Measurement ofAzimuthal Anisotropy
and the QGP
Yasuo MIAKE, Univ. of Tsukubai) What is azimuthal anisotropyii) How it is measurediii) What is learned

Part 1
What is azimuthal anisotropyAzimuthal anisotropy

In non-central col., participant hasalmond shape at initial stage.
!" #" $%&'()" &'*'%

Emission of particle in azimuth isinfluenced by λ & R relation.
+,,-ie., anisotropy in coordinate spaceλ >> R ; isotropic
λ << R ; hydro.elliptic+..

Anisotropy of the coordinate spaceconverted to that of the momentum
space.

Conversion of anisotropy fromcoordinate space to momentum
space/010" 2334)*'53)6" 70809:;<=>?@AA?B

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Azimuthal distr wrt reaction planedN/dφdN/dφ

2v20φ
2π0

φ

2π

Evaluate as Fourier components

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Evaluation with Fourier exp.

•Obtain azimuthal
distributions w.r.t. thereaction plane.

•Evaluate the distribution withFourier components

N (# ) = N {1 + 2v cos(# " ! )+ 2v cos(2(# " ! ) )}0

1

Y.Miake, KPS meeting at APCTP in Pohang, 2005

0205!

Fourier harmonics
1st harmonics“Directed Emission”
Y

2nd harmonics“Elliptic Emission”

ｖ１＞０Reaction Plane

X

ｖ1<０Y

ｖ2＞０

X
ｖ2<０pxv1 = cos(" # $R ) =pt

Y.Miake, KPS meeting at APCTP in Pohang, 2005!

px2 # py2v 2 = cos2(" # $R ) = 2
px + py2

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Sensitivity to the early stage
RQMD Anisotropy incoordinate space
disappears quickly Direct measure ofthe conversion
mechanismY.Miake, KPS meeting at APCTP in Pohang, 2005

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Expect Eccentricity to disappear
quickly
Kolb et.al., PRC62(2000)054909

Ratio of eccentricity after a time delayDisappears quickly v2 senses early stage of collision

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Reasons why I like v2
x2 # y2"ecc = 2
x + y2px2 " py2
v2 = 2px + py2

 Clear origin of the signal !

!

Geometry is!clear From eccentricity to v2
 Centrailty dependence gives goodtests Sensitivity to the early stage ofcollisions !

Y.Miake, KPS meeting at APCTP in Pohang, 2005

Mean free path λ vs. R

9Part 2
How it is measured

How it is analyzed

 Three methods;
 Pairwise Method
 Cumulant Method Reaction Plane Method

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Two Methods

Reaction Plane Method

Event by event determinationof R.P.
Once the R.P. is established,easier to apply other particle
species.

Y.Miake, KPS meeting at APCTP in Pohang, 2005

Pairwise Method

No Reaction Plane.
Measure azimuthal corr. of
all the pairs
Small effects ~v2**2, buthigh statistics
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Analyze me PHENIX; non-uniform in azimuth
 How it works?

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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R. P. method & flattening corr.
Azimuthal acceptanceof PHENIX

Determine azimuthal direction of R.P.
every eventtan 2"cal0

sin 2! I= cos 2! IDefine average of azimuthal angles of
all the measured particles as R.P.
Most probable direction as R.P.
Toy Simulation!

Artificial peak due to detector
acceptance !

Flattening the peak#! c = "( An cos(2n! 0cal )cal0n+ Bn sin( 2n! 0cal ))! 0flat!
Y.Miake, KPS meeting at APCTP in0Pohang, 2005

An = ""! c

Bn =! 0cal

2sin( 2n! 0cal )n2cos(2n! 0cal )n! 0flat = ! 0cal + "! c14

Flattening corr. works for PHENIX
Toy Simulation!で再構成した0! 分布

Toy simulation assuming

"i # !

flat0!

PHENIX acceptancev 1 , v2
multiplicity

After resolution corr., v2can be reconstructedsuccessfully
It works!

Resolution of R. P.
cos 2(" 0 ! " 0flat ) = 0.309

v2 = 0.1

解析

v2 =v2Fitting
Resolution= 0.102 ± 0.01

Ｈ１２・筑波大・卒業論文・進藤美紀
Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Pairwise Method & Acc. Corr.
Azimuthal acceptanceof PHENIX



Azimuthal corr of all the measured
particle pairsAcceptance dominates the shape ofdistribution

Effect of acceptance is evaluated bymixed event

Toy Simulation

Mixed EventReal EventA#! = !i " !

Aj#! * = ! kA " !lBＨ１２・筑波大・卒業論文・進藤美紀
Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Pairwise method works!
Toy simulation assuming

PHENIX acceptancev1, v2
multiplicity



Observed anisotropy ＝v2**2

Good agreement with the input

V２

Real／Mixed"!
V2 = 0.100 " 10 !1± 0.40 " 10 !3F ( x) = F0 (1 + 2V1 cos x + 2V2 cos 2 x)
Ｈ１２・筑波大・卒業論文・進藤美紀
Y.Miake, KPS meeting at APCTP in Pohang, 2005

v2 17

Stability of results
Toy Analysis

With smaller acceptance, weaker effect observed.


Poorer resolution

But, after resolution correction, consistent results obtained.

Y.Miake, KPS meeting at APCTP in Pohang, 200518

Conclusion of Toy model study Even with PHENIX acceptance, we obtainconsistent results both from R.P. method andPairwise method, if they are pure elliptic flow.
 We might get different results if there arehigher harmonics
 non-flow effect such as HBT, particle decay, kinematicalcorrelations
 Reliable determination of R.P. is more important !
avoid non-flow effect as much as possible

Take wide rapidity gap from central detector BBC as main R.P. detector

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Towards reliable R.P.

Beam Beam Counter (BBC)|η|=3-40-5%
5-10%

beam

BBCCentral
Y.Miake, KPS meeting at APCTP inPohang, arm
2005

Wide rapidity gap
from central detector
 Full AzmimuthalCoverage Enough multiplicity
for resolution

10-20%BBC20

R.P. from BBC
Reaction plane distribution

Correlation of two reaction plane
BBC north v.s south

JPS-S02-Sakai



[rad]

[rad]

Clear and consistent correlation among two BBC’s.

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Further R.P. studies

MVDSMD/ZDC

0-5%
5-10%
10-20%BBC

To establish R.P., need to confirm
global(whole event) correlations

Y.Miake, KPS meeting at APCTP in Pohang, 2005

beamBBCBBC

Central arm
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R.P. from elliptic flow
Phenix; S.Esumi JPS/DNP 2005

Participant Region
Φ2BBC1 vs Φ2BBC2

Φ2MVD1 vs Φ2MVD2

Φ2BBC vs Φ2MVD

ellipticplane[−π/2,π/2]
Better resolution with MVD since wider acceptance Confirm clear event-wide correlations among detectors
Y.Miake, KPS meeting at APCTP in Pohang, 2005

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R.P. from directed flow
BBC

ΦBBC1−π vs ΦBBC2 ΦSMD1−π vs ΦSMD2
back-to-backdirectedplaneback-to-backΦSMD−π vs ΦBBCSMD

spectator neutrons vsπs from participants
are flowing opposite.

[−π,π]
Phenix; S.Esumi JPS/DNP 2005



Clear correlation between SMD(spect) and BBC(part) in v1
As seen at SPS, back-to-back corr of Neutrons and Pions.

Y.Miake, KPS meeting at APCTP in Pohang, 200524

Comparison of three methods
Phenix; P.R.L. 94, 232302(2005)

 Striking agreement (!) even with R.P. method.
No strong non-flow effect !?

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Part 3What is learned

What we expected before RHIC

 There is atendency ofsaturation!?
 Hadron cascade
predicts a few %.

Y.Miake, KPS meeting at APCTP in Pohang, 200527

Surprise !
RHICSPSAGSEarly compilation

Y.Miake, KPS meeting at APCTP in Pohang, 200528

Large azimuthal anisotropy
N (" ) = N 0 {1+ 2v1 cos(" # $0 ) + 2v 2 cos(2(" # $0 ))}PHOBOS; nucl-ex/0406021!

 Larger in higher energies.
Scaling w. η-ybeam !?

 As high as 5%

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Failure of hadronic scenarios
M. Bleicher, H. Stocker Phys. Lett. B526 (2003) 309

 Hadronic scenario

underestimates v2 atRHIC.
v2 ~ 1 - 2 % System thermalized

early with themechanism other thanhadronic rescatterings.

Y.Miake, KPS meeting at APCTP in Pohang, 200530

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

v2"!
At low pt region, the ratio stays ~constantScaling with eccentricity shows v2 builds up at early stage

Y.Miake, KPS meeting at APCTP in Pohang, 200531

Success of hydrodynamics
PHENIX : P.R.L. 91, 182301 (2003)

Low pt region;v2(π) > v2(K) > v2(p)Good agreement withhydrodynamics


Deviations from the hydro athigher pt (> 2 GeV/c);v2(π,K) < v2(p)Y.Miake, KPS meeting at APCTP in Pohang, 2005

Very early thermalization (0.6fm/c) required !
 What brings the system
thermalization in such ashort time!
 Partonic degree offreedom

Order Reversed !
Other mechanism?

32Anisotropy at jet region
M. Gyulassy, I. Vitev and X.N. Wang, PRL 86 (2001) 2537

In higher gluon
density, larger energy
loss of partons Anisotropy athigh pt causedby the partonenergy loss.

Y.Miake, KPS meeting at APCTP in Pohang, 200533

What increases from SPS to RHIC
Phenix; NPA 757(2005)184

Filled ; RHIC
Open ; SPS

How we compare RHIC and SPS data; pt-integrated-v2?


Need to separete the effects; increase of <pT> and increase of v2
pt integrated-v2 includes the effect of increase of <pT>

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Saturation of v2 at the same pT
Phenix; P.R.L. 94, 232302(2005)

pT integratedv2 increases,
since <pT>
increases withenergy.

v2 increases up to 62 GeV, then saturate.
May be indication of softening of EOS.

Y.Miake, KPS meeting at APCTP in Pohang, 200535

2nd surprise; baryon dominancePhenix; P.R.L. 91(2003)172301

We had many reasons toconsider > 2GeV/c is the jetregion.
In peripheral, p/π ratio
similar to those in ee/pp
suggesting fragmentatonprocess.

Thanks to high resolution
Time-of flight detector
Y.Miake, KPS meeting at APCTP in Pohang, 2005

Fragmentation process
should show np < nπ as seenin ee/pp.

In central Au+Au, p/π ratio
increases with centrality,
suggesting other mechanism.
Quark Recombination Model(Quark Coalescence Model)
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Quark recombination model
meson

This process wins when thedistribution is very steep

w; universal
phase space
distribution of quarkbaryon
d 3N M
d 3N B
2 pt
E 3 " CM # w ( 2 ), E 3 " CB # w 3 ( pt 3 )
d p
d p
dN M
# (1+ 2v 2,q cos2" ) 2d"$ (1+ 4v 2,q cos2" )!

dN B# (1+ 2v 2,q cos2" ) 3d"$ (1+ 6v 2,q cos2" )v 2,M " 2v 2,q ( pt 2 ), v 2,B " 3v 2,q ( pt 3 )!

Other possible production
mechanism of high pt hadrons
than the frag.
Quarks, anti-quarks combine toform mesons and baryons fromuniversal quark distribution, w.
Mesons from 2 q with 1/2 of pT,baryons from 3 q with 1/3 of pT.
Bacause of the steep distr. of w,
this process wins at mid-pt.
Characteristic scaling features
expected.
Quark number scaling!
Y.Miake, KPS meeting at APCTP in Pohang, 200537

Quark number scaling
Presented by M. Lamont (QM04)

BaryonMeson

Quark number scaling clearly observed in v2.
 Distinct difference between Baryon Meson also seen in RCPY.Miake, KPS meeting at APCTP in Pohang, 2005

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Other particle species
Phenix; H. Masui @ QM05

 Once theR.P. isestablished,
the rest iseasier.

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Quark Number Scaling
Phenix; H. Masui @ QM05

 Quark numberscaling holds.
 Collectivity atpartonic level.

Y.Miake, KPS meeting at APCTP in Pohang, 200540

Electron and charm Origins of electronsγ conversion“photonic”
Dalitz decays of π0,η,ρ,ω, Photon conversions
π0 → γee
η → γee, 3π0ω → ee, π0ee



φ → ee, ηee

ρ → eeη’ → γee“non-photonic”
Semi-leptonic decays of heavy
flavored mesons

 Method of Analysis

Cocktail Photon converter Results are consistent

with those photonic +charm decays.

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Open charm production in AA
Phenix, PRL94(2005)082301

consistent with √s systematics and binary scaling.

Centrality dependence shows Nbinary scaling.
support charm contribution

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Info. of charm from electrons
Phenix, PRC72(2005)024901

 Measure v2 ofinclusive electrons
 Higher than pions inlow pt.
Inclusiveelectrons

Dalitz dominant.

 Lower in high pt?
Effect of charm?

non$#
N e [1+ 2v 2e cos2" ] = N e# [1+ 2v #2e cos2" ] + N enon$# [1+ 2v 2ecos2" ]#e= (N + N

measuredevaluated

Y.Miake, KPS meeting at APCTP in Pohang, 2005!

non$#enon$#
N e# v #2e + N enon$# v 2e)[1+ 2cos2" ]#non$#Ne + Neknown

obtained!

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Charm seems to flow!?
Phenix, PRC72(2005)024901

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



Data seem to favor
flow of the charm.
If so, thermalized &flowing charm
supports quarkcoalescence &formation of QGP.

Star, Nucl-ex/0411007
Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Summary of my talk

v2 is fun!


Establishment of R.P. is great !

v2 is even useful !
Sensitive to the early stage of collisions
Thermalization as early as 0.6 fm/c

Support the quark recombination model

Large azimuthal anisotropy cannot be created with hadronic
process.
Collectivity at parton level
Phenomenological, but universal quark distribution function!
statistical description of quarks QGP

Much fun to come

Even charm seem to flow !

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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One more thing,New text book for graduate students

Y.Miake, KPS meeting at APCTP in Pohang, 2005

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Backups

Npart vs Nbinary
Since nucleus is extended object,centrality of collision plays
important role.
 For comparison with pp or dAu also
for centrality study, we needscaling variables.
 Npart;ParticipantNbinary;Y.Miake, KPS meeting at APCTP in Pohang, 2005

# of participant nucleons
Particle production in hA is prop. toNpart, (Wounded-Nucleon Model)# of binary nucleon-nucleon collisions
Pass through at high energy.

Evaluation of Npart & Nbinary by
Glauber Model.

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Measured vs Real correlationNdG G (%=&1 + ) 2v n cos(n* )#d* 2+ ' n =1$

* = * lab " !realNdGG )&='1 + * 2v n# cos(n+ #)$d+ # 2, ( n =1%+ # = + lab " !measured

v "n = cos(n# ")= cos n(# lab $ %real $ %measured + %real )= cos(n# )cos(n(%measured $ %real )) + sin(n# )sin(n(%measured $ %real ))= G cos(n# )cos(n(%measured $ %real ))= v n cos(n(%measured $ %real ))&v n =v n"cos(n(%measured $ %real ))Y.Miake, KPS meeting at APCTP in Pohang, 2005v Measuredv Real =R.P. Resolution
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R.P. Resolution from sub-event
ΨA：R.P.angle of Sub-event A

ΨAΨB：R.P.angle of Sub-event B

ΨB Split 1 event to sub-event

A and B randomly Determine R.P. in eachsub-event ; ΨA ΨBcos(n(! A " !B ))= cos(n(! A " !real ) cos(n(!B " !real )) + (sin " term)= cos(n(! A " !real ) cos(n(!B " !real ))2# ( cos(n(! A " !real ) )Y.Miake, KPS meeting at APCTP in Pohang, 2005

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