1

Measurements of 1st, 2nd
and 3rd azimuthal anisotropy
in Cu+Au collisions
TAC seminar
May 26th 2016
Hiroshi Nakagomi
High Energy Nuclear Physics GroupOutline✓Introduction- Quark Gluon Plasma(QGP)- Azimuthal anisotropy- CuAu collisions✓Experiment/Analysis- PHENIX- Centrality, event plane- Simulation✓Results/Discussions- System size dependence- Rapidity dependence- Theory comparison✓Summary2

Introduction

Introduction3

Quark Gluon Plasma(QGP)

Introduction

4

QGP is a state of nuclear matter!
- extremely high temperature, density !
- consist of asymptotic free quarks and gluons!
- Almost perfect liquid
Predicted phase transition εc and Tc by Lattice QCD calculation!
- Tc ~ 170 MeV- εc ~ 1 [GeV/fm3]

Relativistic Heavy Ion Collider(RHIC)

PHENIX

Introduction

5Species Energies
Au+Au 200, 130, 62.4GeV39, 27, 22.4GeV
19.6 14.6, 7.7GeV
Cu+Cu 200, 62.4, 22.4GeV
U+U
193GeVCu+Au 200GeV
3He+Au 200GeV
d+Au
200GeV
p+Au
200GeV
p+Al
200GeVp+p510, 500, 200GeV
62.4GeV
Wide range of species and energies
Relativistic heavy ion collision
is unique tool to form QGP
Au+Au 200GeV@RHIC- εBj ~ 5 [GeV/fm3] > εc

Azimuthal anisotropy:Elliptic flow
Initial spatial anisotropy:ε2zzyyx

Introduction

6momentum anisotropy:v2xconverted thoughhydrodynamic expansion

particle production will havean elliptical azimuthal distribution.
- Non-isotropic pressure gradientSensitive to-initial condition(Glauber,KLN..etc.)-viscosity(η/s)

PRL 106.192301

Introduction

Azimuthal anisotropy:Directed,Triangular flow
Directed flow

7Triangular flow

Elliptic flow

Ψ3
Ψ2

Ψ1

Event by event, initial participant fluctuation can lead to-Directed particle production anisotropy v1-Triangular particle production anisotropy v3-v4, v5, v6

vn constrain initial condition & viscosity
Theory model consists ofinitial condition(collision)+hydro with viscosity(QGP)+
hadron gas
time
initial condition

Introduction

8v2, v3 theory comparison
Au+Au

PRL 107. 252301

viscosity

KLN+ 4πη/s=2
Glauber + 4πη/s=1
Glauber + 4πη/s=1

v2, v3 are sensitive to initial condition and viscosity of QGP- Theoretically, initial condition and viscosity have uncertainty->vn are good constraint of both of themIntroduction

9η dependence of v2 with different initial conditions
Glauber + Hydro

QGP only

Au+Au 200GeV

η=0(θ=π/2)

Rapidityη=-log(θ/2)

yη=-0.88(θ=3π/4)

η=0.88(θ=π/4)x

QGP+hadron fluid

KLN + Hydro

Au+Au 200GeV

Phys.Lett.B636:299-304✓v2(η) depends on initial condition- v2 with KLN > v2 with Glauber- v2 with Glauber reproduce data
zin mid-central collision- v2 with KLN reproduce datain central collision

Introduction 10Initial condition on target and projectile nuclei

PhysRevC.90.034915

εn (+η) = εn (-η)=✓Initial spatial anisotropy on target and projectile
nuclei are same event-Symmetric vn (η)εn (+η) = εn (-η)

vn (+η) = vn (-η)

Introduction 11

Initial condition on target and projectile nuclei

PhysRevC.90.034915

εn (+η) > εn (-η)>✓Initial conditions on target and projectile nuclei
are not same event
εn (+η) > εn (-η)
vn (+η) > vn (-η)✓Theory predicts the two different initial conditions
survives collective expansion

Cu+Au collision

Introduction 12

So far, vn have been studied in symmetric collision systems!
First asymmetric Cu+Au collisions were operated in 2012
Asymmetric initial condition provides!
- Different left/right pressure gradient, particle production….!
- Longitudinally, above characteristics could be different in Augoing/Cu-going !
-> Measurement of vn in asymmetric system could be good !
study of initial condition

13

My activity
M1~M2 (2011~2013)

D1(2013~2014)

Repair VTX @BNLJPS Spring & Fall (Talk)
QM2012 (poster)
ATHIC 2012 (Talk)AuAu flow analysis using VTX

Repair VTX @BNL
Shift taking & detector expert
for Run 13, Run14

D2(2014~2015)
D2(2014~2015)

D3(2015~2016)

CuAu flow analysis

QM2014(Talk)
JPS-DNP(Talk)
Shift taking & detector expert
for Run 14, Run15

QM2015(Poster)TGSW2015 (Talk)
WWND2016(Talk)
Submit CuAu flow paper to arXiv

D4(2016~)
D4 (2016~)

Domestic conference
Inter national conference
Hardware and shift

Experiment/Analysis 14

Experiment
Analysis

PHENIX detectors

Experiment/Analysis 15

Trigger, centrality, collision vertex-Beam Beam counter(BBC)(3<|η|<4)-Zero degree calorimeter-Shower max detector

Charged particle Tracking-Drift Chamber(DC) (|η|<0.35)- Momentum-Pad Chamber(PC) (|η|<0.35)- Hit position-Electro magneticcalorimeter(EMC) (|η|<0.35)- Hit position

Collision centrality
Spectator

Bbc Participant

Bbc

Experiment/Analysis 16✓Overlap zone of two nuclei- Impact parameter- Number of participant nucleons- Multiplicity✓ Experimentally, overlap zone isclassified by multiplicity in Bbc- Multiplicity in Bbc
Number of participant nucleonsSpectator∝∝ Overlap zone

10-20%
5-10%✓ Each percentile contains same
number of events- Most central collision 0 %- Most peripheral collisions 100%

0-5%

Bbc charge sumExperiment/Analysis 17

Anisotropy measurement via Event Plane method
Event plane(EP) method- one of the flow measurement methods- produced particles are measured with respect to EP- EP is the azimuthal direction most particles are emitted to- observed vn is corrected by EP resolution
obs< cos(n[n ]) >vn =Res{ obsn }Triangular moment
Elliptic moment
Directed momentyΨ1φix

Ψ2yφi

Ψ3yφixx

Experiment/Analysis 18

Event plane detectors and resolutions

PHENIX η acceptance

Event Plane detectors

Res{obsn,A } =⌦cos(n[obsn-6.5-4true])
n

↵

-3

-0.35 0.35

3

Smd η>6.5

Bbc 3<η<4Cnt |η|<0.35-Estimated from EP
correlations(3sub method)

Bbc -4<η<-3

Event Plane resolutiondN/dη
Smd η<-6.5- 2nd, 3rd Event plane- Bbc, Cnt- 1st Event plane- Bbc, Smd4 6.5ηvn measurement at Bbc(3<|η|<4 )✓vn is measured using 64 Bbc pmts

Experiment/Analysis 19pmt- Bbc can’t reconstruct tracks- pmt based vn include back ground✓Run Giant simulation with PHENIX configuration- pmt based vn -> track based vn

Simv
track
pmtn,input
vn= Rn ⇤ v n
Rn = Simvn,output✓Correction factor Rn- R2 : 0.73
- R3 : 0.65

✓Systematic study-dN/deta- pT spectra- vn(pt)- vn(eta)

Simvn,input
Input vn from particle simulation
Simvn,output
Output vn from Giant simulation

Initial spatial anisotropy
Glauber Monte Carlo simulation-Wood Saxon density profile p- collision is occurred, if d < ( nn /⇡)d:distance between nucleons
σnn:total cross section(pp collision)⌦ 2r cos[n(✏n =hr2 in,P P )]

↵⌦ 2
↵
1
1 r sin(n )[tan+ ⇡]n,P P =2nhr cos(n )iCentrality dependence of εnε2:CuCu>CuAu~AuAu
ε3:CuAu>AuAu

Experiment/Analysis 20

Results/Discussions 21

ResultsDiscussions-v1,v2,v3 at mid-η
v2,v3 at large-η
v1,v2,v3 theory comparison

Results/Discussions 22

Charged hadron v1

arxiv:1509.07784

Sizable v1 at mid-rapidity is observed for 10-50%
High pt particle are emitted to Au side
-Magnitude decreases from central tomore peripheral events-In peripheral events, Left/Right path
length becomes similar

high pT

low pT ?

Charged hadron v2

Results/Discussions 23

arxiv:1509.07784

Similar pT and centrality dependence of v2 as seenin symmetric collisions- Strong centrality dependence, magnitude increase
from central to peripheral

Charged hadron v3

Results/Discussions 24

arxiv:1509.07784

Similar pT and centrality dependence of v3 as seenin symmetric collisions- Weak centrality dependence, magnitude slightly increase
from central to peripheral

Results/Discussions 25

ε2Npart1/3 scaling
Sale with ε2Sale with Npart1/3

PhysRevC.92.034913✓v2 is scaled with ε2- Cancel initial geometry- ε2 is initial geometry- Strong Npart dependence✓v2 is scaled with ε2 Npart1/3- Cancel system size
- Npart1/3 is proportional tolength scale or expansion time

System size dependence of v2

Results/Discussions 26

arxiv:1509.07784

v2 for different systems has similar centrality and pT dependence
v2 in CuAu is always between those in AuAu and CuCu
Except in 0-10%, v2 are not ordered according to ε2

System size dependence of v2

Results/Discussions 27

arxiv:1509.07784

v2 scaled with ε2 (initial ellipticity)
For all centrality, order of magnitude of v2 is AuAu>CuAu>CuCu->System size contribute magnitude of v2

Scaling v2 with ε2*Npart(1/3)

Results/Discussions 28

arxiv:1509.07784

v2 is scaled with ε2Npart(1/3)-Npart(1/3) is proportional to length scale or expansion time
ε2Npart(1/3) scaling works well in CuAu!

System size dependence of v3

Results/Discussions 29

arxiv:1509.07784
arxiv:1509.07784

v3 for different systems has weak centrality dependence
v3 in CuAu is always bigger than those in AuAu
Unlike v2, v3 are ordered according to ε3->v3 doesn’t depend on system size

System size dependence of v3

Results/Discussions 30

arxiv:1509.07784

v3 scaled with ε3 forUnlike v2, scaled v3 are good agreement between AuAu and CuAu
-For 0-10%, the deviation is seen pT>(2.5GeV/c)

Scaling v3 with ε3*Npart(1/3)

Results/Discussions 31

arxiv:1509.07784

v3 is scaled with ε3Npart(1/3)-Npart(1/3) is proportional to length scale or expansion time
ε3Npart(1/3) scaling works well in v3!

Results/Discussions 32

ResultsDiscussions-v1,v2,v3 at mid-η
v2,v3 at large-η
v1,v2,v3 theory comparison

Results/Discussions 33

System size dependence of v2 at F/B

Centrality dependence of v2 is seen for all collision systems !
In CuAu collisions, !
-central & peripheral collisions: v2(Au-going) ~ v2(Cu-going) !
-mid-central collisions :v2(Au-going) > v2(Cu-going)!
->caused by different initial geometries in Au and Cu ?

Results/Discussions 34

Calculation of ε2,Au and ε2,Cu

ΨPP

ΨPPε2,Auε2,CuIn CuAu, ε2,Cu and ε2,Au calculated by Cu and Au nucleons separately.
- ε2,Cu and ε2,Au are determined with respect to ΨPP- ΨPP is determined by all participant nucleons !
- ε2,Au > ε2,CuAu > ε2,CuComparison of ε2 and v2

Results/Discussions 35

In CuAu, ε2,Cu and ε2,Au calculated by Cu and Au nucleons separately.
- ε2,Cu and ε2,Au are determined with respect to ΨPP- ΨPP is determined by all participant nucleons !
- ε2,Au > ε2,CuAu > ε2,Cu-> v2,Au > v2,Cu !
-> Target nucleons geometry and projectile nucleons geometry
survive hydrodynamic expansion

Results/Discussions 36

Scaling with ε2,Cu , Npart,Cu and ε2,Au , Npart,Auv2 scaled with ε2-In CuAu, v2 is scaled with ε2,Au and ε2,Cu separately- v2(Cu-going) in CuAu : consistent with those in AuAu and CuCu !
- v2(Au-going) in CuAu : consistent with those in AuAu and CuCu for lower Npart
inconsistent with those in AuAu for higher Npart
v2 scaled with ε2Npart(1/3)- In CuAu, Npart,Au(1/3) and Npart,Cu(1/3) are calculated separately- In AuAu,CuCu, Npart/2 is used.!

-v2(Au-going) are not consistent for higher Npart

Results/Discussions 37

System size dependence of v3 at F/B

Weak centrality dependence of v3 is seen for all collision systems !
AuAu:same centrality dependence as seen mid η
CuAu: v3 decrease as centrality decrease
In CuAu collisions, v3(Au-going) > v3(Cu-going) for all centrality bins !
-> Like v2, the different initial geometry cause the different v3 ?

Results/Discussions 38

System size dependence of v3 at F/B

In CuAu, ε3,Cu and ε3,Au calculated by Cu and Au nucleons separately.
- ε3,Cu and ε3,Au are determined with respect to ΨPP- ΨPP is determined by all participant nucleons !
- ε3,Au > ε3,CuAu > ε3,Cu-> v3,Au > v3,Cu !
-> Target nucleons geometry and projectile nucleons geometry
survive hydrodynamic expansion

Results/Discussions 39

Scaling with ε3,Cu , Npart,Cu and ε3,Au , Npart,Au

v3 scaled with ε3- v3(Au-going) and v3(Cu-going) are consistent with each otherbut in consistent with those in AuAu for higher Npart- v3(Au-going) and v3(Cu-going) are inconsistent for lower Npart
v3 scaled with ε3Npart(1/3)- In CuAu, Npart,Au(1/3) and Npart,Cu(1/3) are calculated separately !
- In AuAu, Npart/2 is used !
- v3(Cu-going) is inconsistent with those in AuAu and v3(Au-going)Results/Discussions 40

Results
Discussions-v1,v2,v3 at mid-η
v2,v3 at large-η
v1,v2,v3 theory comparison

Results/Discussions 41

MC-Glauber E-by-E hydro v1(pt) at mid-η
arxiv:1509.07784

In hydro calculation,-More low pT , particles are emitted to Cu side
-More high pT, particles are emitted to Au side
-Ideal hydro reproduce experimental data wellResults/Discussions 42

MC-Glauber E-by-E hydro v2, v3 at mid-η

arxiv:1509.07784

For both centrality, both value of η/s agree with data

Parton cascade and hydro v2(η)

AMPT(parton cascade and hadron cascade)and Ideal hydrodynamic predict different v2 value
in Au going and Cu-going side->Theory model predict different initial geometry
survive collective expansion
In peripheral and central collisions,- data and hydro calculation show v2 (Au-going)~ v2(Cu-going)- AMPT show v2 (Au-going) > v2(Cu-going)->Hydro calculation reproduce the ratio ofv2 (Au-going) and v2(Cu-going)

43

Parton cascade and hydro v3(η)

Unlike v2-data and AMPT show
v3 (Au-going) > v3(Cu-going)-Hydro calculation showv3(Au-going) ~ v3(Cu-going)->Hydro calculation doesn’t reproduce theratio of v3 (Au-going) and v3(Cu-going)

44

Summary✓v2, v3-mid-η

v2 and v3 are similar centrality and pT dependence as
seen in symmetric collisions
Empirical scaling of ε2Npart1/3 works v2 in CuAu, CuCu, AuAu
Empirical scaling of ε3Npart1/3 works v3 in AuAu, CuAu

- Large-ηv2, v3 show different magnitude at forward/backward η originatingfrom different initial participant anisotropy in Cu and Au nuclei
Empirical scaling of εnNpart1/3 doesn’t work well
- Theory comparison (mid-η)
Hydro calculation needs η/s(0.08-016) to reproduce v2, v3- Theory comparison(large-η)
Ideal hydro and AMPT doesn’t agree with magnitude of v2, v3
Ideal hydro reproduce the ratio of v2(Au) and v2(Cu)
But Ideal hydro doesn’t show the difference of v3(Au) and v3(Cu)✓-v1High pT particles are emitted to Au side
Ideal hydro calculation agree with v145

Back Up46

Charged pion v2, v3 in AuAu

March 2nd 2016 WWND H.Nakagomi

47

pi, K, p flow

Introduction 48

arXiv:1412.1038

v2,v3 have similar particle dependence
v3 scaled with nq3/2

Introduction 49

Scaling property : quark number scaling

arXiv:1412.1038

v2,v3 have similar particle dependence
v3 scaled with nq3/2

Track identification at CNT(|η|<0.35)

Experiment/Analysis 50

TOF.E and TOF.W are used
-TOF.E : Scintillation counter 130ps-TOF.W : MRPC 95ps

Time of flight method
2m =p2✓ctL◆2!

1

TOF.E positive particles

Charged pi,K,p-pi/K up to 3GeV-K/p up to 4GeV

Mass square

m:particle mass, p:momentum, L:flight passc:light velocity, t:time of flightproton
KaonpionmomentumResults/Discussions
51

Results&Discussions-System size dependence
PID vnRapidity dependence
Theory comparison

Identified particle v2 in Cu+Au

Results/Discussions 52

arxiv:1509.07784

Mass ordering at low pT for v2 for all centralities
Baryon and meson splitting at mid-pT is seen

Identified particle v1, v3 in Cu+Au

Results/Discussions 53

arxiv:1509.07784

Same particle dependence of v3 is seen as seen in v2
Mass ordering is also seen for v1- At 1<pT<2.5GeV, Mass ordering is seen
- At low and high pt region, baryon v1 ~ meson v1-Not same trend as seen in v2, v3

Quark Number Scaling of v2

Quark Number Scaling works v2 in CuAu
54

Quark Number Scaling for v3

Quark Number Scaling work v3 in CuAu55

Npart1/3 is proportional system size

56

annurev.nucl.55.090704.151533

57

dif eCu, eAu
same NpartCu and NpartAu

58

dif eCu, eAu
same NpartCu and NpartAu

Scaling with ε3,CuAu and Npart, CuAu

Results/Discussions 59

v3 scaled with ε3-v3(Au-going) is not consistent with AuAu v3 !
-v3(Cu-going) is consistent with AuAu v3!
v3 scaled with ε3Npart(1/3)-v3(Au-going) is not consistentScaling with ε2,CuAu and Npart, CuAu

Results/Discussions 60

v2 scaled with ε2,AB- Scaled CuCu and AuAu v2 show universal curve-v2(Au-going) is consistent with CuCu, AuAu v2 !
-v2(Cu-going) is not consistent with CuCu, AuAu v2 except for
peripheral !
v2 scaled with ε2Npart(1/3)-v2(Cu-going) are not consistent for mid-central collisions

Comparison to AMPT v2
arxiv:1509.07784

AMPT with 3mb reproduce v2-In 0-30%, up to 2GeV-In 30-60%, up to 1GeVMarch 2nd 2016 WWND H.Nakagomi

61

Comparison to AMPT v3
arxiv:1509.07784

AMPT with 3mb reproduce v3-In 0-30%, up to 2GeVMarch 2nd 2016 WWND H.Nakagomi

62

Azimuthal anisotropic flow
In relativistic heavy ion collisions, the azimuthal distributionof produced particles is anisotropic

Anisotropic initial overlap region(εn)
If λ≪R, pressure gradient ΔP becomes anisotropic.
λ=Mean free path R=Size of the system
Less particle production
Smaller pressure gradientAnisotropic particle emission(vn)Expansion to short axis direction
by anisotropic pressure gradientMagnitude of azimuthal anisotropic !
particle emission is evaluated asΨnLarger pressure gradientMore particle emissionvn=<cos(n[ϕ-Ψn])> ellipticity with respect to Ψn63

Flow in symmetric collisions system

PRL 107,252301 

H-31 Poster, Reynollds 64Experiment/Analysis 65

3sub method

PHENIX η acceptance

Event Plane detectors< cos(n[obsn,Aobs
obsn,B ]) >=< cos(n[ n,Aobs=< cos(n[ n,A= Res{3truetrueobsn + nn,B ]) >truetruen ]) >< cos(n[ nn,A }Res{n,B }Smd η>6.5-Estimated from EP-6.5 -4-3-0.35 0.35
correlations(3sub method)
sobsobs ]) >< cos(n[ obs<cos(n[n,An,Bn,Aobs
Res{ n,A } =obs ]) >< cos(n[ obsn,Bn,CBbc 3<η<4Cnt |η|<0.35

Bbc -4<η<-3Event Plane resolutiondN/dη
Smd η<-6.5- 2nd, 3rd Event plane- Bbc, Cnt- 1st Event plane- Bbc, Smd4 6.5

ηobs ]) >n,Cobsn,B ]) >