Understanding of Radial and Elliptic expansion
with Quark number scaling
and Blast wave modelin 200GeV Au+Au at RHIC-PHENIX
Yoshimasa Ikeda
for the PHENIX collaboration(Riken)Azimuthal anisotropy
Spatial anisotropy in noncentral collision provides
azimuthal anisotropy ofparticle emission.
The large anisotropy is anevidence of the formation ofa hot and dense partonicmatter.

dN∝12 v 2 cos 2Φ−Ψ dΦΨ : reaction plane angle2

Motivation of v2 measurement
Large v2 was observed inRHIC.
The values agreed withhydro-dynamical models.
It suggests rapid
thermalization and quarkflow.
The v2 values aredifferent for each particle.
3●

Motivation of measurementof PID hadron v2

Comparison with rare particle.
●●●

Deuteron that is formed by p-n (or 6 quarks) shouldhave higher v2 than proton.
Φ meson have small cross section for hadronscattering. The mass is similar to proton or Λ rather
than π or K.
arXiv:0710.5795

The slope difference by mass can be used to BW
model calcuration.

4

Motivation of RP detector●●

Measurement of more precise v2 is expected.
Poor reaction plane resolution was a major
limiting factor of PHENIX v2 measurement ofrare probes such as d, Φ.

Reaction Plane Detector (RxP) has been
constructed and installed to PHENIX in 2007.
● Reaction plane resolution of <cos2 ⊿ψ> ~0.75
for minimum bias Au+Au collisions

5Reaction Plane Detector
The reaction plane detector wasinstalled just before Run7 (2007).

35cm

Collision piont

6

Res =〈 cos2  real− observe 〉Reaction Plane Resolution
RxP (Run7)
BBCthe reaction planeresolution was improvedby a factor of two.
●The observed v2
strength is only lessthan 40% of its realvalue.

v 2 observe=v 2 real×〈cos2  real−observe 〉11 v 2~×〈cos 2 real −observe 〉  N

7

PID for π, K and proton
πKTOF.Wp

M2 [GeV2/c4]
pT = 3 - 6GeV/c

TOF.W was installed
before Run7, too

Only TOF.W
ACC photon >8
ACC photon <48

M2 [GeV2/c4]

PID for deuteron
πKp

TOF.W
pT = 1 – 2 GeV/cdM2 [GeV2/c4]
TOF.W
Green = red(gauss) + blue(exp)pT = 4 - 5 GeV/cπKTOF.E
pT = 1 – 2 GeV/cd9

M2 [GeV2/c4]

M2 [GeV2/c4]

PID for Λ and ΦπKpPbSc (EMC)
pT = 1 – 2 GeV/cd
M2 [GeV2/c4]

EMC + TOF.E
KK continuum

EMC + TOF.E
p-π continuum
10

Invariant mass [GeV/c2]

Invariant mass [GeV/c2]

v2 on PHENIX-Run7
●

Run7

●

Centrality 0 - 60%
PHENIX. PRL. 99, 052301 (2007)

Run4

Centrality 20 - 60%●

Run7 have 2 timesof RP resolution
and 4 times ofstatistic from Run4.
TOF.W and ACC
work well, too.
pT range isextended to pT = 6GeV/c.
11Comparison with last onev2deuteron● Run7■ Run4

Φ● Run7+ Run4

pT [GeV/c]●pT range is extended to pT ~ 4.5 GeV/c.
12

Nucleon number scalingv2

Centrality 20 – 60%
× proton■ deuterond2

arXiv:nucl-th/0312081

Run7
preliminaryCentrality 0-60%)■ddTv ~2 v , p ~2 p●

●pT[GeV/c]

p2

●

●pT

The peak of d v2 isexpected at pT=6GeV/c.
D v2 and p v2 are very
similar on pT/A scaling.
It means p v2 and n v2
are very similar.
Coalescence of p-n or 6quarks?
13

v2/A

Nucleon number scaling
Centrality 20 – 60%
× proton■ deuterond2

arXiv:nucl-th/0312081

Run7
preliminaryCentrality 0-60%)■ddTp
Tv ~2 v , p ~2 p●

●pT/A[GeV/c]

p2

●

●

The peak of d v2 isexpected at pT=6GeV/c.
D v2 and p v2 are very
similar on pT/A scaling.
It means p v2 and n v2
are very similar.
Coalescence of p-n or 6quarks?
14

v2 as pT for 6 particles●●●D v2 is higher than p v2
at pT> 3 GeV/c
Λ v2 similar to p v2
Φ v2 similar to meson(π or K) rather thanbaryon (p or Λ) at midpT range (pT= 2 – 5GeV/c).
15

KET scaling●

The pT shift depend on
mass is rejected on KET●●●

KE T =M T −M 0= M P −M 0202
T

They are consistent
between mesons orbaryons.
The values are
determined by centrality,
KET and quark number.

Meson line and baryon
line approach at high16KET.

Quark number and KET scaling
●

●

●0.8

Consistent for allparticles on KET andquark number scalingat KET/nq<0.8GeV.
They deviate at highKET/nq
This indicate a changeof particle and v2
production mechanism.
17

Function of Blast wave for spectra
dNpdp=dx
W
BesselK1BesselI0∫TT▼πCentrality 20-60%
 −
▲Kmm
TT e e×p
= cosh =
●Λ
TT 2
*Φ
■dpT
pT e−e−= sinh =TT 2
1 1G T
=artanhG T = log
2 1−G T
W : SpaceWeightx , ypT[GeV/c]
G :Gradient x , yGlauber Monte CarloT : Freezeout temperatureGeV Free ParametersT : Radial flow velocity

dNpTdpTFunction of Blast wave
for elliptic flowv 2=∫ dxW BesselK1BesselI 2,cos2B ▼π▲K×p●Λ
*Φ■dGlauber Monte Carlo
Free Parameter
Given by spectra fit

mTmT ee−= cosh =TT 2
pTp T e −e−
= sinh =TT 2
1 1G T
=artanh G T = log
2 1−G T
W : SpaceWeight x , y
G :Gradient x , y
B : Boost anglex , y
T : Freeze out temperatureGeV 
T : Radial flow velocity

Temperature of BW
for spectra and elliptic flow
T [GeV]●● v2 fit (6 particles)● v2 fit (no pion)○ spectra fit (6 particles)○ spectra fit (no poin)●Centrality [%]Temperature of v2 is
not consistent withthat of spectra since
βT or anotherparameter is fixed by
distribution of GlauberMonte Carlo
Is it should be consist
or not?

Expanded Glauber Monte Carlo
T [GeV]＊ v2 fit expanded (6 particles)＊ v2 fit expanded (no pion)

Density distributionof Glauber Monte Carlo● v2 fit (6 particles)● v2 fit (no pion)○ spectra fit (6 particles)○ spectra fit (no poin)

Centrality [%]The eccentricity of density distribution isadjusted to fit both of the temperature.

Expanded for X-axis

Final Eccentricity by BW fit
Eccentricity final●

HBT [JPS2011fall, T. Niida](PHENIX preliminary)
BW (6 particles)
BW (no pion)●epsiron●εfinal < εinitial
The eccentricity
estimated by BW fit with
spectra and v2 agree
that of HBT analysis.
They agree system
expansion from initialstate before freeze out.
2Eccentricity initial

2〈 y 〉−〈x 〉= 22〈 y 〉〈 x 〉Summary1●The new reaction plane detector worked well.

We can see rare particles by the good resolution.
● .v is depend on n .
2q●

●

●

●

Consistent for all particles on KET and nq scaling at
KET/nq<0.8GeV.
Φ v2 is similar to other mesons on KET.

v2 have no depend on the quark number at high pT range.

Production mechanism is different.
● D v is higher than p at p >3 GeV/c2T●●d2dTp2p
Tv ~2 vp ~2 pd v2 and p v2 are consistent on parton number scaling or23
KET/nq scalingSummary2●●●T of spectra of 6 particles BW fit by glauber seems flatto centrality.
T of v2 of BW fit with initial glauber system is not flat tocentrality and it is higher than that of spectra,especially at peripheral.
The same T of bwfit of v2 and spectra can be
described by expanded glauber distribution●

The eccentricity of final state of system is consistent
with that of HBT analysis.

Next step
●Low energy scan of quark number scaling (200,63, 39 GeV on Run10)●●

D meson v2 by VTX on Run11●Res =〈cos2  real− observe 〉Threshold of collision energy for QGP?
Charm production is faster than other quarks?
Run10
200 GeV
63GeV
39GeV

25

AN678

AN416

AN440

BW fit for spectra● : run2final (pi, K, p)
PRC72, 014903(2005)

T [GeV] ● : pi,K,p (flat system) βT● : 6 particles (flat)● : 5 particles (flat)(K, p, d, Λ, Φ)○ : pi,K,p (glauber)○ : 6 particles (glauber)○ : 5 particles (glauber)Centrality [%]Centrality [%]Expansion for X-axis
on Glauber Monte Carlo
initialglauber

expanded

Centrality
0-10% 10-20%

20-40%

40-60%

60-93%

Comparison of bw fit ofv2 and spectra○ : 6 particles spectra○ : 5 particles spectra● : 6 particles v2● : 5 particles v2

T [GeV]

Centrality [%]T [GeV]βT

Centrality [%]Centrality [%]Estimated Eccentricity
Eccentricity final

HBT (Run7, T.Niida)
BW fit for 6 particles
BW fit for 5 particles○ : 6 particles spectra○ : 5 particles spectra● : 6 particles v2● : 5 particles v2* : 6 particles v2 (expanded)* : 5 particles v2 (expanded)
T[GeV]

Eccentricity initialcentrality