Transcript Document 7276713

Energy Loss and Flow in Heavy Ion Collisions at RHIC
Niels Bohr was almost right about the liquid drop model
Jim Thomas
Lawrence Berkeley National Laboratory
Berkeley, CA
University of Notre Dame
February 20th, 2008
Jim Thomas - LBL
1
The Phase Diagram for Nuclear Matter
The goal is to explore nuclear matter under extreme
conditions – T > mpc2 , r > 10 * r0 and rnet  0
Jim Thomas - LBL
•
One of the
goals of RHIC is
to understand
the QCD in the
context of the
many body
problem
•
Another goal is
to discover and
characterize the
Quark Gluon
Plasma
•
RHIC is a
place where
fundamental
theory and
experiment can
meet after many
years of being
apart
2
Who is RHIC and What Does He Do?
BRAHMS
PHOBOS
PHENIX
h
STAR
RHIC
•
Two independent
rings
•
3.83 km in
circumference
•
Accelerates
everything, from
p to Au
s
L
p-p
500 1032
Au-Au 200 1027
(GeV and cm-2 s-1)
•
Polarized protons
•
Two Large
and two small
detectors were
built
And for a little while longer, it is the highest energy
heavy ion collider in the world
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3
The Large Detectors – PHENIX and STAR
STAR
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PHENIX
4
STAR is a Suite of Detectors
Time
Projection
Chamber
Magnet
Coils
Silicon
Tracker
SVT & SSD
TPC
Endcap
& MWPC
FTPCs
Beam
Beam
Counters
Endcap
Calorimeter
Central
Trigger
Barrel
& TOF
Barrel EM
Calorimeter
PMD
Not Shown: pVPDs,
ZDCs, and FPDs
4.2 meters
A TPC lies at the heart of STAR
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Au on Au Event at CM Energy ~ 130 GeV*A
Data taken June 25, 2000.
The first 12 events were captured on tape!
Real-time track reconstruction
Pictures from Level 3 online
display. ( < 70 mSec )
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Au on Au Event at CM Energy ~ 130 GeV*A
A Central Event
Typically 1000 to 2000 tracks
per event into the TPC
Two-track separation 2.5 cm
Momentum Resolution < 2%
Space point resolution ~ 500 mm
Rapidity coverage –1.8 < h < 1.8
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Particle ID
using Topology & Combinatorics
Secondary vertex:
Ks  p + p
Lp +p
X  L+p WL +K
g  e++e-
Ks  p + + p L  p + p-
dn/dm
f  K++Kr  p++pf from K+ K- pairs
background
subtracted
m inv
dn/dm
K+ K- pairs
same event dist.
mixed event dist.
m inv
“kinks”
K m + 
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Identified Mesons and Baryons:
Au+Au @ 200 GeV
p and p yields .vs. pT
Phys. Rev. Lett. 97 (2006) 152301
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Nomenclature: Rapidity vs xf
• xf = pz / pmax
– A natural variable to describe physics at forward scattering angles
• Rapidity is different. It is a measure of velocity but it stretches
the region around v = c to avoid the relativistic scrunch
1  E  pz 

y  ln 
2  E  pz 
or
y  tanh 1 ( pz / E )
β
– Rapidity is relativistically invariant and cross-sections are invariant
1. 6
1. 4
dn
dy
1. 2
1
y  y  tanh 1 
0. 8
0. 6
0. 4
0. 2
0
-6
-4
-2
0
y
2
4
6
Rapidity and pT are the natural kinematic variable for HI collisions
( y is approximately the lab angle … where y = 0 at 90 degrees )
When the mass of the particle is unknown, then y  h
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Strange Baryons and Mesons:
Au+Au @ 200 GeV
L, X, W and f yields .vs. pT
Phys. Rev. Lett. 98 (2007) 060301
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Transverse Radial Expansion: Isotropic Flow
Au+Au at 200 GeV
pT ≈ 215 MeV
Kp
T ≈ 310 MeV
T ≈ 575 MeV
The transverse radial expansion
of the source (flow) adds kinetic
energy to the particle distribution.
So the classical expression for
ETot
suggests a linear relationship
Slopes decrease with mass.
<pT> and the effective
temperature increase with mass.
Jim Thomas - LBL
TObs  TKFO  mass   2
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Kinetic
freeze-out
time
Chemical and Kinetic Freeze-out
Chemical
freeze-out
elastic
interactions
inelastic
interactions
blue beam
• Chemical freeze-out (first)
– End of inelastic interactions
– Number of each particle species
is frozen
• Useful data
– Particle ratios
Jim Thomas - LBL
yellow beam
•
space
Kinetic freeze-out (later)
– End of elastic interactions
– Particle momenta are frozen
•
Useful data
– Transverse momentum distributions
– and Effective temperatures
13
Chemical Freeze-out – from a thermal model
Thermal model fits
Tch (RHIC)  177  7 MeV
μB (RHIC)  29  6 MeV
Tch (SPS)  160  170 MeV
μB (SPS)  270 MeV
Compare to QCD on the
(old) Lattice:
Tc = 154 ± 8 MeV (Nf=3)
Tc = 173 ± 8 MeV (Nf=2)
(ref. Karsch, various)
• The model assumes a thermally and chemically equilibrated fireball
at hadro-chemical freeze-out which is described by a temperature T
and (baryon) chemical potential m : dn ~ e-(E-m)/T d3p
• Works great, but there is not a word of QCD in the analysis. Done
entirely in a color neutral Hadronic basis!
input: measured particle ratios output: temperature T and baryo-chemical potential mB
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Putting RHIC on the Phase Diagram
•
Final-state analysis
suggests RHIC reaches
the phase boundary
•
Hadron spectra cannot
probe higher
temperatures
•
Hadron resonance ideal
gas (M. Kaneta and N. Xu,
Lattice results
nucl-ex/0104021 & QM02)
– TCH = 175 ± 10 MeV
– mB = 40 ± 10 MeV
Neutron STAR
•
<E>/N ~ 1 GeV
(J. Cleymans and K. Redlich,
PRL 81, p. 5284, 1998 )
We know where we are on the phase diagram but eventually
we want to know what other features are on the diagram
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RHIC Physics is Relativistic Nuclear Physics
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Unlike Particle Physics, the initial state is important
• Only a few of the nucleons
participate in the collision as
determined by the impact parameter
• There is multiple scattering in the
initial state before the hard
collisions take place
– Cronin effect
• The initial state is Lorentz contracted
• Cross-sections become coherent.
– The uncertainty principle allows wee
partons to interact with the front and
back of the nucleus
– The interaction rate for wee partons
saturates ( ρσ = 1 )
• The intial state is even time dilated
– A color glass condensate
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• proton • neutron • delta • pion
string
17
f Dependent Distributions – Flow
•
•
•
•
The overlap region in peripheral
collisions is not symmetric in
coordinate space
Almond shaped overlap region
– Larger pressure gradient in
the x-z plane drives flow in
that direction
– Easier for high pT particles to
emerge in the direction of x-z
plane
Spatial anisotropy  Momentum
anisotropy
Perform a Fourier decomposition of the
momentum-space particle distribution in the  plane
– For example, v2 is the 2nd harmonic Fourier
coefficient of the distribution of particles with
respect to the reaction plane
dN 3
E 3
d p

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1
d 2N
( 1  2v1 cos(f )  2v2 cos( 2f )   )
2p pT dpT dy
isotropic directed
elliptic
18
Interpreting Flow – order by order
n=1: Directed Flow has a period of 2p
(only one maximum)
– v1 measures whether the flow goes to
the left or right – whether the
momentum goes with or against a
billiard ball like bounce off the
collision zone
n=2: Elliptic flow has a period of p
(two maximums)
– v2 represents the elliptical shape of
the momentum distribution
dN 3
E 3
d p

1
d 2N
( 1  2v1 cos(f )  2v2 cos( 2f )  2v4 cos( 4f )   )
2p pT dpT dy
isotropic directed
Jim Thomas - LBL
elliptic
higher order terms
19
V1: Pions go opposite to Neutrons
62 GeV Data
At low energy, the pions go
in the opposite direction to
the ‘classical’ bounce of the
spectator baryons
200 GeV Data
At the top RHIC energy,
the pions don’t flow
(v1 at h=0 )
but at ALICE, v1 may
have a backward wiggle.
Reveals the EOS
Jim Thomas - LBL
• hi
20
Interpreting Flow – order by order
n=1: Directed Flow has a period of 2p
(only one maximum)
– v1 measures whether the flow goes to
the left or right – whether the
momentum goes with or against a
billiard ball like bounce off the
collision zone
n=2: Elliptic flow has a period of p
(two maximums)
– v2 represents the elliptical shape of
the momentum distribution
dN 3
E 3
d p

1
d 2N
( 1  2v1 cos(f )  2v2 cos( 2f )   )
2p pT dpT dy
isotropic directed
Jim Thomas - LBL
elliptic
21
V2 vs. pT and Particle Mass
• v2 is large
• The mass dependence
is reproduced by
hydrodynamic models
– Hydro assumes local
thermal equilibrium
– At early times
– Followed by
hydrodynamic
expansion
PRL 86, 402 (2001) & nucl-ex/0107003
D. Teaney et al., QM2001 Proc.
P. Huovinen et al., nucl-th/0104020
Anisotropic transverse flow is large at RHIC
Jim Thomas - LBL
– 6% in peripheral
collisions (for pions
average over all pT )
• Flow is developed
very rapidly
– Data suggests very
early times ~ fm/c
• Hydro calculations are
in good agreement
with the data
– Hydro assumes local
thermal equilibrium
– Followed by
hydrodynamic
expansion
– The mass
dependence is
reproduced by the
models
22
Elliptic
Flow: in
ultra-cold
A Simulation
ofan
Elliptic
Flow Fermi-Gas
Li-atoms released from an optical trap exhibit elliptic
flow analogous to what is observed in ultra-relativistic
heavy-ion collisions
– Elliptic flow is a general feature of strongly interacting
systems!
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v2 at high pT shows meson / baryon differences
Bulk PQCD Hydro
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Asym. pQCD Jet Quenching
qn Coalescence
24
f-meson Flow: Partonic Flow
f-mesons are special:
- they show strong collective flow and
- they are formed by coalescence of thermalized s-quarks
‘They are made via coalescence of seemingly thermalized quarks in central
Au+Au collisions, the observations imply hot and dense matter with
partonic collectivity has been formed at RHIC’
Phys. Rev. Lett. 99 (2007) 112301 and Phys. Lett. B612 (2005) 81
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The Recombination Model
( Fries et al. PRL 90 (2003) 202303 )
The flow pattern in v2(pT) for hadrons
is predicted to be simple if flow is
developed at the quark level
pT → pT /n
v2 → v2 / n ,
n = (2, 3) for (meson, baryon)
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Elliptic flow scales with the number of quarks
Implication: quarks, not hadrons, are the relevant
degrees of freedom at early times in the collision history
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Hints of Elliptic Flow with Charm
•
D  e +X
Single electron spectra from
PHENIX show hints of
elliptic flow
Is it charm or beauty?
•
The RHIC upgrades will
cut out large photonic
backgrounds:
g  e +e and reduce other large stat.
and systematic
uncertainties
Shingo Sakai, QM 2006
PRL 98, 172301 (2007)
Better if we can do direct topological
identification of Charm
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Constituent Quark Scaling?
• Hadrons are created by the recombination of quarks and
this appears be the dominant mechanism for hadron
formation at intermediate pT
• Baryons and Mesons are produced with equal abundance at
intermediate pT
• The collective flow pattern of the hadrons appears to reflect
the collective flow of the constituent quarks.
Partonic Collectivity
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Lets look at some collision systems in detail …
Initial state
Final state
Au + Au
d + Au
p + p
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Partonic energy loss via leading hadrons
Energy loss 
softening of fragmentation 
suppression of leading hadron yield
d 2 N AA / dpT dh
RAA ( pT ) 
TAAd 2 NN / dpT dh
Binary collision scaling
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p+p reference
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Au+Au and p+p: inclusive charged hadrons
PRL 89, 202301
p+p reference spectrum measured at RHIC
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PHENIX data on the suppression of p0s
lower energy
Pb+Pb
lower energy aa
Factor ~5 suppression for
central Au+Au collisions
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The Suppression occurs in Au-Au but not d-Au
No quenching
d+Au
Quenching!
Au+Au
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Heavy Flavor Energy Loss … RAA for Charm
• Heavy Flavor energy
loss is an unsolved
problem
Theory from Wicks et al. nucl-th/0512076v2
– Gluon density
~ 1000 expected from
light quark data
– Better agreement
with the addition of
inelastic E loss
– Good agreement only
if they ignore Beauty
…
• Beauty dominates
single electron spectra
above 5 GeV
Where is the contribution from Beauty?
Jim Thomas - LBL
• RHIC upgrades will
separate the Charm
and Beauty
contributions
35
Partonic energy loss
No quenching
d+Au
Quenching!
Au+Au
Energy loss 
suppression of leading hadron yield
The jet can’t get out!
d 2 N AA / dpT dh
RAA ( pT ) 
TAAd 2 NN / dpT dh
Binary collision scaling
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p+p reference
36
Jet Physics … it is easier to find one in e+eJet event in ee collision
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STAR Au+Au collision
37
Angular Distribution:
Peripheral Au+Au data vs. pp+flow
C2 (Au  Au)  C2 ( p  p)  A * (1 2v 22 cos(2f ))
Ansatz:
A high pT
triggered
Au+Au event is a
superposition of
a high pT
triggered
p+p event plus
anisotropic
transverse flow
v2 from reaction
plane analysis
“A” is fit in nonjet region
(0.75<|f|<2.24)
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Angular Distribution:
Central Au+Au data vs. pp+flow
C2 (Au  Au)  C2 ( p  p)  A * (1 2v 22 cos(2f ))
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Lessons learned – Dark Matter … its opaque
•
The backward going jet is missing in
central Au-Au collisions when compared to
p-p data + flow
•
The backward going jet is not suppressed
in d-Au collisions
•
These data suggest opaque nuclear matter
and surface emission of jets
Jim Thomas - LBL
Surface emission
Suppression of back-to-back correlations in central Au+Au collisions
40
Where does the Eloss go?
PHENIX
Away-side jet
p+p
Au+Au
Trigger jet
Lost energy of away-side jet is redistributed to rather large angles!
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Mach Cone: Theory vs Experiment
STAR preliminary
0-12% 200 GeV Au+Au
mach cone
near
deflected jets
near
• Hint of
a Mach
Cone?
Jim Thomas - LBL
Medium
away
Medium
away
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Nuclear Fluid Dynamics ... with friction
• The energy momentum tensor for a viscous fluid
T m  (  p) u m u  pg m   m
• Conservation laws:  mT m  0
and
m j m  0
where
jim  r i u m
• The elements of the shear tensor,  m, describe the viscosity of the
fluid and can be thought of as velocity dependent ‘friction’
• Simplest case: scaling hydrodynamics
–
–
–
–
–
assume local thermal equilibrium
assume longitudinal boost-invariance
cylindrically symmetric transverse expansion
no pressure between rapidity slices
conserved charge in each slice
• Initially expansion is along the Z axis, so viscosity resists it
– Conservation of Tm means that energy and momentum appear in the
transverse plane … viscosity drives radial flow
• Viscosity is velocity dependent friction so it dampens v2
– Viscosity (h/z ) must be near zero for elliptic flow to be observed
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AdS/CFT correspondence (from H. Liu)
Maldacena (1997) Gubser, Klebanov, Polyakov, Witten
N = 4 Super-Yang-Mills
theory with SU(N)
A string theory in
5-dimensional
anti-de Sitter spacetime
anti-de Sitter (AdS) spacetime: homogeneous spacetime with a
negative cosmological constant.
N = 4 Super-Yang-Mills (SYM):
maximally supersymmetric gauge theory
scale invariant
A special relative of QCD
The value
h
s

1
turns out to be universal for all strongly coupled
4p
QGPs with a gravity description. It is a universal lower bound.
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PHENIX PRL 98, 172301 (2007)
• RAA of heavy-flavor
electrons in 0%–10%
central collisions
compared with p0 data
and model
calculations
p0
• V2 of heavy-flavor
electrons in minimum
bias collisions
compared with p0 data
and the same models.
• Conclusion is that
heavy flavor flow
corresponds to h/s at
the conjectured QM
lower bound
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Viscosity and the Perfect Fluid
H2O
N2
He
hadronic
partonic
The universal tendency of flow to be
dissipated due to the fluid’s internal
friction results from a quantity
known as the shear viscosity. All
fluids have non-zero viscosity. The
larger the viscosity, the more rapidly
small disturbances are damped
away.
Quantum limit: h/sAdS/CFT ~ 1/4p
pQCD limit: ~ 1
At RHIC: ideal (h/s = 0)
hydrodynamic model calculations fit
to data 
Caption: The viscosity to entropy
ratio versus a reduced temperature.
Perfect Fluid at RHIC?!
Lacey et al. PRL 98:092301(07)
hep-lat/0406009; hep-ph/0604138
Csernai et al, PRL97, 152303(06)
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Old Chinese Proverb
Beware of theorists waiting for data
– Confusion
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PRL 99, 172301 (2007) … new insights
• Romatschke2 perform
relativistic viscous
hydrodynamics calculations
• Data on the integrated elliptic
flow coefficient v2 are
consistent with a ratio of
viscosity over entropy
density up to h/s 0.16
• But data on minimum bias v2
seem to favor a much smaller
viscosity over entropy ratio,
below the bound from the
anti–de Sitter conformal field
theory conjecture
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Did a meteor impact on the Yucatan kill the Dinosaurs?
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Conclusions About Nuclear Matter at RHIC
• Its hot
– Chemical freeze out at 175 MeV
– Thermal freeze out at 100 MeV
• Its fast
– Transverse expansion with an average velocity greater than 0.55 c
– Large amounts of anisotropic flow (v2) suggest hydrodynamic expansion
and high pressure at early times in the collision history
• Its opaque
– Saturation of v2 at high pT
– Suppression of high pT particle yields relative to p-p
– Suppression of the away side jet
• There are hints that it is thermally equilibrated
– Excellent fits to particle ratio data with equilibrium thermal models
– Excellent fits to flow data with hydrodynamic models that assume
equilibrated systems
– Hints of heavy flavor flow
• And it has nearly zero viscosity and perhaps a Mach cone
– Perhaps it is at or below the quantum bound from the AdS/CFT conjecture
Jim Thomas - LBL
Niels Bohr was almost right … he just didn’t know about q and g
50
STAR
Tth [GeV]
STAR Preliminary
PHENIX
<r> [c]
Kinetic Freezeout from Transverse Flow
<ßr> (RHIC) = 0.55 ± 0.1 c
TKFO (RHIC) = 100 ± 10 MeV
Thermal freeze-out determinations are done with
the blast-wave model to find <pT>
Jim Thomas - LBL
Explosive Transverse Expansion at RHIC  High Pressure
51
3<pt,trigger<4 GeV
pt,assoc.>2 GeV

Au+Au 0-10%
preliminary

h
f
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The Development of a Weibal Instability
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Charm Cross Sections at RHIC
1) Large systematic uncertainties in the measurements
2) Theory under predict by a factor ~ 2 and
STAR ~ 2 x PHENIX
3) Directly reconstructed charm hadrons Upgrades
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A pQCD Study
- At RHIC energy, baryons are
mostly from gluons and pions
are mostly from quark jets.
- Observation at high pT :
RCP( p) ~ RCP (p)
RCP (K) ~ RCP (L)
- pQCD color factor effects:
E(g)/E(q) ~ 9/4
A clear challenge to pQCD
predictions!
Future tests with charm
hadrons(quarks) and fmeson(gluon).
STAR: nucl-ex/0703040. Phys. Lett. B, in
print
Jim Thomas - LBL
Nu
57
Inclusive cross-section (jets, p0,±,p±)
p p po

Mid-y jets, p0,± and p± productions are well reproduced by NLO pQCD
calculations over many orders of magnitude 
1) powerful tool for analyzing spin physics.
2) reliable reference for study high-energy nuclear collisions.
STAR: PRL 97, 252001(06); PL B637, 161(06)
Jim Thomas - LBL
Nu
58
Hadron Spectra from RHIC p+p and Au+Au
collisions at 200 GeV
ud
ss
uud
sss
more central collisions
0-5%
mT  pT2  m 2
Multi-strange hadron spectra are exponential in their
shapes.
STAR white papers - Nucl. Phys. A757, 102(2005).

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Current State of Affairs
• A theory is something nobody believes, except the person
who made it.
• An experiment is something everybody believes, except the
person who made it.
– attributed to Albert Einstein
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Recombination Tested
The complicated observed flow pattern in v2(pT)
d2n/dpTdf ~ 1 + 2 v2(pT) cos (2 f)
is predicted to be simple at the quark level under
pT → pT / n , v2 → v2 / n , n = 2,3 for meson,baryon
if the flow pattern is established at the quark level
Compilation
courtesy of H.
Huang
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Quark Coalescence
 At low pt: mass ordering 
hydrodynamics
 At larger pt: Baryons – mesons
S.A. Voloshin, Nucl. Phys. A715, 379 (2003).
 quark coalescence
Z. Lin et al., Phys. Rev. Lett., 89, 202302 (2002).
 We need v2 of f and r
Jim Thomas - LBL
0
R. Fries et al., nucl-th/0306027.
D. Molnar and S.A. Voloshin, PRL 91, 092301(2003).
62
Multi-Strange Baryons v2
 Multi-strange baryons flow !
Partonic Collectivity !
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Summary of Performance Achieved to date
•
Features of the STAR TPC
–
–
–
–
–
–
–
–
–
•
•
4 meters in diameter, 210 cm drift
No field wires in the anode planes
Pad readout, Low gain on anodes
•
Low drift field
Very compact FEE electronics
Analog Delay with SCA then onboard ADC
Data delivered via optic fiber
Uniform E and B fields
‘ExB’ and most Electrostatic distortions
•
correctable to 50 – 100 mm level
Position resolution
– 500 mm in the real world with calibration
errors
– Space point resolution ~ 100 mm for select
laser events, 250 - 350 mm for select
tracks
– Function of dip angle and crossing angle
Jim Thomas - LBL
Good particle separation using dE/dx
– 6.5% dE/dx resolution @ 100 cm
– p-proton separation : > 1 GeV/c
2-Track resolution
– 2.5 cm for HBT pairs
– 1.5 cm for laser tracks
– limited by 3 pad response function
and desire for fast algorithms
Momentum resolution
– 2% minimum at 0.25 Tesla (half field)
– for pT > 1.5 GeV in 0.25 T field
• dk/k = 0.016 pT + 0.012 (central)
• dk/k = 0.011 pT + 0.013 (peripheral)
• 2.9%  3.3% peripheral/central
@ 1.5 GeV
STAR performance is excellent
and meets essentially all design
specifications!
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TPC Gas Volume & Electrostatic Field Cage
420 CM
• Gas: P10 ( Ar-CH4 90%-10% ) @ 1 atm
• Voltage : - 28 kV at the central membrane
Jim Thomas - LBL
135 V/cm over 210 cm drift path
Self supporting Inner Field Cage:
Al on Kapton using Nomex
honeycomb; 0.5% rad length
65
Identified Particle Spectra at 200 GeV
Bose-Einstein fits
A /( e
m / Teff
mt exponential fits
 1)
p+
Ae
 m / Tm
K-
p+, p-, K+, K- spectra versus centrality
PRL 92 (2004) 171801 and Phys. Lett. B595 (2004) 143
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Anti-Proton Spectra at 200 & 130 GeV / N
Au + Au  p + X
p
200 GeV data
gaussian fits
Ae p / 2
2
p
2
130 GeV data
p andp spectra versus centrality
PRL 92 (2004) 171801 and PRL 87 (2001) 262302
Jim Thomas - LBL
67
Anti-Baryon/Baryon Ratios versus sNN
•
In the early universe
–
p / p ratio = 0.999999
•
At RHIC, pair-production
increases with s
•
Mid-rapidity region is not yet
baryon-free!
Ypbar
Ypair

 0.8
Yp
Ypair  YTrans
•
Pair production is larger
than baryon transport
Ypair
 4
YTr
In HI collisions at RHIC, more baryons are
pair produced than are brought in by the
initial state
Jim Thomas - LBL
•
80% of protons from pair
production
•
20% from initial baryon
number transported over 5
units of rapidity
68
Anti-Particle to Particle Ratios
K+/K- ratios

p/p ratios
STAR results on thep/p ratio
• p/p = 0.11 ± 0.01 @ 20 GeV
• p/p = 0.71 ± 0.05 @ 130 GeV
• p/p = 0.80 ± 0.05 @ 200 GeV
Jim Thomas - LBL
Excellent agreement between
experiments at y = 0, s = 130
69
Jim Thomas - LBL
70
Equation of State Parameters at RHIC
In central Au+Au collisions:
- partonic freeze-out:
*Tp = 165 ± 10 MeV
p ≥ 0.2 (c)
weak centrality dependence
- hadronic freeze-out:
*Tfo = 100 ± 5 (MeV)
fo = 0.6 ± 0.05 (c)
strong centrality dependence
Systematic study are needed to understand the
centrality dependence of the EOS parameters
* Thermalization assumed
Jim Thomas - LBL
71
Bjorken Estimate of Initial Energy Density
Boost invariant hydrodynamics:
Bjorken Estimate of Initial Energy
Density
1 dET
1
3 dN ch
 2

pT
2
pR  dy pR 
2 dh
Cold nuclear matter:
r0 ~ 0.16 GeV/fm3

 4.5 GeV / fm3
 C  0.7 GeV / fm3
~ 6.5 fm

~ 0.2 - 1 fm/c
time to thermalize the
system
30xr0
pR2
nucl-ex/0311017
PRL 87 (01) 52301
dz   0dy
Jim Thomas - LBL
72
Slope Parameters
f  A exp mT /Tslope

RHIC results:
Collective motion for
multi-strange and charm
hadrons!
p ≥ 0.2c
SPS results:
No collective motion for
multi-strange and charm
hadrons!
At RHIC, f, X, W, and J/ show collective motion in 200 GeV Au + Au central collisions!
PHENIX (p, K, p, J/): PRC69, 034909(04), QM05;
Jim Thomas - LBL
STAR (f, X, W): QM05.
73
QCD is a Rich Theory with Many Features
1 ~ m a
LHadron
 i D
 diagram
Fa F m  Mˆ 
'level'
4
We have a theory of the strong
interaction
Hadron “level” Diagram
1500
Low(er) energy nuclear physics
uses OPEP or descriptions in
terms of a pion gas. These
worked because QCD is a
theory with a mass gap.
This gap is a
manifestation of
the approximate
SU(2)R x SU(2)L
chiral symmetry of QCD
with pions as the
Nambu-Goldstone bosons
1000
Mass
(MeV)
{
r,w
fo
h
500
K
p
W. Zajc
0
0
Jim Thomas - LBL
10
20
Degeneracy
30
40
74
Something Funny Happens at T > mpc2
An exponentially increasing density of hadronic states suggests
– A “limiting temperature” TH
– A phase transition(?) in hadronic matter
This was noticed before quarks were identified as the constituents of matter
– ( Hagedorn, Nuovo Cimento Supp., 3 (147) 1965 )
Density of States vs Energy
Density of States .vs. Energy
250
Fit this form
with TH = 163 MeV
r ( m) 
200
dn
~ m a e m / TH
dm
Thermal equilibrium suggests
Number of 150
available
states 100

50
~
m /T
r
(
m
)
e
dm


ma e
m(
1 1
 )
TH T
dm
0
0
Jim Thomas - LBL
500
1000
Mass (MeV)
1500
2000
Which requires T < TH
75
Three Particle Correlations  Conical Emission
P/ = cs2  Mach cone. Data: Unambiguous evidence for conical emission in
central Au+Au collisions. Trigger at higher pT, more statistics are needed.
d+Au
Δf1
0-12% Au+Au
Δf1
0-12% Au+Au
jet v2=0
Δf1
pTtrig=3-4 GeV/c
pTassoc=1-2 GeV/c
J. Ulery, HP2006, C. Pruneau, QM2006
f=(f1f2)/2
Jim Thomas - LBL
f=(f1f2)/2
76
j correlations vs the reaction plane
p/4
Out-of-plane
3p/4
pTtrigger=4-6 GeV/c, 2<pTassociated<pTtrigger, |h|<1
y
x
in-plane
-3p/4
-p/4
Back-to-back suppression out-of-plane stronger than in-plane
Effect of path length on suppression is experimentally accessible
Jim Thomas - LBL
77
Lattice QCD predictions
Energy Density
Stephan
Boltzman
limits for a
free Quark
Gluon gas
TC ~ 170  15 MeV
C ~ 0.7 GeV/fm3
0 ~ 0.16 GeV/fm3
Karsch QM2004
Temperature
TC ~ 170 MeV, was a very stable prediction over time &
technologies … until recently when it went up to 190 MeV
(F. Karsch, hep-lat/0106019 and M. Cheng et al., hep-lat/0710.0354)
Jim Thomas - LBL
78
A Macroscopic many body system: It Flows
Spatial anisotropy  Momentum
anisotropy
– For example, v2 is the 2nd harmonic Fourier
coefficient of the distribution of particles with
respect to the reaction plane
dN 3
E 3
d p

Jim Thomas - LBL
1
d 2N
( 1  2v1 cos(f )  2v2 cos( 2f )   )
2p pT dpT dy
isotropic directed
elliptic
79
Suppresion of inclusive hadron yield
RAA
Au+Au relative to p+p
RCP Au+Au central/peripheral
nucl-ex/0305015
• central Au+Au collisions: factor ~4-5 suppression
• pT >5 GeV/c: suppression ~ independent of pT
Jim Thomas - LBL
80
Identifying jets on a statistical basis in Au-Au
•
You can see the jets in p-p data at
RHIC
•
•
Identify jets on a statistical basis in Au-Au
Given a trigger particle with pT > pT (trigger),
associate particles with pT > pT (associated)
C2 (f , h ) 
Jim Thomas - LBL
1
NTRIGGER
1
N (f , h )
Efficiency
STAR Data
Au+Au @ 200 GeV/c
0-5% most central
4 < pT(trig) < 6 GeV/c
2 < pT(assoc.) < pT(trig)
81
v2 vs. Centrality
• v2 is large
Hydro predictions
– 6% in peripheral
collisions
– Smaller for central
collisions
• Hydro calculations
are in reasonable
agreement with the
data
– In contrast to lower
collision energies
where hydro overpredicts anisotropic
flow
PRL 86, (2001) 402
more central 
Anisotropic transverse flow is large at RHIC
Jim Thomas - LBL
• Anisotropic flow
is developed by
rescattering
– Data suggests early
time history
– Quenched at later
times
82