Study*Of*Iden:ﬁed*Par:cle*Higher*Order*Azimuthal*
Anisotropy*At*RHIC%PHENIX*Experiment



RHIC%PHENIX* 

Sanshiro*Mizuno*
for*PHENIX*collabora:on*
University*of*Tsukuba,*RIKEN*
29a%HA%12*
13/03/29

JPS*2013*in*HIROSHIMAAzimuthal*anisotropyEvent*Plane(Ψn)

Ψ4
Ψ3
Ψ2

Because*higher*harmonics*ﬂows*are*more*sensi:ve*to*ini:al*geometry*and*η/s*of*
QGP,*they*are*studied*ac:vely*in*order*to*determine*the*calcula:ng*model*of*ini:al*geometry*and*constrain*η/s.*

13/03/29

JPS*2013*in*HIROSHIMACharged*parHcle*azimuthal*anisotropy P.R.L.*107,*252301(2011)

v2*
*v3*
*v4

v3*and*v4*have*weak*centrality*dependence*while*v2*has*strong*dependence.*
It*indicates*v3,v4*are*created*by*the*ini:al*geometry*deforma:on.*

13/03/29

JPS*2013*in*HIROSHIMAThe*number*of*consHtuent*quark*scaling*of*v2
v2

π+πU*v2/nq

*K+KU**pp*
PHENIX*
PreliminaryKET =pT[GeV/c]

KET/nq[GeV]

q

m20 + p2T

m0v2*has*mass*ordering*in*low*pT*and*meson/baryon*dependence*higher*pT*region.*v2(KET)*is*well*scaled*by*the*number*of*cons:tuent*quarks,*less*than*1.0[GeV].*
It*is*known*that*hydrodynamic*model*can*describe*v2*in*low*pT*region.*

13/03/29

JPS*2013*in*HIROSHIMAData*set*and*PHENIX*detector
Time*of*Flight*|η|*<*0.35

ReacHon*Plane*detector*
1.0*<*|η|*<*2.8
Data*set*is*Au+Au*200*GeV*taken*in*2007*period.**
In*order*to*reduce*the*eﬀect*of*non%ﬂow,*the*detectors*which*measure*Event*Plane**
and*emiced*par:cle*angles*should*have*some*distances.*

13/03/29

JPS*2013*in*HIROSHIMAvn*of*charged*π,K,p*result
200 GeV Au+Au 0-50%v2{Φ2}

0.2

π+πK+Kpp

0.15

Vn0.2

PHENIX Preliminaryv3{Φ3}x1.5

0.2

v4{Φ4}x1.50.2

v4{Φ2}x5.0

 -

0.15

0.15

0.15

0.1

0.1

0.1

0.1

0.05

0.05

0.05

0.05

0000:pT correlated sys. of π±01234012340123401234pT [GeV/c]

Azimuthal*anisotropy*has*par:cle*species*dependence,*which*are*mass*dependence**
and*meson/baryon*dependence.*
Higher*harmonics*are*created*from*ini:al*geometry*deforma:on,*they*are*aﬀected**by*the*eﬀect*of*QGP*expansion.*

13/03/29

JPS*2013*in*HIROSHIMAPIDed*vn*with*ﬁne*centrality*bin

VnAu+Au sNN=200 GeV PHENIX Preliminary
0.3
0.25
0.2
0.15
0.1
0.05
00.3 00.25
0.2
0.15
0.1
0.05
000.3
0.25
0.2
0.15
0.1
0.05
00.3 00.25
0.2
0.15
0.1
0.05
0v 2{Φ2}π+πK+Kpp

0-10%-1 }x2, 2v 3{Φ
31 }x1.8,2v 4{Φ
41 }x5.0,2v 4{Φ
2013/03/29

12

0.3
0.25
0.2
0.15
0.1
0.05
03
40
0-10% 0.3
0.25
0.2
0.15
0.1
0.05
03
40
0-10% 0.3
0.25
0.2
0.15
0.1
0.05
03
40
0-10% 0.3
0.25
0.2
0.15
0.1
0.05
03

40

10-20% 0.3

12

1

2

12

1

2

0.2
0.15
0.1
0.05
03
40
10-20% 0.3
0.25
0.2
0.15
0.1
0.05
03
40
10-20% 0.3
0.25
0.2
0.15
0.1
0.05
03
40
10-20% 0.3
0.25
0.2
0.15
0.1
0.05
0340



20-30% 0.3:p correlated sys. 0.25of π±T 121212

120.25
0.2
0.15
0.1
0.05
03
40
20-30% 0.3
0.25
0.2
0.15
0.1
0.05
03
40
20-30% 0.3
0.25
0.2
0.15
0.1
0.05
03
40
20-30% 0.3
0.25
0.2
0.15
0.1
0.05
0pT [GeV/c]

JPS*2013*in*HIROSHIMA

340

30-50%

12

330-50%412

330-50%4

12330-50%41234Break*the*number*of*consHtuent*quark*scaling
200 GeV Au+Au 0-50%

0.1 v {Φ }/n22q0.1 v {Φ }/n x1.5
44q0.1 v {Φ }/n x5.0
42q0.08  

0.08

0.08

0.06

0.06

0.06

0.04

0.04

0.04

0.04

0.02

0.02

0.02

0.02

0000π+π-0.08

V n/nqPHENIX Preliminary

0.1 v {Φ }/n x1.5
33qK+Kpp

0.06-

:KET correlated sys. of π±-0.02

00.5

11.5-0.02
2 00.5

11.5-0.02
2 00.5

11.5-0.02
2 00.5

11.5

2KET/nq [GeV]While*v2*is*well*scaled,*higher*harmonics*have*devia:on.*The*scaling*for*all*harmonics*and*par:cle*species*are*searched.*

13/03/29

JPS*2013*in*HIROSHIMAvn1/n*scaling*among*harmonics
arXiv:1105.3782(2011)

20*U*30%*

0.3

1v2*
v3*
v4

0.2

0.5

2

v21/2*
v31/3*
v41/4

1.5
10.1

v3(1/3)/v2(1/2)*
v4(1/4)/v2(1/2)

0.5

00

123pT[GeV/c]

000

123pT[GeV/c]

0123pT[GeV/c]

Charged*par:cle*vn(1/n)*is*scaled*beyond*harmonics.*
vn1/n/v21/2*ra:o*shows*ﬂat*dependence*on*pT.**

v2(KET/nq)/nq**U>**(v2(KET/nq)/nq)n/2*U>**vn(KET/nq)/nqn/2
13/03/29

JPS*2013*in*HIROSHIMAModiﬁed*the*quark*number*scaling
200 GeV Au+Au 0-50%

0.1 v {Φ }/n2/2
22q0.1 v {Φ }/n4/2x4.0
44q

0.1 v {Φ }/n4/2x15
42q0.08  

0.08

0.08

0.06

0.06

0.06

0.04

0.04

0.04

0.04

0.02

0.02

0.02

0.02

0000

π+π-n/20.08

V n/nqPHENIX Preliminary

0.1 v {Φ }/n3/2x2.5
33qK+Kpp0.06-

:KET correlated sys. of π±-0.02

00.5

11.5-0.02
2 00.5

11.5-0.02
2 00.5

11.5-0.02
2 00.5

11.5

2KET/nq [GeV]

Modiﬁed*scaling*works*well*for*all*harmonics.**
v2(KET/nq)/nq**%>**(v2(KET/nq)/nq)n/2*%>**vn(KET/nq)/nqn/2

13/03/29

JPS*2013*in*HIROSHIMA(a)*:*v2(KET)/nq*(b)*:*vn1/n*scaling*(a)+(b)*:*vn(KET)/nqn/2

Summary
v2,v3,v4,v4(Ψ2)*of*charged*π,K,p*are*measured.*It*is*found*that*there*are*mass*ordering*in*low*pT*and*meson/baryon**dependence*larger*than*2*[GeV/c]*as*v2.***
The*number*of*cons:tuent*quarks*scaling*are*tested.*
The*scaling*which*works*well*for*v2(KET),*doesn’t*work*for*vn(KET)n>2.*
Modiﬁed*scaling*vn(KET/nq)/nqn/2*is*checked*to*work*well*for*all*harmonics.*

Next*step
vn*of*φ*will*be*measured,*because*it*is*meson*and*heaver*than*proton.*And*scaling*test*will*be*operated.**
vn*of*photon*will*be*measured.*

13/03/29

JPS*2013*in*HIROSHIMA13/03/29

JPS*2013*in*HIROSHIMABACK*UP
13/03/29

JPS*2013*in*HIROSHIMABlast*Wave*Model*

v3
0.1

QGP*valuables*are*extracted*by*comparison*with*Blast*Wave*model,*which*can*describe*ﬁnal*state**
from*informa:on*at*freeze%out*such*as*temperature.*0.0500

π+πU
K+KUpp***

123pT[GeV/c]

Tf*:*temperature*ρ(φ,*r)*=*ρ0(1+2ρncos(nφ))*r*ρ0*:*average*velocity*
αT(φ,*r)*=*(pT/Tf)sinh(ρ(φ,*r))*ρn*:*velocity*anisotropy*βT(φ,*r)*=*(mT/Tf)cosh(ρ(φ,*r))********(anisotropy*in*velocity)*
sn*:*geometrical*anisotropy********(like*eccentricity*at*freezeUout)
JPS*2013*in*HIROSHIMA
13/03/29The*number*of*consHtuent*quark*scaling*of*v2
P.R.L.91,*182301
v2

v2/nq

π+πU
K+KU
pp*

*

*

pT[GeV/c]

PHENIX*
PreliminaryKET/nq[GeV] KET =qm20 + p2T

m0v2*has*mass*ordering*in*low*pT*and*meson/baryon*dependence*higher*pT*region.*v2(KET)*is*well*scaled*by*the*number*of*cons:tuent*quarks,*less*than*1.0[GeV].*
It*is*known*that*hydrodynamic*model*can*describe*v2*in*low*pT*region.*

13/03/29

JPS*2013*in*HIROSHIMAFreezeUout*parameters*extracted*by*comparison*with*BW

120
100

100
0.8800(c)2040

spectra+v4*

0.88060 0(d)0.1 0.1

2040

600.1

*

0.05

0.05 0.05

00.05

0 002040

60002040

sn

spectra+v4(Ψ2)

sn*geometrical*
anisotropyρn*velocity*ρnanisotropy

0.1

ρ0140

1.2
1.2(b)
v2spectra+v+spectra
v3+spectra 2*
140 PHENIX*Preliminary
v4*+spectra
v4spectra+v{Φ 2}+spectra3
1 120
1<ρ0>*
average*velocity

Tf*
Tf [MeV]temperature

(a)

60

Centrality %ρn*behavior*is*similar*to*centrality*dependence*of*charged*par:cle*vn.*s3*and*s4*are*smaller*than*s2*but*not*zero*in*non%central.

13/03/29

JPS*2013*in*HIROSHIMASummary
v2,v3,v4,v4(Ψ2)*of*charged*π,K,p*are*measured.*It*is*found*that*there*are*mass*ordering*in*low*pT*and*meson/baryon**dependence*larger*than*2*[GeV/c]*as*v2.***
The*number*of*cons:tuent*quarks*scaling*doesn’t*work*for*vn(KET)n>2.*
Modiﬁed*scaling*vn(KET/nq)/nqn/2*is*checked*to*work*well*for*all*harmonics.***
QGP*at*freeze%out*is*parameterized*by*comparison*with*Blast*Wave*model.*It*is*found*that*ρn(velocity*anisotropy)*behavior*looks*like*charged*par:cle**vn*behavior.*s2(Geometry*anisotropy)*is*larger*than*s3*and*s4.*
There*are*geometrical*anisotropy*at*freeze%out.*13/03/29

JPS*2013*in*HIROSHIMARxN*:*1.0*<*η*<*2.8*
MPC*:*3.1*<*η*<*3.7*
BBC*:*3.1*<*η*<*3.9

Event*Plane*resoluHon
1Res{Ψ2}

Res{Ψ2}

Res{Ψ3}

Res{Ψ3}
0.4

0.30.2

Res{Ψ4}Res{Ψ4}
RxN All combined
MPC South&North
BBC South&North

0.6

4th Res{Ψ2}4th*Res{Ψ2}

0.4

0.5
0.2

000204060

Centrality[%]

0204060

Centrality[%]⌫n,true = ⌫n,obs /Res{ n }Res{ n } =< cos {n( n,real0.10.2000204060

Centrality[%]0204060

Centrality[%]n,obs )} >Res{Ψn}*is*es:mated*from*correla:on*observed*Ψn.*
Because*RxN*has*best*resolu:on,*Ψn*measured*by*RxN*is*used*in*this*analysis.

13/03/29

JPS*2013*in*HIROSHIMATimeUOfUFlight*detector
Par:cle*species*are*iden:ﬁed*by*TOF*method.*
AGEL*and*RICH*are*used*to*separate*them*ﬁner.

momentum*x*chargemass2*distribuHon*via*TOF.E

TOF.E*detector

13/03/29

π KaonJPS*2013*in*HIROSHIMA

protonmass2



Hydrodynamic*model*describe*idenHﬁed*parHcle*valuable*
P.R.L.91,*182301

pion(x10)*
kaon(x5)*
protonSpectra*and*PID*v2*have*mass*ordering*in*low*pT*region,*and*they*are*known**
that*they*can*be*described.*
QGP*parameters*are*extracted*by*comparison*with*model*calcula:ng.

13/03/29

JPS*2013*in*HIROSHIMAs2*behavior*is*similar*with*HBT*analysis
Takafumi*(QM2012)

εfinalsn

HBT*(2nd*order*geometrical*anisotropy)

BW
n=2*:*spectra+v2**

0.5+ +Au+Au 200GeV π π +π- π+

n=3*:*spectra+v3*+-Au+Au 200GeV K K +K K

0.4-STAR (PRL,93,12301)*

εinitial = εfinal

n=4*:*spectra+v4*

0.3*sn*=*εn*

PHENIX Preliminary

0.20.1εn000.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

εinitials2*behavior*is*similar*to*HBT*result.*
13/03/29

JPS*2013*in*HIROSHIMAComparison*model
π*:*0.5*U*1.13[GeV/c]*
K*:*0.4*U*1.40[GeV/c]*
within*ﬁkng*range*
Centrality*0U50%*
extrapolate*range
p*:*0.6*U*1.70[GeV/c]*410
spectra* 0.2 v2(Ψ2)*
v3(Ψ3)x2.3* v4(Ψ4)x2.3* v4(Ψ2)x6.0*
1020.1

110-2 00

113/03/29

20

12 0

12 0pT[GeV/c]*

JPS*2013*in*HIROSHIMA

12 012The*number*of*consHtuent*quark*scaling*of*v2
v2

v2/nq

pT[GeV/c]

P.R.C*85,*064914

KET/nq[GeV]

v2*has*mass*ordering*in*low*pT*and*meson/baryon*dependence*higher*pT*region.*v2(KET)*is*well*scaled*by*the*number*of*cons:tuent*quarks,*less*than*1.0[GeV].*KET =q13/03/29

m20 + p2Tm0JPS*2013*in*HIROSHIMAarXiv:1105.3782*
P.R.B*642*227U231

Scaling

vn/v2n/2*is*scaled.

13/03/29

JPS*2013*in*HIROSHIMAComparison*iniHal*geometry*anisotropy
0.5

ε2*0.45

*
*

0.4

ε3*

0.35

*
*

0.3

ε4*

0.25

*
*

ε4{Ψ2}

0.2
0.15
0.1
0.05
0050

100

150

200

250

300

350400

Npart

Eccentricity*is*calculated*by*Glauber*model.*ε2*Npart*dependence*is*larger*than*higher*order.*This*dependence*resembles*vn*centrality*dependence.*

13/03/29

JPS*2013*in*HIROSHIMAv21/2*v31/3*
v41/4

Charged*parHcle*scaling

10*U*10%

10*U*20%

20*U*30%

v3(1/3)/v2(1/2)*
v4(1/4)/v2(1/2)

30*U*40%

40*U*50%

0.502012

3012301230

1230

1231230

1230

12

30

12

30

12

3

1.5
10.50pT[GeV/c]

Charged*par:cle*are*scaled*by*vn1/n*beyond*harmonics.*

13/03/29

JPS*2013*in*HIROSHIMAv2(KET)/nq*is*scaled**
vn1/n*is*able*to*be*scaled*to*v21/2**So,*vn(KET)*is*scaled*by*v2(KET)n/2**v2(KET/nq)/nq**%>**v2n/2(KET/nq)/nqn/2*%>**vn(KET/nq)/nqn/2

13/03/29

JPS*2013*in*HIROSHIMAEvent*Plane

13/03/29

JPS*2013*in*HIROSHIMAP.R.L.*109,*122302(2012)

v2*of*photon*result

pT[GeV/c]

Because*photon*doesn’t*correlate*with*QGP,*it*can*provide*ini:al*informa:on.*v2*of*direct*photon*is*as*large*as*ones*of*hadron*in*low*pT.*
What*causes?**
If*it*is*aﬀected*by*Magne:c*ﬁeld*created*by*collision,*v3*may*have*0.*

13/03/29

JPS*2013*in*HIROSHIMA110110

1000.6 100

9090800.580100200300

Npart400 00.1 (c)100200300

Npart400(d)0.1 0.1

BW Fit0.1

ρnsn = εnv2+spectra
v3+spectra
v4+spectrav4{ψ }+spectra 0.05 0.05

0.05

0.05

2000
00.1

<εn>

0.2

000.1

<εn>

JPS*2013*in*HIROSHIMA

sn*geometrical*
anisotropyρn*velocity*
anisotropy

0.6

0.5
013/03/29

0.7

snTf [MeV](b)

0.7 120

<ρ>

(a)

120

<ρ0>*
average*velocityTf*temperature

Model*comparison

0.2



Event*Plane*calculaHon

2nd*Event*Plane*correlaHon
RxN(In)S&N*
RxN(Out)S&N*
RxN(In+Out)S&N

13/03/29 Centrality[%]

ReacHon*Plane*detector(RxN)*
Inner**:*1.5*<*|η|*<*2.8*
Outer*:*1.0*<*|η|*<*1.5*
2nd*Event*Plane*resoluHon

Res{Ψn}

<cos{n(Ψn,A%Ψn,B)}>

Event*Plane*is*calculated*by*three*steps.*
1.*gain*correcHon*
2.*reUcentering*
3.*ﬂarening*

JPS*2013*in*HIROSHIMARxN(In)S+N*
RxN(Out)S+N*RxN(In+Out)S+N
Centrality[%]



13/03/29

JPS*2013*in*HIROSHIMAEvent*Plane*CalculaHon
1.*Gain*correc:on*φi*wi*=*adci/<adc>**Qx,n*=*Σwicos(nφi)*,*Qy,n*=*Σwisin(nφi)**Φn*=*atan2(Qx,n*,*Qy,n)*/*n*2.*Re%centering**Q’x,n*=*(Qx,n%<Qx,n>)/σQx,n*,*Q’y,n*=*(Qy,n%<Qy,n>)/σQy,n**Φ’n*=*atan2(Q’x,n*,*Q’y,n)*/*n*
3.*Flacening**nΦ”n*=*nΦ’n*+*Σ2/i{%<sin(inΦ’n)>cos(inΦ’n)+<cos(inΦ’n)>sin(inΦ’n)}*

2012/11/15

reac:on*plane*detector(RxN)******inner*1.5*<*|η|*<*2.8*
Sanshiro*Mizuno*ATHIC2012*****outer*1.0*<*|η|*<*1.5* Comparison*scaling*among*diﬀerent*energy
Pb+Pb*2760GeV

Au+Au*200GeV

Au+Au*39GeV

! Proton*is*shised*
Is*the*strength*of*radius*expansion*related?
2012/11/15

Sanshiro*Mizuno*ATHIC2012

Fit*funcHon*dependence*w.r.t.*v2
20*U*30*%*2.5<pT<3.0*[GeV/c]
1.04

data*/*N0[1+2v2cos{2dφ}+2v4cos{4dφ}]*data*/*N0[1+2v2cos{2dφ}]*Black*line*is*1+2v4cos{4dφ}**
These*v2*are*consistent*within*3%.*
1.05

1.03
1.02
1.01
10.99
0.98
0.97
0.96
0.95
00.2

0.4

0.6

0.8

11.2

1.4

dφ*=*φ*%*Ψ2
v2*extracted*by*v2*and*v4*
v2*extracted*by*v2*only*v4(Ψ2)

0.25
0.2
0.15
0.1

v2(ﬁred*by*v2*only)/v2(ﬁred*by*v2+v4)
1.1

1.05

10.05
0.95
0-0.05012

34567

pT[GeV/c]

13/03/29

8910

0.9
0123

4567pT[GeV/c]
JPS*2013*in*HIROSHIMA

8910