helen caines - yale university april 2003 hot matter and cool results from rhic qcd at the interface...
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Helen Caines - Yale University
April 2003
Hot Matter and Cool Results from
RHIC
QCD at the Interface between Particle and Nuclear Physics
Every sentence I utter must be understood not as an affirmation, but as a question.
- Niels Bohr (1885-1962)
Helen Caines - Yale
APS – April 2003 2
Quarks confined within hadrons via strong force
v(r) = /r + *r
At large r -second term dominates
At small r -Coulomb-like part dominates
However function of q( mtm transfer) and -> 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.The Quark-Gluon Plasma!
QCD For Beginners
Helen Caines - Yale
APS – April 2003 3
Lattice QCD at Finite Temperature
Recently extended to B> 0, order still unclear (2nd, crossover ?)
F. Karsch, hep-ph/0103314
Critical energy density:4)26( CC T
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
Tc ~ 150-170 MeV
c ~ 1 GeV/fm3
Helen Caines - Yale
APS – April 2003 4
TWO different phase transitions at work!
– Particles roam freely over a large volume
– Masses change
Calculations show that these occur at approximately the same point
Two sets of conditions:
High Temperature
High Baryon Density
Deconfinement transition
Chiral transition
(QCD) Phase Diagram of Nuclear Matter
Helen Caines - Yale
APS – April 2003 5
Time Scales of a Relativistic Heavy Ion Collisions
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
Helen Caines - Yale
APS – April 2003 6
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
• 2000 run: • Au+Au @ sNN=130 GeV
• 2001 run: • Au+Au @ sNN=200 GeV • polarized p+p @ s=200 GeV (P ~15%)
Helen Caines - Yale
APS – April 2003 7
Number binary collisions (Nbin): number of equivalent inelastic
nucleon-nucleon collisions
Geometry of Heavy Ion Collisions
Preliminary sNN = 200 GeV
Uncorrected
peripheral (grazing shot)
central (head-on) collision
spectatorsParticle production
scales with increasing centrality
Nbin ≥ Npart
participants
Number participants (Npart): number of nucleons in overlap region
Helen Caines - Yale
APS – April 2003 8
Au-Au Central Events at RHIC
STAR
Helen Caines - Yale
APS – April 2003 9
Central at 130 GeV: 4200 charged particles !
Charged Particle Multiplicityd
Nc
h/d
19.6 GeV 130 GeV 200 GeV
PHOBOS Preliminary
Central
Peripheral
Total multiplicity per participant pair scales with Npart
Not just a superposition of pp
Helen Caines - Yale
APS – April 2003 10
B/B Ratios
All data:• mid-rapidity• ratios from raw yields
B - all from pair production B - pair production +
transported
B/B ratio =1 - Transparent collisionB/B ratio ~ 0 - Full stopping, little pair
production~2/3 of proton from pair productionFirst time pair production dominatesStill some baryons from beam
RHIC Preliminary Au-Au 130 GeV
Helen Caines - Yale
APS – April 2003 11
PHENIX
EMCAL
R2
Do We Reach the Critical Energy Density?
Bjorken ~ 4.5 GeV/fm3
~30 times normal nuclear density~ 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
dy
dE
RT
Bj0
2
11
dydz 0
130 GeV
For Central Events:
Helen Caines - Yale
APS – April 2003 12
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
Is There Collective Motion?
Look at “Elliptic” Flow
Helen Caines - Yale
APS – April 2003 13
Hydro Calculation of Elliptic Flow
P. Kolb, J. Sollfrank, and U. Heinz Large v2 is an indication of early
thermalization
Heavy-Ion Collisions create a system which approaches hydrodynamic limit
A pressure build up -> Explosion zero for central events
self quenching
Elliptic flow observable sensitive to early evolution of system
Collective motion + large energy density ->Hydrodynamics Assumes continuum matter with local equilibrium, “thermalization”
Hydrodynamic model
Nch/Nmax
SPS
AGS
PRL 86 (2001) 402
V2
Equal Energy Density lines
Helen Caines - Yale
APS – April 2003 14
Identified Particle V2
STAR PRL87 (2001)182301
1
STAR PreliminaryAu-Au 200 GeV
V2
Hydro-inspired model also predicts mass dependence well
Helen Caines - Yale
APS – April 2003 15
Kinetic Freeze-Out and Radial Flow
mT1/m
T d
N/d
mT
light
heavyT
purely thermalsource
explosivesource
T,mT1/
mT d
N/d
mT
light
heavy
If there is radial flow
Look at pt or mt = (pt2 +
m2 ) distribution
Slope = 1/T
dN/dmt- Shape depends on mass and size of flow
Want to look at how energy distributed in system.
Look in transverse direction so not confused by longitudinal expansion
A thermal distribution gives a linear distribution
dN/dmt e-(mt/T)
Heavier particles show curvature
Helen Caines - Yale
APS – April 2003 16
Radial Flow and Hydrodynamical Model
PHENIX Prelimina
ry
STAR Preliminary
PHENIX:Tfo ~ 104 21 MeV, < t > ~ 0.5
0.1cSTAR
Tfo ~ 107 8 MeV, < t > ~ 0.55 0.1c
Models differ slightly in details but same concept
Helen Caines - Yale
APS – April 2003 17
Tfo and <r> vs √s
r increases continously
Tfo
saturates around AGS energy
Slightly model dependenthere: blastwave model (Kaneta/Xu)
Strong collective radial expansion at RHIC high pressure high rescattering rate Thermalization likely
Helen Caines - Yale
APS – April 2003 18
Models to Evaluate Tch and B
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
Helen Caines - Yale
APS – April 2003 19
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 20
Phase Diagram from AGS to 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
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
Again slight variations in the models
QCD on LatticeTc = 173±8 MeV, Nf=2Tc = 154±8 MeV, Nf=3
Remember: Measure hadrons not partons so can’t measure T> Tc with this method
Helen Caines - Yale
APS – April 2003 21
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 anti-baryon/baryon ratio (0.7-0.8) close to net baryon-free but not quite
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 explosive expansion
Particles ratios suggest chemical equilibrium Tch170 MeV, b<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 22
High-pT Hadrons at RHIC
All 4 experiments have an impressive array of data out to high pT
Now even have own pp measurements so detector effects “cancel”
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APS – April 2003 23
q
q
hadronsleadingparticle
leading particle
schematic view of jet production
hadrons
q
q
hadronsleadingparticle
jet production in quark matter
Why study high pT physics at RHIC ?
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
Early production in parton-parton scatterings with large Q2.Direct probes of partonic phases of the reaction
Helen Caines - Yale
APS – April 2003 24
Nuclear Modification Factor
“Hard” Physics - Scales with Nbin: Number of binary collisions number of equivalent inelastic nucleon-nucleon collisions
ddpdT
ddpNdpR
TNN
AA
TAA
TAA /
/)(
2
2
<Nbinary>/inelp+p
N-N cross sectionNuclear Modification Factor:
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 25
Hadron Suppression: Au+Au at 200 GeV
PHENIX preliminary
Suppression of central yields persists up to pT=10 GeV/c
charged hadrons:
Helen Caines - Yale
APS – April 2003 26
Hadron Suppresion for Identified Particles
and p show different behaviour to Ks and p
STAR Prelimimary
s
Seem to come together at ~6GeV/c - “standard” fragmentation?
Suppression of sets in at higher pT
Is this a mass effect or a baryon/meson effect ?
Helen Caines - Yale
APS – April 2003 27
Bulk (Hydrodynamic) Matter
Pressure gradient converts position
space anisotropy to momentum space
anisotropy
Jet Propagation
Energy loss results in anisotropy due to different “length” of matter passed
through by parton depending on location of
hard scattering
y
x
y
x
low pT high pT
Azimuthal Anisotropy (v2)of Particle Emission
Helen Caines - Yale
APS – April 2003 28
Elliptic “Flow” at High-pT
STAR @ 200 GeV
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
Significant in-medium interactions even at 10 GeV/c
Helen Caines - Yale
APS – April 2003 29
Jets in Heavy Ion Collisions
ee q q (OPAL@LEP)
pp jet+jet (STAR@RHIC)
Au+Au ??? (STAR@RHIC)
No, but a bit tricky…
Jets in Au-Au hopeless Task?
Helen Caines - Yale
APS – April 2003 30
•Trigger on high pT leading particle
•Jet core×~ 0.5 × 0.5
• study near-side correlations (Df~0) of high pT
hadron pairs
• Complication: elliptic flow high pT hadrons correlated with the reaction plane (~v2
2)
• Solution: compare azimuthal correlation functions for
short range) particles in jet cone + background(long range) background only
< 0.5 > 0.5
Leading Particle Correlations
associated h
incoming partons
Leading Particle
Near-side correlation shows jet-like signal in central Au+Au
Helen Caines - Yale
APS – April 2003 31
Back-to-Back Jets?
• away-side (back-to-back) jet can be “anywhere”can’t use large subtraction “trick“
• Ansatz: correlation function: high pT-triggered Au+Au event =
high pT-triggered p+p event + elliptic flow+ background
A: from fit to “non-jet” region v2 from reaction plane analysis
PHENIX Preliminary
2-4 GeV
200 NNs GeV
pp
))2cos(21()()( 2222 vAppCAuAuC •black = real
•green = mixed event •purple = black-green
Helen Caines - Yale
APS – April 2003 32
Away Side Jets are Suppressed
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
STAR Preliminary
))2cos(21()()( 2222 vAppCAuAuC
Helen Caines - Yale
APS – April 2003 33
Charm at RHIC
Large charm production cross section (300-600 b) which scales roughly with Nbin
Suppression of high pT ’s relative to binary scaling
Assuming that all single e- signal is from charm decay and the binary scaling, charm cross section at 130 GeV
Charm decay is expected to be dominant component of single e- with pT > 1.5 GeV/c:
Observe an “excess” in single e-’s over expectation from light meson decays and conversions
Observation of charm signal at RHIC
bcc 20060380%100 bcc 25033420%920
Data are consistent with s systematics(within large uncertainties)!
PHENIXPRL 88
Helen Caines - Yale
APS – April 2003 34
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 36
• 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
Leading Charged Particle Correlations
),()(11
)(2 NdefficiencyN
Ctrigger
Near-side correlation shows jet-like signal in central Au+Au
Helen Caines - Yale
APS – April 2003 37
Charm and single electron at RHIC
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
Simulation before RHIC PHENIX data (PRL88)
Helen Caines - Yale
APS – April 2003 38
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 asEdNe/dp3 = TAAEd/dp3
TAA: nuclear overlap integral Ed/dp3: electron spectrum from
charm decay calculated using PYTHIA
The agreement is reasonably good.
0 10%cc 380 60 200 b and 0 92%
cc 420 33 250 b
Assuming that all single electron signal is from charm decay and the binary scaling, charm cross section at 130 GeV is obtained as
PHENIX PRL88 192303
Helen Caines - Yale
APS – April 2003 39
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 40
Leading Photon Correlationstrigger
associated h
incoming partons
0
PHENIX Preliminary
2-4 GeV
•black = pair distribution•green = mixed event pair distribution•purple = bkg subtracted distribution
200 NNs GeV
Select events with a photon of
pt > 2.5 GeV/c. Mostly ’s from decay of a high pt (leading particle)
Build distributions in delta -space of the charged hadrons relative to the trigger photons.
pp AuAu
In AuAu: add v2 component
Helen Caines - Yale
APS – April 2003 41
Helen Caines - Yale
APS – April 2003 42
Parton recombination and high pParton recombination and high pTT
Hwa & Yangnucl-th/0211010
Greco, Ko, Levainucl-th/0301093
Fries, Mueller, Nonaka,Bassnucl-th/0301087
Recombination p
T(baryons) > p
T(mesons) > p
T(quarks)
(coalescence from thermal quark distribution ...) Pushes soft physics for baryons out to 4-5 GeV/c Some exotic explanations (e.g. gluon junctions)
The “buzz’’ word in the last few months: quark recombination/coallescence
Helen Caines - Yale
APS – April 2003 43
Coils Magnet
Silicon Vertex Tracker
E-M Calorimeter
Time of Flight
Time Projection Chamber
Forward Time Projection Chamber
Electronics Platforms
STAR Solenoidal field
Large- TrackingTPC’s, Si-Vertex Tracking
RICH, EM Cal, TOF~420 Participants
• Measurements of Hadronic Observables using a Large Acceptance
• Event-by-Event Analyses of Hadrons and Jets
PHENIXAxial Field
High Resolution & Rates2 Central Arms, 2 Forward Arms TEC, RICH, EM Cal, Si, TOF, -ID
~450 Participants
• Leptons, Photons, and Hadrons in Selected Solid Angles
• Simultaneous Detection of Various Phase Transition Phenomena
The Two “Large” Detectors at RHIC
Helen Caines - Yale
APS – April 2003 44
The Two “Small” Experiments at RHIC
BRAHMS
2 “Conventional” Spectrometers
Magnets, Tracking Chambers, TOF, RICH
~40 Participants
• Inclusive Particle Production Over Large Rapidity Range
PHOBOS
“Table-top” 2 Arm Spectrometer
Magnet, Si -Strips, Si Multiplicity Rings, TOF
~80 Participants
• Charged Hadrons in Select Solid Angle• Multiplicity in 4• Particle Correlations
Ring Counters
Paddle Trigger Counter
Spectrometer
TOF
Octagon+Vertex
Helen Caines - Yale
APS – April 2003 45
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 46
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 47
Experimental Determination of Geometry
5% Central
Paddles/BBCZDC ZDC
Au Au
Paddles/BBC Central
Multiplicity Detectors
Paddle signal (a.u.)
STAR
Helen Caines - Yale
APS – April 2003 48
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
• 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)
Days into RHIC Run
Days into RHIC Run
2000
2001
Au+Au integrated luminosity~80 b-1
Helen Caines - Yale
APS – April 2003 49
Midrapidity: Centrality Dependence at RHIC
_pp
PHOBOS Au+Au ||<1
19.6 GeVpreliminary
130 GeV
200 GeV
binpppart
pp NxNN
Nxd
dNch
2)1(
hard and soft scaling:
hard processes are important even for Nch%10x
Kharzeev and Nardi PLB 507, 121 (2001)
Helen Caines - Yale
APS – April 2003 50
Nch(sNN) – Universality of Total Multiplicity?
pQCD e+e- Calculation
)/exp( sBsch CAN
Total charged particle multiplicity / participant pair
Accidental, trivial?
(A. Mueller, 1983)
2/sseff
Same for all systems at same s(seff for pp)
Helen Caines - Yale
APS – April 2003 51
pT of Charged Hadrons
STAR preliminary
2212
R
ddNccp ch
T
Saturation model:J. Schaffner-Bielich, et al. nucl-th/0108048D. Kharzeev, et al. hep-ph/0111315 Many models predict similar
scaling (incl. hydrodynamic models)
increase only ~2%
Helen Caines - Yale
APS – April 2003 52
ET/ Nch from SPS to RHIC
Independent of energyIndependent of centrality
PHENIX preliminaryPHENIX preliminary
Surprising fact: SPS RHIC: increased flow, all particles higher pTstill ET/ Nch changes very littleDoes different composition (chemistry) account for that?
A. Bazilevsky (PHENIX)
Helen Caines - Yale
APS – April 2003 53
Fireball dynamics: Collective expansion
tanh 1 r r (r) s f (r)
R
s
Flow profile used
r =s (r/R)0.5
dn
mT dmT r dr mT K1
mT coshT
0
R
I0pT sinh
T
Shape of the mT spectrum depends on particle mass
Inverse-slope depends on mT-range
where and
The model is from E.Schenedermann et al. PRC48 (1993) 2462 and based on Blast wave model
Description of freeze-out inspired by hydrodynamics
Helen Caines - Yale
APS – April 2003 54
Blastwave Fits at 130 & 200 GeV
200 GeV
Results depend slightly on pT coverageSTAR:Tfo ~ 100 MeV T ~ 0.55c (130) & 0.6c (200)PHENIX:Tfo ~ 110 MeV (200)T ~ 0.5c (200)
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APS – April 2003 55
suppression: comparison to theory
--- Wang dE/dx = 0--- dE/dx =0.25 GeV/fm
• Wang: X.N. Wang, Phys. Rev. C61, 064910 (2000).
--- Levai L/ = 0--- 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.
PHENIX preliminary
Helen Caines - Yale
APS – April 2003 56
2 Particle Correlations at High-pT:
Direct Evidence for Jets?
),()(11
)(2 NdefficiencyN
Ctrigger
• Jet core×0.5 × 0.5 look at near-side correlations (~0) of high pT hadron pairs
• Complication: elliptic flow
• high pT hadrons correlated with the reaction plane orientation also correlated with each other (~v2
2)
• but elliptic flow has long range correlation ( >> 0.5)
• Solution: compare azimuthal correlation functions forshort rangeand long range
Helen Caines - Yale
APS – April 2003 57
Reality Check: Charge-Sign Dependence
||<0.5 - ||>0.5 (scaled)
0<||<1.4
Au+Au
p+p
System
()/( & )
p+p 2.7 0.6
0-10% Au+Au 2.4 0.6
Jetset 2.6 0.7
DELPHI, PL B407, 174 (1997)
• Compare same-sign (++, --) and opposite-sign (+-) pairs• Known jet physics: charge ordering in fragmentation
Opposite/same correlation strength similar in Au+Au, p+p, JETSETpT~3-4 GeV are jet fragments
STAR preliminary
Helen Caines - Yale
APS – April 2003 58
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/~0.3)Phys. Rev. Lett. 88, 242301 (2002)
p
STAR: different behaviour of strange mesons vs. strange baryons for pT < 5 GeV/c
• Exotic explanation: baryon junction interactions enhanced in A+A (Vitev and Gyulassy)• Mundane explanation: transverse radial flow (common velocity)
ISR
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APS – April 2003 59
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 60
Reality Check: Charge-Sign Dependence
||<0.5 - ||>0.5 (scaled)
0<||<1.4
Au+Au
p+p
System
()/( & )
p+p 2.7 0.6
0-10% Au+Au 2.4 0.6
Jetset 2.6 0.7
DELPHI, PL B407, 174 (1997)
• Compare same-sign (++, --) and opposite-sign (+-) pairs• Known jet physics: charge ordering in fragmentation
Opposite/same correlation strength similar in Au+Au, p+p, JETSETpT~3-4 GeV are jet fragments
STAR preliminary
Helen Caines - Yale
APS – April 2003 61
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, max (b=0) = 24.6 GeV/fm3, <>(=1 fm/c) = 5.4 GeV/fm3
Tmax(b=0) = 340 MeV, Tch = 165 MeV, Tfo = 130 MeV
K+p
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APS – April 2003 62
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
lattice QCD input
Works qualitatively at lower energy but always overpredicts collective effects - infinite scattering limit not valid there