I
What we havelearned at RHIC
Yasuo MIAKE
Univ. of Tsukuba

Fall 2007, JPS @Sapporo

1Quark Gluon Plasma
˜fm✓Size of hadrons ˜ fm
✓At high ρ or high T, theyoverlap each other.
✦Not confined to eachhadron.
➡New state of matter:quark-gluon plasma.
➡Phase transition
Fall 2007, JPS @Sapporo

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FAQ: is it the QGP insideproton?
kr “Confining”

V(r)

r

−4 αs
3 r

“Coulomb”✓Asymptotic freedommeans a QGP inside aproton?
➡No!

✓We want many free quarks
and gluons over a large
volume as a matter.

✓Applicability of Statistical
Physics is essential!
Fall 2007, JPS @Sapporo

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What we expect:
Statistical Nature
3!QGP ∼ 2 [GeV/fm ]Ex. Lattice QCD!QGP2GeV< nq,q̄ > ∼∼∼5
< mT >
0.4GeV1
λq =nσqq
1∼= 0.5 [fm]5 × 0.4
λq # Rsystem
4[fm2 ]
σN N
∼
∼ 0.4
∵ σqq ∼
3×3
9✓What we can expect:

Animation by Jeffery Mitchell (Brookhaven NationalLaboratory). Simulation by the UrQMD Collaboration✦Statistical physics at quark level✦Hydrodynamical behavior at quark level
Fall 2007, JPS @Sapporo

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RHIC since 2000

✓Series of measurements;
Au+Au collisions at √sNN = 200 GeV
as highest & largest (240 µb-1)

Au+Au at √sNN = 19.6, 130, 200
GeV as Energy Scan

p+p at √sNN = 200 GeV as
Comparison data
Fall 2007, JPS @Sapporo

d+Au √sNN = 200 GeV as Controlled
Comparison

5How thecollisions look
likeAnimation by Jeffery Mitchell (Brookhaven National Laboratory). Simulation by the UrQMD Collaboration

Fall 2007, JPS @Sapporo

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Time Evolution of collision✓Time evolution which
we expect.

✦Parton cascade✦Quark Gluon Plasma✦Chemical freeze-out➡no more hadronproduced✦Kinematical freeze-

Fall 2007, JPS @Sapporo

out➡no more scattering✦If the beam energy ishigh enough, we thinkobservable to be
Lorentz invariant. 7

Peripheral ˜ Central coll.

Fall 2007, JPS @Sapporo

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Npart vs Nbinary✓For comparison with pp or dAu
also for centrality study, weneed scaling variables.

✓Npart;Participant# of participant nucleons

Particle production in hA is known to be
proportional to Npart. (Wounded-NucleonModel)

Au+Au collisions✓Nbinary;# of binary nucleon-nucleon collisions

Pass through at high energy.

✓Evaluation of Npart & Nbinary byGlauber Model.
Fall 2007, JPS @Sapporo

9Particle production(η distr.)
Phobos; P.R.L. 91, 052303(2003)

Phobos; J.Phys.G:Nucl.34,S217(2007)✓All the data taken at RHIC-Phobos.
✓ dn/dη ; wider & larger in higher energies.
✓Not very flat even at 200 GeV despite our naive expectation
Note that it is plotted in η.

✓Features of ʻlimiting fragmentationʼ seen

NoʻLorentz Invarianceʼyet!

Fall 2007, JPS @Sapporo

10Particle production(total mult.)✓Total multiplicity per Npartstays constant.
WNM holds even at RHIC.

Slight deviation at higher
collision energies.

✓Deviation from Npart scaling
more visible at mid-rapidity.

Hard Process !?

Fall 2007, JPS @Sapporo

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ThermalEquilibrium★

Chemical Eq. fromparticle yield ratio★ Kinematical Eq.
from transverse
mom. distr.
Fall 2007, JPS @Sapporo

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Chemical Eq. from particle
yield ratio
M.Kaneta, N.Xu, nucl-th/0405068

gini =2π 2! ∞0p2 dpe(Ei −µi )/T ± 1

Tch [MeV]

2001501005000100 200 300 400
Npart✓Only few parameters fit every ratio very well !
✓Tch stays constant from peripheral to central collisions
Fall 2007, JPS @Sapporo

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Kinematical Distr.:
Transverse mass distr.
mt =pt2 + m 2

PHENIX, PRC69,034909(2004)€✓ Exponential in mt✦ Known as mt scaling✦ Thermal distr.
✓ Flatter mt distr for heavier

particle mass
✦ Mass Ordering of Slope param.
✦ Effect of Collective Flow

Fall 2007, JPS @Sapporo

12T ≈ T0 + m v r2

CollectiveFlow
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Blast Wave Model p sinh ρ   m cosh ρ R1 dN= A ∫ 0 f (r)rdrmT I 0  T K1 TmT dmT Tfo   Tfo


PRC48(1993)2462.

ρ(r) = tanh−1 (βT ) ⋅ r/R

I0 , K1: modified Bessel function
Phobos, J.Phys.G34,S1103-7(2007)€PHENIX, PRC69,034909(2004)€✓Good tool to separate
Fall 2007, JPS @Sapporo

thermal and collective✓Well describe < 2 GeV/c15

Distinct feature offreeze-out conditions
Adiabatic Expansion Model (M.Konno)

TchdN / dySdN / dy

S = π r 2 = π r02 A2/ 3Gluon saturation scale:
QS ≈TkindN / dy≈ 1 GeV
π r2TCTch✓Kinematical & Chemical
freeze-out show difference incentrality dependence!

✦Kinematical :➡Tkincent. < Tkinper. < Tch
Freeze-out with λ~R✦Chemical :

<β>
200
400
dNch/dη

600

Central collisions freeze-out late.

➡Tchcent. ˜ Tchper. ˜ 160 MeVFreeze-out with T~ Tcrit✓Nature of Freeze-out✦Kinematical freeze-out isFall 2007, JPS @Sapporo

collisional, while chemical isnot.
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Two Major
Discoveriesat RHIC
1) Large Elliptic Flow2) Jet Modification

Fall 2007, JPS @Sapporo

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Elliptic Flow, v2(Azimuthal Anisotropy)
PyRe
pl acan tio
e nZPzPx
YXy 2 − x2#εecc = ! 22y +x

p2y − p2x#v2 = ! 22
py + px✓ In non-central collisions, participant region has almond shape.
➡azimuthal anisotropy in coordinate space✓ If λ<< R, azimuthal anisotropy of the coordinate space isconverted to that of the momentum space.

➡v2 ; second Fourier harmonics of azimuthal distribution✓ Goodies :N (φ ) = N 0 {1+ 2v1 cos(φ − Ψ0 ) + 2v 2 cos(2(φ − Ψ0 ))}✦ Clear origin of the signal✦ Collision geometry can be determined experimentally
Fall 2007, JPS @Sapporo

18€v2 vs. Eccentricity
Phenix; PRL 89(2002)212301

Phobos; nucl-ex/0610037

200 GeVv2Cu+Cu

εAu+AuarXiv:nucl-ex/0610037, submitted to PRL

Q v2 ∝ ε✓Eccentricity is evaluated from centrality of collisions✓Ratio stays ˜constant✦Eccentricity scaling observed in comparison of€ Au+Au, Cu+Cu
Scaling with eccentricity shows v2 builds up at early stage

Fall 2007, JPS @Sapporo

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Large azimuthal
anisotropy
N (φ ) = N 0 {1+ 2v1 cos(φ − Ψ0 ) + 2v 2 cos(2(φ − Ψ0 ))}PHOBOS; nucl-ex/0406021€✓Getting larger & larger inhigher energies.

✦Hadronic scenario fails✦Scaling w. η-ybeam !?
Fall 2007, JPS @Sapporo

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v2 of identified particle
PHENIX : P.R.L. 91, 182301 (2003)✓Mass Ordering of v2 at low
pt region:➡Existence of collective flow
✦Good agreement withhydrodynamics of perfectfluid➡Early thermalization (˜0.6 fm/c)➡High energy density (˜20 GeV/fm3)➡Very low viscosity✓Departure at high pt region(> 1.5 GeV/c);➡Other mechanism?
Fall 2007, JPS @Sapporo

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Fall 2007, JPS @Sapporo

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Puzzles in the mid-pt regionp/π enhances above 1.5 GeV/cv2 deviates from the mass ordering
above 2 GeV/c

Phenix; P.R.L. 91(2003)172301

lyamnoyaronAB✓ In central col., p/π ratio is very large, while in peripheral, p/π ratio similar tothose in ee/pp suggesting fragmentaton process.
Fragmentation process should show np < nπ as seen in ee/pp.

✓ While mass ordering of v2 seen at low pt region, clear departure observed.
✓ Suggesting other production mechanism.
Fall 2007, JPS @Sapporo
Quark Recombination Model(Quark Coalescence Model)

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Quark recombination model(RECO)✓ Quarks, anti-quarks combine to form

Hadronmesons and baryons from universal quark
distribution, w(pt).
Mom. distr. of meson (2q)；

W M ( pt ) ≈ CM ⋅ w 2 ( pt 2 )Mom. distr. of baryon (3q)；

W B ( pt ) ≈ CB ⋅ w 3 ( pt 3 )€w(pt)；

Universalmom.
€distr. of quarks｛steep in pt｝

QGP
Because of the steep distr. of w(pt), RECO
wins at high pt even w. small Cx.
Fall 2007, JPS @Sapporo

Characteristic scaling features expected.
Quark number scaling24

V2 from RECO✓Characteristic scaling behavior→Quark Number Scaling

HadronAzimutal distr. of meson (2q)；dN M∝ w 2 = (1+ 2v 2,q cos2φ ) 2dφ≈ (1+ 4v 2,q cos2φ )Azimuthal distr. of baryon (3q)；€QGP
Fall 2007, JPS @SapporodN B∝ w 3 = (1+ 2v 2,q cos2φ ) 3dφ≈ (1+ 6v 2,q cos2φ )Azimuthal distr of quark; w€w ∝ (1+ 2v 2,q cos2φ )25

Quark Number Scaling !!
M. Issah, A. Taranenko, nucl-ex/0604011

KET = mT – m

Kinetic energy of constituent quarks✓ Mesons and baryons made of light quarks seem to be consistent with therecombination model and there seem to be universal quark distribution,w(pt,Φ).

Fall 2007, JPS @Sapporo

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Even charm flows!
v2 of single electrons
S.Esumi & S. Sakai@SQM2006

V.Greco, C.M.Ko,R.Rapp,PLB595(2004)202.

✓ Charm decay produces highenergy electrons.

✓ v2 of single electrons aremeasured.

✓ Observed data favors flow ofcharm, suggesting
thermalization of heavy quarks.

✓ This supports quark-

coalescence & formation ofQGP.

Fall 2007, JPS @Sapporo

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Jet
Modification

Fall 2007, JPS @Sapporo

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What is Jet ?
✓At ISR in 1972, deviation fromthe mt scaling at high pt region
is observed as a first time.
✓Binary parton scattering
followed by fragmentation
produces back-to-back jet.
✓Origin of high pt particles inelementary particle collisions.
back-to-backFall 2007, JPS @Sapporo

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Comparison of Au+Auand pp✓For comparison, Au+Au & pp spectra
scaled by Nbinary.
Scaled pp
spectraCentral✓In peripheral
collisions,
Au+Au ˜ pp

✓In central collisions,
Peripheral

Au+Au < pp
 Suppression of yield ?
 Loss of pT ?
Jet Quench?

Fall 2007, JPS @Sapporo

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Suppression of high pt
particles
NuclearModification RAu+Au =Factordn Au+Au /dpT dy
N binary ⋅ dn pp /dpT dy

Cronin effect

RAA€10.34

binary collisionscaling

participant scalingpT✓Pions are suppressed, direct photons are not

Fall 2007, JPS @Sapporo

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Au+Au vs d+Au
Phenix; P.R.L. 91, 072303 (2003)

Au+Au at sNN = 200 GeV

d+Au→h +X at sNN = 200 GeV✓High pt suppression in Au+Au, while notobserved in d+Au.
Fall 2007, JPS @Sapporo➡Effect is not due to initial state, but final state.

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near side

Disappearance ofback-to-back corr.
away side✓Direct evidence ofloss of ʻjetʼ✓Azimuthal
correlation w.r.t. highpt leading particle(trigger).

pedestal and flow
subtracted

Fall 2007, JPS @Sapporopp ; clean di-jetdAu; similar to pp

Au+Au; Similar on thesame side (suggestingjet-like mechanism), but bto-b disappeared

Effect is not in initial
but in final stage

Energy loss of partonsin dense matter
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created in Au+Au

Energy Loss of Parton ?
+ZeNg
dE GLVE−∝ln( )dx
f (E) µdE
N− Bethe ∝ 2e ln(β 2 ⋅ ⋅⋅)dx
β✓Energy loss of charged particle in matter;
Collisions with atomic electrons, proportional to the electron densityRadiative energy loss.

€Bethe-Heitler Formula€✓In QCD, major loss will be radiativeEnergy loss of parton should be proportional to the gluon density

Fall 2007, JPS @Sapporo

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Shape change of awayside
pTtrig = 3˜4 GeV/cPHENIX, arXiv:0705.3238 [nucl-ex]✓From broad to distinct two shoulders at
ΔΦ＝π1.1 with decreasing momentum➡Location of shoulders independent of centrality
Fall 2007, JPS @Sapporo

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Separate contributions atΔΦ＝π 1.1 & ΔΦ＝πPHENIX, arXiv:0705.3238 [nucl-ex]✓Shoulders
appear at lower
momentum.

✓Location & <pt>of shoulder
seem to be
independent ofcentrality andpt.

Fall 2007, JPS @Sapporo✦ Not cherenkov✦ Not deflection✦ But, Mach Cone !?
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Jet Tomography
Positron EmissionTomography

Jet Tomography
M. Gyulassy ?

✓Tool to prove structure of the densematter✓Large azimuthal anisotropy is major
background now.

➡“Discovery of yesterday isbackground of today andcalibration of tomorrow”
Fall 2007, JPS @Sapporo

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Summary✓We have seen partonic matter, ie, a QGP!
✓Successful description of the system in terms ofstatistical thermo-dynamics;✦Particle ratios in Tch, μ, Kinematical distr. in Tth and β✓Partonic✦Large azimuthal anisotropy cannot be created with hadronicprocess.
✦High pt suppression and disappearance of back-to-back is atparton level.
✦Successful description of quark recombination;➡Phenomenological, but universal quark distribution function!
✓We are in the state of studying property of plasma, like cs.
Fall 2007, JPS @Sapporo

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