAR Preliminary
away side
Away side jets are suppressed!
Helen Caines - Yale
APS – April 2003
32
Charm at RHIC
Charm decay is expected to be
dominant component of single e- with
pT > 1.5 GeV/c:
Large charm production cross
section (300-600 mb) which scales roughly
with Nbin
Suppression of high pT p’s relative
to binary scaling
Observe an “excess” in single e-’s
over expectation from light meson
PHENIX
decays and g conversions
PRL 88
 Observation of charm
signal at RHIC
Assuming that all single e- signal is from charm decay and the binary
scaling, charm cross section at 130 GeV
s c0c-92%  420  33  250mb
s c0c-10%  380  60  200mb
Data are consistent with sAPS
systematics(within
large uncertainties)! 33
– April 2003
Helen Caines - Yale
Summary
Soft physics:
• System appears to be in equilibrium (hydrodynamic behaviour)
•Low baryon density
• Explosive expansion, rapid hadronization
Hard physics:
• Jet fragmentation observed
• Strong suppression of inclusive yields
?
• Azimuthal anisotropy at high pT
• Suppression of back-to-back hadron pairs
• large parton energy loss and surface emission?
•Open charm cross section scales with Nbin
Coming Attractions:
• d+Au: disentangle initial state effects in jet production
(shadowing, Cronin enhancement)  resolution of jet quenching picture
• J/ and open charm: direct signature of deconfinement?
• Polarized protons: DG (gluon contribution to proton spin)
Surprises
Helen•Caines
- Yale
…
APS – April 2003
34
Leading Charged Particle Correlations
• Jet core: D × Dh ~ 0.5 × 0.5
 study near-side correlations (D~0) of high pT hadron pairs
• Complication: elliptic flow  high pT hadrons correlated with the reaction plane (~v22)
• Solution: compare azimuthal correlation functions for
Dh<0.5 short range  particles in jet cone + background
Dh>0.5 long range  background only
Dh < 0.5
Dh > 0.5
• Azimuthal correlation function:
C2 (D ) 
1
N trigger
1
d (Dh ) N (D , Dh )
efficiency 
• Trigger particle pT trig> 4 GeV/c
• Associate tracks 2 < pT < pTtrig
Caveat: Away-side jet contribution
subtracted by construction,
needs different method…
Near-side correlation shows jet-like signal in central Au+Au
Helen Caines - Yale
APS – April 2003
36
Charm and single electron at RHIC
Simulation before RHIC
PHENIX data (PRL88)
At RHIC, it is expected that charm decay can be the dominant component of single electron in pt
> 1.5 GeV/c
 Large production cross section of charm ( 300-600 ub)


Production of the high pt pions is strongly suppressed relative to binary scaling
Production of charm quark roughly scale with binary collisions.
PHENIX observed “excess” in single electron yield over expectation from light meson decays and
photon conversions  Observation of charm signal at RHIC
APS – April 2003
37
Helen Caines - Yale
PHENIX single electron data
PHENIX observed excess of single
electron yield over the contribution
from light meson decays and photon
conversoins
Spectra of single electron signal is
compared with the calculated charm
contribution.
Charm contribution calculated as
EdNe/dp3 = TAAEds/dp3
 TAA: nuclear overlap integral
 Eds/dp3: electron spectrum from
charm decay calculated using
PYTHIA
The agreement is reasonably good.
PHENIX PRL88 192303
Assuming that all single electron signal is from charm decay and the binary scaling,
charm cross section at 130 GeV is obtained as
0-10%
scc
 380  60  200mb and
Helen Caines - Yale
APS – April 2003
0-92%
scc
 420  33  250mb
38
Comparison with other experiments
PHENIX single electron cross section
is compared with the ISR data
single electron data
Charm cross section derived from the
electron data is compared with
fixed target charm data
Single electron cross sections and
charm cross sections are
compared with
 Solid curves: PYTHIA
 Shaded band: NLO QCD
Assuming binary scaling, PHENIX data are consistent with s systematics o
(within large uncertainties)!
Helen Caines - Yale
APS – April 2003
39
Leading Photon Correlations
trigger g
Select events with a photon of
pt > 2.5 GeV/c. Mostly g’s from decay of a high pt p0
(leading particle)
Build distributions in delta  -space of the charged
hadrons relative to the trigger photons.
p0
incoming partons
associated h
pp
sNN  200 GeV
AuAu
PHENIX Preliminary
2-4 GeV
•black = pair distribution
•green = mixed event pair distribution
APS
Helen
Caines
- Yale
•purple
= bkg
subtracted distribution
In AuAu: add v2 component
– April 2003
40
Helen Caines - Yale
APS – April 2003
41
Parton recombination and high pT
The “buzz’’ word in the last few months: quark recombination/coallescence
Hwa & Yang
nucl-th/0211010
Fries, Mueller, Nonaka,Bass
nucl-th/0301087
Greco, Ko, Levai
nucl-th/0301093
Recombination
pT(baryons) > pT(mesons) > pT(quarks)
(coalescence from thermal quark distribution ...)
Pushes soft physics for baryons out to 4-5 GeV/c
Some exotic explanations (e.g. gluon junctions)
Helen Caines - Yale
APS – April 2003
42
The Two “Large” Detectors at RHIC
STAR
PHENIX
Solenoidal field
Large- Tracking
TPC’s, Si-Vertex Tracking
RICH, EM Cal, TOF
~420 Participants
Axial Field
High Resolution & Rates
2 Central Arms, 2 Forward Arms
TEC, RICH, EM Cal, Si, TOF, m-ID
~450 Participants
Coils
Silicon
Vertex
Tracker
Magnet
E-M
Calorimeter
Time
Projection
Chamber
Time
of
Flight
Electronics
Platforms
Forward Time Projection Chamber
• Measurements of Hadronic Observables
using a Large Acceptance
• Leptons, Photons, and Hadrons in Selected
Solid Angles
• Event-by-Event Analyses of Hadrons and
• Simultaneous Detection of Various Phase
APS
–
April
2003
43
Helen
Jets Caines - Yale
Transition Phenomena
The Two “Small” Experiments at RHIC
BRAHMS
PHOBOS
2 “Conventional” Spectrometers
“Table-top” 2 Arm Spectrometer
Magnets, Tracking Chambers, TOF, RICH
Magnet, Si m-Strips, Si Multiplicity Rings, TOF
~40 Participants
~80 Participants
Paddle Trigger Counter
TOF
Spectrometer
Ring Counters
• Inclusive Particle Production Over Large
Rapidity Range
Helen Caines - Yale
APS – April 2003
Octagon+Vertex
• Charged Hadrons in Select Solid Angle
• Multiplicity in 4p
• Particle Correlations
44
Phase transition in high (energy-) density
matter?
Hagedorn (1960’s):
 Spectrum of excited hadronic states: exponentially increasing level density
 Heat a hadron gas  excite more massive resonances
 Hadronic gas has limiting temperature T ~ 170 MeV
But cannot continue to arbitrary
energy density: hadrons have finite
size
 transition to phase of hadronic
constituents at T 170 MeV?
Helen Caines - Yale
APS – April 2003
45
Exploring the Phases of Nuclear Matter
Can we explore the phase diagram of nuclear matter ?
 We think so !
• by colliding nuclei in the lab
• by varying the nuclei size (A) and colliding energy (s)
• by studying spectra and correlation of the produced particles
 Requirements
• system must be at equilibrium (for a short time)
 system must be dense and large
Can we find and explore the Quark Gluon Plasma ?
 We hope so!
• by colliding large nuclei at the highest possible energy
Helen Caines - Yale
APS – April 2003
46
Experimental Determination of
Geometry
Paddles/BBC
ZDC
Au
Paddles/BBC
ZDC
Au
Central Multiplicity
Detectors
Paddle signal (a.u.)
STAR
5% Central
Helen Caines - Yale
APS – April 2003
47
RHIC – Runs & Machine Parameters
Performance
Au + Au
p+p
Max snn
200 GeV
500 GeV
L [cm-2 s -1 ]
2 x 1026
1.4 x 1031
Interaction rates
1.4 x 103 s -1 3 x 105 s -1
Au+Au integrated
luminosity~80 mb-1
2001
2000
Days into RHIC Run
Run – April 2003
Helen Caines - Yale Days into RHIC APS
• 2000 run:
• Au+Au @ sNN=130 GeV
• 2001 run:
• Au+Au @ sNN=200 GeV (80 mb-1)
• polarized p+p @ s=200 GeV
(P ~15%, ~1 pb-1)
48
Midrapidity: Centrality Dependence at
RHIC
PHOBOS Au+Au |h|<1
200 GeV
130 GeV
_
pp
19.6 GeV
preliminary
Kharzeev and Nardi PLB 507, 121 (2001)
hard and soft scaling:
dNch
dh

(1 - x ) Npp
 Npart
+ xNpp Nbin
2
x  10%  hard processes are important even for Nch
Helen Caines - Yale
APS – April 2003
49
Nch(sNN) – Universality of Total
Multiplicity?
Total charged particle multiplicity / participant pair
seff  s / 2
Same for all
systems at same
s(seff for pp)
pQCD e+e- Calculation
N ch  Aa sB exp( C / a s )
(A. Mueller,
1983)
Accidental, trivial?
Helen Caines - Yale
APS – April 2003
50
pT of Charged Hadrons
increase only ~2%
STAR preliminary
Saturation model:
J. Schaffner-Bielich, et al. nucl-th/0108048
D. Kharzeev, et al. hep-ph/0111315
dN ch dh
 pT   c1 + c2
2
p
R
APS – April 2003
2
Helen Caines - Yale
Many models predict similar
scaling (incl. hydrodynamic
models)
51
ET/ Nch  from SPS to RHIC
A. Bazilevsky (PHENIX)
PHENIX preliminary
Independent of centrality
PHENIX preliminary
Independent of energy
Surprising fact:
SPS  RHIC: increased flow, all particles higher pT
still ET/ Nch changes very little
Does different composition (chemistry) account for that?
Helen Caines - Yale
APS – April 2003
52
Fireball dynamics: Collective
expansion
Shape of the mT spectrum depends
on particle mass
Inverse-slope depends on mT-range
R
dn
m cosh    pT sinh  
  r dr mT K1  T
I

 0

mT dmT 0
T
T
where
  tanh -1 br
and br (r)  bs f (r)
Description of freeze-out inspired by hydrodynamics
bs
R
Flow profile used
br =bs (r/R)0.5
Helen Caines - Yale
APS – April 2003
The model is from E.Schenedermann et al. PRC48
(1993) 2462 and based on Blast wave model
53
Blastwave Fits at 130 & 200 GeV
Results depend slightly on pT
coverage
STAR:
Tfo ~ 100 MeV
bT ~ 0.55c (130) & 0.6c (200)
PHENIX:
Tfo ~ 110 MeV (200)
bT ~ 0.5c (200)
200 GeV
Helen Caines - Yale
APS – April 2003
54
p0 suppression: comparison to theory
--- Wang dE/dx = 0
--- dE/dx =0.25 GeV/fm
•
PHENIX preliminary
Wang: X.N. Wang, Phys.
Rev. C61, 064910 (2000).
--- Levai L/l = 0
--- L/l = 4
•
Gyulassy, Levai, Vitev:
P.Levai, Nuclear Physics
A698 (2002) 631.
--- Vitev dNg/dy = 900
• GLV, Nucl. Phys. B 594, p.
371 (2001) + work in
preparation.
Helen Caines - Yale
APS – April 2003
55
2 Particle Correlations at High-pT: Direct
Evidence for Jets?
• Jet core: D × Dh ~ 0.5 × 0.5
 look at near-side correlations (D~0) of high pT hadron pairs
• Complication: elliptic flow
• high pT hadrons correlated with the reaction plane orientation also
correlated with each other (~v22)
• but elliptic flow has long range correlation (Dh >> 0.5)
• Solution: compare azimuthal correlation functions for
Dh<0.5 short range and
Dh>0.5 long range
C2 (D ) 
Helen Caines - Yale
1
N trigger
1
d (Dh ) N (D , Dh )

efficiency
APS – April 2003
56
Reality Check: Charge-Sign
Dependence
• Compare same-sign (++, --) and opposite-sign (+-) pairs
• Known jet physics: charge ordering in fragmentation
DELPHI, PL B407, 174 (1997)
|Dh|<0.5 - |Dh|>0.5 (scaled)
Au+Au
0<|Dh|<1.4
p+p
STAR preliminary
Opposite/same correlation strength similar
in Au+Au, p+p, JETSET
 pT~3-4 GeV are jet fragments
Helen Caines - Yale
APS – April 2003
System
(+ -)/(+ + & - -)
p+p
2.7  0.6
0-10% Au+Au
2.4  0.6
Jetset
2.6  0.7
57
Particle Composition at pT  2 - 4 GeV/c
PHENIX: large excess of protons in central
collisions relative to p+p at ISR and standard jet
fragmentation (p/p~0.3)
STAR: different behaviour of
strange mesons vs. strange
baryons for pT < 5 GeV/c
Phys. Rev. Lett. 88, 242301 (2002)
p/p
ISR
• Exotic explanation: baryon junction
interactions enhanced in A+A (Vitev and
Gyulassy)
• Mundane explanation: transverse radial
flow
(common velocity)
APS – April 2003
Helen Caines - Yale
58
Consider two particles (1 and 2) with azimuthal angles . Then, the standard way to
extract v2 is via the equation:
where  is the angle of the reaction plane. Likewise, the same can be written for
particle 2, as well. Then, we can write the pair distribution as averaged over as
We can expand this as
The middle two terms integrate to zero, leaving us with
We can then write this as
Once again, the last term integrates to zero, leaving us with
Helen Caines - Yale
APS – April 2003
59
Reality Check: Charge-Sign
Dependence
• Compare same-sign (++, --) and opposite-sign (+-) pairs
• Known jet physics: charge ordering in fragmentation
DELPHI, PL B407, 174 (1997)
|Dh|<0.5 - |Dh|>0.5 (scaled)
Au+Au
0<|Dh|<1.4
p+p
STAR preliminary
Opposite/same correlation strength similar
in Au+Au, p+p, JETSET
 pT~3-4 GeV are jet fragments
Helen Caines - Yale
APS – April 2003
System
(+ -)/(+ + & - -)
p+p
2.7  0.6
0-10% Au+Au
2.4  0.6
Jetset
2.6  0.7
60
Single Particle Spectra and Radial Flow
Au+Au @ 130 GeV, central and peripheral (STAR, PHENIX):
p
Hydrodynamics
even works for
peripheral
collisions up to
b ~ 10 fm!
p
p
p
p
(Heinz & Kolb
hep-ph/0204061)
p
p
p
Problem with
pions at low pT
K+
 mp > 0
required
t = 0.6 fm/c, max (b=0) = 24.6 GeV/fm3, <>(t =1 fm/c) = 5.4 GeV/fm3
APS – April 2003
61
Helen Caines - Yale
Tmax(b=0) = 340 MeV,
Tch = 165 MeV, Tfo = 130 MeV
Hydrodynamics: Modeling High-Densities
Such high Energy Densities should make Hydrodynamics become
applicable
 Assume local thermal equilibrium (zero mean-free-path limit) and solve
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
Works qualitatively at lower
energy but always overpredicts
collective effects - infinite
scattering limit not valid there
Helen Caines - Yale
APS – April 2003
62
lattice QCD input