Results from RHIC Measurements of High
Density Matter
Thomas S. UllrichBrookhaven Nation Laboratory and Yale University
January 7, 2003
• Introduction
• Soft Physics
• Hard Physics
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(QCD) Phase Diagram of Nuclear Matter
• T >> QCD: weak coupling deconfined phase (Quark Gluon Plasma)• T << QCD: strong coupling confinement
phase transition at T~ QCD?
e.g. two massless flavors (Rajagopal and Wilczek, hep-ph/-0011333)
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Lattice QCD at Finite Temperature
• Coincident transitions: deconfinement and chiral symmetry restoration • Recently extended to B> 0, order still unclear (2nd, crossover ?)
F. Karsch, hep-ph/0103314
Critical energy density:4)26( CC T
TC ~ 175 MeVC ~ 1 GeV/fm3
Ideal gas (Stefan-
Boltzmann limit)
q
q
q
q
q
q
q
q
q
q
q
q
q
q q
q
q
q
q
q
q
q
q
q
q
qqq
qqq
qqq
q q
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The Phase Transition in the Laboratory
Chemical freezeout (Tch Tc) : inelastic scattering stops
Kinetic freeze-out (Tfo Tch): elastic scattering stops
e.m. probes (ll)
hard (high-pT) probes
soft physics regime
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RHIC @ Brookhaven National Laboratory
h
Long Island
Long Island
Relativistic
Heavy
Ion
Collider
• 2 concentric rings of 1740 superconducting magnets• 3.8 km circumference• counter-rotating beams of ions from p to Au
STAR
PHENIX
PHOBOSBRAHMS
• 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)
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Geometry of Heavy Ion Collisions
Number of participants (Npart): number of incoming nucleons (participants) in the overlap regionNumber of binary collisions (Nbin): number of equivalent inelastic nucleon-nucleon collisions
Reaction plane
x
z
y
Non-central collision
“peripheral” collision (b ~ bmax)“central” collision (b ~ 0)
Nbin Npart
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Peripheral EventFrom real-time Level 3 display.
STARSTAR
color code energy loss
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Mid-Central EventFrom real-time Level 3 display.
STARSTAR
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Central EventFrom real-time Level 3 display.
STARSTAR
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Charged Particle Multiplicityd
Nc
h/d
19.6 GeV 130 GeV 200 GeVPHOBOS Preliminary
Central
Peripheral
Central at 130 GeV: 4200 charged particles !
Total multiplicity per participant pair scales with Npart
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For the most central events:
PHENIX
EMCAL
R2
Energy Density at RHIC
Bjorken ~ 4.6 GeV/fm3
~30 times normal nuclear density~1.5 to 2 times higher than at SPS (s = 17 GeV)~ 5 times above critical from lattice QCD
Bjorken formula for thermalized energy density
time to thermalize the system (0 ~ 1 fm/c)~6.5 fm
What is the energy density achieved?
How does it compare to the expected phase transition value ?
dy
dE
RT
Bj0
2
11
dydz 0
130 GeV
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Hydrodynamics: Modeling 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
Works qualitatively at lower energybut always overpredicts collectiveeffects - infinite scattering limitnot valid there
RHIC is first time hydro works!
lattice QCD input
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RHIC Spectra - an Explosive Source
data: STAR, PHENIX, QM01model: P. Kolb, U. Heinz
• various experiments agree well
• different spectral shapes for particles of differing mass strong collective radial flow
mT1/m
T d
N/d
mT
light
heavyT
purely thermalsource
explosivesource
T,mT1/
mT d
N/d
mT
light
heavy• very good agreement with hydrodynamic
prediction
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Single Particle Spectra and Radial Flow
Au+Au @ 130 GeV, central and peripheral (STAR, PHENIX):
Hydrodynamicseven works forperipheralcollisions up tob ~ 10 fm!
(Heinz & Kolbhep-ph/0204061)
Problem withpions at low pT
> 0required
= 0.6 fm/c, emax (b=0) = 24.6 GeV/fm3, <e>(=1 fm/c) = 5.4 GeV/fm3
Tmax(b=0) = 340 MeV, Tch = 165 MeV, Tfo = 130 MeV
K+p
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Tfo and <r> vs. s
r increases continously
Tfo
saturates around AGS energy
Strong collective radial expansion at RHIC high pressure high rescattering rate Thermalization likely
Slightly model dependenthere: blastwave model (Kaneta/Xu)
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Azimuthal Anisotropy of Particle Emission: Elliptic Flow
Almond shape overlap region in coordinate space
y2 x2 y2 x2
Anisotropy in momentum space
AGS
SPS, RHIC
Interactions
2cos2 vx
y
p
patan
1
2
3
3
cos212
1
nrn
tt
nvdydpp
Nd
pd
NdE
v2: 2nd harmonic Fourier coefficient in dN/d with respect to the reaction plane
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Time Evolution: When Does Elliptic Flow Develop?
Equal energy density lines
P. Kolb, J. Sollfrank, and U. Heinz
Elliptic flow observable sensitive to early evolution of system
Mechanism is self-quenching
Large v2 is an indication of early
thermalization
v2
Zhang, Gyulassy, Ko, PL B455 (1999) 45
Au+Au at b=7 fm
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Charged Particle v2 vs. Centrality
midrapidity : |h| < 1.0
Hydrodynamic model
Nch/Nmax
SPS
AGSPRL 86 (2001) 402
V2
Hydrodynamical models can describe data at low pT (~2 GeV/c) compatible with early equilibration
Contrast to lower collision energies where hydro overpredicts elliptical flow
Peripheral Central
STAR PRL87 (2001)182301
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Models to Evaluate Tch and B: Statistical Thermal Models
Compare particle ratios to experimental data
Qi : 1 for u and d, -1 for u and d
si : 1 for s, -1 for s
gi : spin-isospin freedom
mi : particle mass
Tch : Chemical freeze-out
temperatureq : light-quark chemical potential
s : strangeness chemical potential
s : strangeness saturation factor
Particle density of each particle:Statistical Thermal ModelF. Becattini; P. Braun-Munzinger, J. Stachel, D. MagestroJ.Rafelski PLB(1991)333; J.Sollfrank et al. PRC59(1999)1637
Assume: • Ideal hadron resonance gas • thermally and chemically equilibrated fireball at hadro-chemical freeze-out
Recipe:• grand canonical ensemble to describe partition function density of particles of species i
• fixed by constraints: Volume V, ,
strangeness chemical potential S,
isospin• input: measured particle ratios• output: temperature T and baryo-chemical potential B
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Statistical Models work well at RHIC
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Statistical Models: from AGS to RHIC
Different implementation ofstatistical modelFact: all work well at AGS, SPS and RHIC
Tch [MeV] B [MeV]
AGS s = 2-4 GeV 125 540
SPS s = 17 GeV 165 250
RHIC s = 130-200 GeV 175 30
Does the success of the modeltell us we are dealing indeed with locally chemically equilibrated systems? this+flow If you ask me YES!neutron stars
Baryonic Potential B [MeV]
early universe
Chem
ical Tem
pera
ture
Tch
[M
eV
]
0
200
250
150
100
50
0 200 400 600 800 1000 1200
AGS
SIS
SPS
RHIC quark-gluon plasma
hadron gas
deconfinementchiral restauration
Lattice QCD
atomic nuclei
Slight variations in the models, but roughly:
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Summary on “Soft” (pT < 2 GeV/c) Physics
Particle production is large Total Nch ~ 5000 (Au+Au s = 200 GeV) ~ 20 in p+p
Nch/Nparticipant-pair ~ 4 (central region) ~2.5 in p+p
Vanishing baryon/antibaryon ratio (0.7-0.8) close to net baryon-free but not quite (net proton dN/dy~10)
Energy density is high 4-5 GeV/fm3 (model dependent) lattice phase transition ~1 GeV/fm3, cold matter ~ 0.16 GeV/fm3
System exhibits collective behavior (radial + elliptic flow) strong internal pressure that builds up very early
The system appears to freezes-out very fast explosive expansion (HBT, correlation studies)
Particles ratios suggest chemical equilibrium Tch170 MeV, b<50 MeV near lattice phase boundary
Large system at freeze-out 2 size of nuclei
Overall picture: system appears to be in equilibrium but explodes and hadronizes rapidly
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Products of parton fragmentation (jet “leading particle”).
Early production in parton-parton scatterings with large Q2.
Direct probes of partonic phases of the reaction
Sensitive to hot/dense medium: parton energy loss (“jet quenching”).
Info on medium effects accessible through comparison to scaled "vacuum" (pp) yields (“binary scaling”):
Production yields calculable via pQCD:
High-pT Particles @ RHIC – Jet Tomography
q
q
leading particle
leading particle
),()()( 2/
2,,
2,, ccchcdabbbBbaaAa
hardhXAB QzDQxfQxf
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Jets in Heavy Ion Collisionsee q q
(OPAL@LEP)pp jet+jet
(STAR@RHIC)
Au+Au ??? (STAR@RHIC)
Hopeless task? No, but a bit tricky…
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Partonic Energy Loss: Theory
• Elastic scattering (Bjorken 1982):
• Gluon radiation is factor ~10 larger:
• Thick plasma (Baier et al.):
glueSglue
Debye
sRBDMS
q
vLqC
E
2
2
ˆ
~ˆ4
22~ plasmas Tdz
dE
• Thin plasma (Gyulassy et al.):
L
ELogrdCE jet
glueSRGLV 23 2
,
Linear dependence on gluon density glue• measures gluon density • is continuous function of energy density not a direct signature of deconfinement
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Energy Loss in Cold Matter
Modification of fragmentation functions in e-Nucleus scattering:dE/dx ~ 0.5 GeV/fm for 10 GeV quark
Existing data is extensively studied but p+A measurements at RHICare desperately needed Run III (2003) d+Au
Wang and Wang, hep-ph/0202105
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High-pT Hadrons: Au+Au at RHIC
Preliminary sNN = 200 GeV
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Measuring Hadron Suppression
ddpdT
ddpNdpR
TNN
AA
TAA
TAA /
/)(
2
2
<Nbinary>/inelp+p
N-N cross section
1. Compare Au+Au to nucleon-nucleon cross sections2. Compare Au+Au central/peripheral
Nuclear Modification Factor:
If no “effects”: R < 1 in regime of soft physics R = 1 at high-pT where hard scattering dominates Suppression: R < 1 at high-pT
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Leading Hadrons in Fixed Target Experiments
AA
Multiple scattering in initial state(“Cronin effect”)
p+A collisions: Central Pb+Pb collisions at SPS
SPS: any parton energy loss effects buried by initial state multiple scattering, transverse radial flow,…
tppA ppA
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Hadron Suppression: Au+Au at 130 GeV
Phenix: PRL 88 022301 (2002) and charged hadrons, central collisions
STAR: nucl-ex/0206011Charged hadrons, centrality dependence
Clear evidence for high pT hadron suppression in central nuclear collisions
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Hadron Suppression: Au+Au at 200 GeV
Preliminary sNN
= 200 GeV
PHENIX preliminary
200 GeV preliminary data: suppression of factor 4-5 persists to pT=12 GeV/c
Phenix peripheral and central over measured p+p
STAR charged hadrons: central/peripheral
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Hadron Suppression: Central Au+Au (Data vs. Theory)
Parton energy loss : dE/dx ≈ 0.25 GeV/fm (expanding)
dE/dx|eff
≈ 7 GeV/fm (static source)
~ 15 times that in cold Au nuclei
Opacities: <n> = L/≈ 3 – 4
Gluon densities:
dNg/dy ~ 900
S.MioduszewskiPHENIX Preliminarynucl-ex/0210021
All models expect a moderate increase of RAA at higher pT
What does it tell us about the medium ?
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Elliptic “Flow” at High-pT: Theory
Snellings; Gyulassy, Vitev and Wang (nucl-th/00012092)
Jet propagation through anisotropic matter (non-central collisions)
• Finite v2: high pT hadron correlated with reaction plane from “soft” part of event (pT<2 GeV/c)• Finite asymmetry at high pT sensitive to energy density
jet
jet
STAR @ 130 GeV
STAR @ 200 GeV
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• Jet core×0.5 × 0.5 study near-side correlations (~0) of high pT hadron pairs
• Complication: elliptic flow high pT hadrons correlated with the reaction plane (~v22)
• Solution: compare azimuthal correlation functions forshort range particles in jet cone + backgroundlong range background only
• Azimuthal correlation function:
• Trigger particle pT trig> 4 GeV/c
• Associate tracks 2 < pT < pTtrig
Caveat: Away-side jet contribution subtracted by construction,needs different method…
< 0.5 > 0.5
2-Particle Correlations at High-pT: Direct
Evidence for Jets
),()(11
)(2 NdefficiencyN
Ctrigger
Near-side correlation shows jet-like signal in central Au+Au
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2 Particle Correlations at High-pT: Back-to-Back Jets?
• away-side (back-to-back) jet can be “anywhere”
• Ansatz: correlation function: high pT-triggered Au+Au event =
high pT-triggered p+p event + elliptic flow+ background
))2cos(21()()( 2222 vAppCAuAuC
A: from fit to “non-jet” region v2 from reaction plane analysis
0<||<1.4
p+punlike signlike sign
p+p measured in RHIC detectors
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Suppression of Back-to-Back Pairs
Central Au + Au
Peripheral Au + Au
• Near-side well-described• Away-side suppression in central collisions
Away side jets are suppressed!
near side
away side
STAR Preliminary
))2cos(21()()( 2222 vAppCAuAuC
STAR Preliminary
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High pT phenomena: suppression of inclusive rates, finite elliptic flow, suppression of back-to-back pairs
compatible with extreme absorption and surface emission
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Summary
?
Soft physics:• Low baryon density• System appears to be in equilibrium (hydrodynamic behaviour)• Explosive expansion, rapid hadronization
Hard physics:• Jet fragmentation observed, agreement with pQCD• Strong suppression of inclusive yields• Azimuthal anisotropy at high pT• Suppression of back-to-back hadron pairs• large parton energy loss and surface emission?
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? (Charm via single electrons: PHENIX, PRL 88, 192303 (2002))
• Polarized protons: G (gluon contribution to proton spin)• Surprises …