My first experiment and Tamura &Udagawa
Y. Miake, Thesis for Master degree, Osaka Univ.,1979

2 stepDWBAbyUdagawa& Tamura✓Measurement of 12B polarization• 100Mo(14N,12B), EBeam= 130 GeV, 200 GeV✓Working with N. Takahashi, Osaka Univ.

Nov., 2008,Tamura Symposum, Austin

1

My name appeared as a firsttime in PRL of their paper
Phys. Rev. Lett. 41(1978)1770

Nov., 2008,Tamura Symposum, Austin

2But, spell of my name waswrongek→ekY.

yaiMaiM
Y.

Nov., 2008,Tamura Symposum, Austin

3

Flow measurementsin heavy ion coll.
Scaling properties of v2 revisited with Blast Wave ModelYasuo MIAKE
Univ. of Tsukuba
Nov., 2008,Tamura Symposum, Austin

4

RHIC since 2000

Nov., 2008,Tamura Symposum, Austin

5Tsukuba Contribution
1) PID with TOF & Aerogeln index = 1.012
n pe ≈ 20

σ TOF ≤ 100ps

200cm

€€

385cm

200cm

-p (p) ID up to 8 GeV/c
Preliminary+e+ πPHENIX

K+ProtonpKe-π--p (p) ID up to 4 GeV/c✓High resolution TOF and low index of 1.01 Aerogel Cherenkov
Both Tsukuba contribution

Nov., 2008,Tamura Symposum, Austin

6

Tsukuba Contribution2) R.P. determination
S. Esumi, Tsukuba

0-5%
5-10%
10-20%

beamBBCCentral armBBC✓Wide rapidity gap from central detector• Free from other source of corr such as HBT, decays, jets & auto-corr.

✓Corr. between SMD(spect) and BBC(part) also confirmed➡R.P. determination from whole event wide

✓Detector for Reaction Plane determination
Nov., 2008,Tamura Symposum, Austin

7

Key ; Statistical Nature
3!QGP ∼ 2 [GeV/fm ]!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:

Ex. Lattice QCD

Animation by Jeffery Mitchell (Brookhaven NationalLaboratory). Simulation by the UrQMD Collaboration• Statistical physics at quark level• Hydrodynamical behavior at quark level
Nov., 2008,Tamura Symposum, Austin

8Key; Time Evolution✓It is like Big Bang.
✓Time evolution in
statistical nature• Parton cascade followedby partonic
thermalization (QGP)• Hadron production• Freezeout of v2 ?
• Chemical freeze-out• Kinematical freeze-out

Need consistent understanding of these epocs,
in particular, aspects of statistical nature.
Nov., 2008,Tamura Symposum, Austin

9

Thermal Eq.
andCollective Flow★

Chemical Eq. fromparticle yield ratio★ Kinematical Eq.
from transverse
mom. distr.
★
Nov., 2008,Tamura Symposum, Austin

Blast Wave10

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 400Npart✓Only few parameters fit every ratio very well !
✓Tch stays constant from peripheral to central collisions

Nov., 2008,Tamura Symposum, Austin

11

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

Nov., 2008,Tamura Symposum, Austin

12T ≈ T0 + m v r2CollectiveFlow
12

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
Nov., 2008,Tamura Symposum, Austin

thermal and collective✓Well describe < 2 GeV/c13

Original Blast Wave Model✓Collective Flow
✓Adiabatic expansion
Nov., 2008,Tamura Symposum, Austin

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Tested Robustness ofBlast Wave results
A Kiyomichi, Tsukuba✓Result of Blast Wave analysis
depends very much on the pt
range for the fitting.

➡ Significant amount of decayed particles at lowpt region✓Substract decay products first,
then fit the spectra with BlastWave Model.

• Thesis of Akio Kiyomichi

Lower Tkin incentralcollisions
Nov., 2008,Tamura Symposum, Austin

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Distinct feature offreeze-outconditions
S =πr =πr A
dN / dyS

dN / dy2

202/ 3Gluon saturation scale:QS ≈dN / dy≈ 1STARGeVExperiment
π r2TCTch✓Difference of Tch and Tkincorresponds to time
evolution of the system.

✓Kinematical & Chemical

<β>
200
400
dNch/dη600

freeze-out show differencein centrality dependence!

➡Might be difference inNature of Freeze-out

Nov., 2008,Tamura Symposum, Austin

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Adiabatic Expansion Model✓Intuitive Model✓Assuming,• Cylindrical expansion• Freeze-out condition
V (t) = ctπR(t) = ctπ(R0 + βT t)
2V (tfo )∼ R(tfo )knpart σ!
R02 + 4 kσ
cπ βT npart − R0
tfo =2βTT (tfo ) = T0 (V0)1/3
2
tfo (R0 + βT tfo )

21
λ=
∼Rnσ

• Adiabatic expansion

T 3 (t)V (t) = Const.
(∵ s ∝ T 3 )✓Larger fireballfreeze out later

Nov., 2008,Tamura Symposum, Austin

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Kinematical Freeze-out w.
Adiabatic Expansion
M. Konno, Tsukuba

Adiabatic Expansion Model (M.Konno,Y.M. 2008)

Tch
Tkin

✓Adiabatic Expansion Modelexplains centrality
dependence very well.
• Freeze-out conditions ; λ~R✓In central collsions, the F.B. istfo (A.U.)

Central collisions freeze-out late.

Nov., 2008,Tamura Symposum, Austin

so large that F.O. occurs
later than peripheral.

➡Kinematical freeze-out iscollisional, while chemical isnot.
18

Further Study
ofCollective Flow
Azimuthal Anisotropy
ofCollective Flow,
Elliptic Flow
Nov., 2008,Tamura Symposum, Austin

19

Elliptic Flow, v2
Re
pl ac
an tioe n(Azimuthal Anisotropy)
PyZ

PzPx
YX

y 2 − x2
#εecc = ! 22y +x

p2y − p2xv2 = ! 2#2
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
Nov., 2008,Tamura Symposum, Austin20€

Early study of v2 vs. εecc
Phenix; PRL 89(2002)212301

v2ε 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

Nov., 2008,Tamura Symposum, Austin

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v2 of identified particle
S. Esumi, Tsukuba

PHENIX : P.R.L. 91, 182301 (2003)✓Mass Ordering of v2 at low
pt region:➡Existence of collective flow
• Good agreement withhydrodynamics of perfect
fluid➡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?
Nov., 2008,Tamura Symposum, Austin

22Extended Blast Wave Fit 1
Initial Density Profile

H. Masui, Tsukuba

Extended Blast Wave Fitting (H. Masui,Y.M. 2007)✓With hydrodynamics, ∇pgenerates collective flow.

✓Assuming p∝ρ, velocity
profile is obtained frominitial density profile ρ.
Final Velocity Profile➡Freeze-out time for v2 =0➡Yes, very/too naive, but see
what happens. Fun!

✓Choice of density profile
Nov., 2008,Tamura Symposum, Austin• Glauber Model ; Npart• Glauber Model ; Ncoll
23

Extended Blast Wave Fit 2Npart Profile✓ It was fun to see;H. Masui, Tsukuba

D.Thesis, H. Masui, Univ. of Tsukuba (2008)

Ncoll Profile• Ncoll distr. seems togive better fitting• T from v2 is muchhigher than T fromspectra, while β isvery similar.

✓But, fitting does notwork at all,• for pions,• for centrality dep.
• High T from v2 may
Nov., 2008,Tamura Symposum, Austin

imply finite freeze-outtime.
24

Beautiful scalings of v2
PHENIX PRL 98(2007)162301

Au+Au 200 GeV✓mt scaling & quark number scaling
Nov., 2008,Tamura Symposum, Austin

25

Hadronization via Quark
Coalescence✓ 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.
Nov., 2008,Tamura Symposum, Austin

Characteristic scaling features expected.
Quark Number Scaling (QNS)
26

Hadronization via Quark
Coalescence (QNS in v2)✓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
Nov., 2008,Tamura Symposum, Austin

dN 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 )27

FurtherSystematicsof v2
Centrality dep.
Energy dep.

H. Masui, Tsukuba→200 vs 64 GeV

System size dep.
→Au+Au vs Cu+Cu
Nov., 2008,Tamura Symposum, Austin

28

Au+Au 200 vs 64 GeV
D. Thesis soon, M. Shimomura, Univ. of Tsukuba (2008)

M. Shimomura, Tsukuba

PHENIX PRELIMINARY

Produced by!

Mean pT

Nov., 2008,Tamura Symposum, Austin✓No significant change in v2✓A little larger radial flow seenin <pt> of 200 GeV

29

Au+Au vs Cu+Cu
v2 vs. Npart

0.2<pT<1.0 [GeV/c]

v2/! vs. Npart

M. Shimomura, Tsukuba

PHENIX PRELIMINARY

Phobos; nucl-ex/0610037
200 GeV

Cu+Cu
Au+Au
arXiv:nucl-ex/0610037, submitted to PRL

Nov., 2008,Tamura Symposum, Austin✓Simlar v2/ε for Au+Au
and Cu+Cu, while there isclear Npart dep. !!??????
30

“Grand Universal” Scaling
M. Shimomura, Tsukuba✓Although you cannot
distinguish, there are• Au+Au, Cu+Cu,• 200 GeV, 64GeV, and• pion, kaon, proton.

Nov., 2008,Tamura Symposum, Austin

31

Blast Wave re-visited !
M. Konno, Tsukuba

Fitting pt range:
0.6-1.2 GeV/c for pi0.4-1.4 GeV/c for K
0.6-1.7 GeV/c for p!

By Masahiro Konno()*#+,#$%&"'!

!"#"!

!"#$%&"'!

!"#$%$"&'()%*"+,&&-./"()!&0$)-1"""2(330-/"()40,*(5-1"0'6-./"',%!'7!&0$)-8"!"9()-*/":0$*%!6$5-";%".-*,0%*!

✓pt distributions measured in plane andout-of plane are B.W. fitted independently
Nov., 2008,Tamura Symposum, Austin

32

B.W. Fitting Results
M. Konno, Tsukuba

in-planeβT

By Masahiro Konno

Tfo

out-of plane✓T are the same in plane and out-of plane, whileβT(in-plane) > βT(out-of plane) !
Nov., 2008,Tamura Symposum, Austin

33

Modulations wrt theφRP
Au+Au 200 GeV 20-30 %Tfo

Tfo (φ) = 1 + 2T2 cos(φ − φRP )T2 = (-5.4 +/- 4.0) x 10-3!

βTβ2

By Masahiro Konno

T2

M. Konno, Tsukuba

βT (φ) = 1 + 2β2 cos(φ − φRP )!2 = (3.3 +/- 0.2) x 10-2!

✓T2 ≃ 0, while clear modulation in β.
✓Reaction Plane is determined independently.

Nov., 2008,Tamura Symposum, Austin34

Plotted against Npart
M. Konno, Tsukuba

By Masahiro Konno

β2Cu+Cu

Au+Au

T2✓T2 stays 0, while β2 shows centrality dep.
which is different in Au+Au and Cu+Cu, but,,,
Nov., 2008,Tamura Symposum, Austin

35

Plotted against εM. Konno, Tsukuba

By Masahiro Konno

v2

β2✓β2 is prop. to eccentricity, while v2 is not
Nov., 2008,Tamura Symposum, Austin36

β２/ε is the constant !
Adiabatic Expansion (M.Konno,Y.M. 2008)

v２/ε

β２/εTfo✓β２/ε is the constant in Au+Au and Cu+Cu,
while v２/ε shows ˜ Npart1/3 .
➡Difference comes from the fact that v2 is sensitive to Tfo aswell. Strength of v2 is diluted if the Tfo is high.
➡Central collision shows lower Tfo because of the late freeze-out.
Nov., 2008,Tamura Symposum, Austin37

ʻBrightʼ future of v2;
heavy flavor and thermalphoton

S. Sakai, Tsukuba

PRL 98 172301 (2007)!

✓S. Sakai founds even charm flows✓K. Miki is in his PhD defense of his

positive results of thermal photon.

Nov., 2008,Tamura Symposum, Austin➡v2 is interesting business!!

38

Summary✓Systematic study of v2 done in Au+Au, Cu+Cu,
200 GeV & 64 GeV.

✓Scaling properties of v2 has been re-visited
with Blast Wave picture.
Please note that Blast Wave fits the low pt region ofprotons, kaons and pions.

• T2 ˜0 ; No φRP dep. of freeze-out temperature.
• β2/ε stays constant in Au+Au, Cu+Cu, whilev2/ε shows ˜Npart1/3 dependence.

➡β2 seems to be the good scaling quantity in the region.

✓Even charm flow!? and thermal photons?

Nov., 2008,Tamura Symposum, Austin39

Many thanks to mycolleagues/students
S. Esumi, Tsukuba

T. Chujo, Tsukuba

M. Shimomura, Tsukuba

M. Konno, Tsukuba

H. Masui, Tsukuba

S. Sakai, Tsukuba✓ShinIchi Esumi, Tsukuba✓Tatsuya Chujo, Tsukuba✓Masahiro Konno,Tsukuba✓Akio Kiyomichi, now at KEK✓Hiroshi Masui, now at LBL✓Shingo Sakai, now at UCLA
✓Maya Shimomura, Tsukuba✓Kentaro Miki, Tsukuba✓Yoshimasa Ikeda, Tsukuba✓Rei Tanabe, Tsukuba

A Kiyomichi, Tsukuba
Nov., 2008,Tamura Symposum, Austin

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Now, paperback is available!

Nov., 2008,Tamura Symposum, Austin

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