1. The azimuthal anisotropy in high energy heavy ion collisions at RHIC
Shingo Sakai
Univ. of Tsukuba

2. Azimuthal anisotropy ｙ ｘ pｙ pｘ dN/dφ ∝ N0(1+2v2cos(2φ))
A powerful probe of the initial state of
the high energy heavy ion collision
Low pT
pressure gradient of
early stage of collision
High pT
parton energy loss in hot &
dense medium
Initial spatial anisotropy pｘ pｙ
Spatial anisotropy
Thermal equilibrium
The azimuthal anisotropy of particle emission is sensitive to the early stages of system evolution
Probe of jet quenching
Hydro model
Measurement of identified particle v2 give up much more
Information of the collision dynamics
Momentum space anisotropy
of particle emission
　　dN/dφ ∝ N0(1+2v2cos(2φ))

3. Reaction plane method Reaction plane ; defined beam direction &
impact parameter direction
particle’s φ measured with respect to
the reaction plane
v2 is obtained (1) by fitting dN/dφ
(2) <cos(2(-))> Y
 wi*sin(2i)
tan2  rp =
 wi*cos(2i)
Reaction
Plane X
dN/d(-) ∝ N (1 + 2v2obscos(2(-)))

4. Today’s topics Identified particles v2 (Au+Au 200 GeV)
pions, kaons, protons φ
electrons
photons
Energy dependence of v2
62.4, 130 and 200 GeV
System size dependence
Au+Au & Cu+Cu
These measurement gives us much more information of the collision dynamics and particle productions

5. Identified particles v2

6. Identified hadron v2 pT<1.5 GeV/c mass dependence
v2(π)>v2(K)>v2(p)
consistent with
hydro model prediction
(τ0 = 0.6 fm/c)
System thermalizes very early
pT>2.0 GeV/c
v2(ｂ) > v2(ｍ)
consistent with quark
coalescence model (N.Q.S)
Low pT (pT<1.5 GeV/c)

7. v2 already developed in partonic phase ?
identified hadrons v2 after
scaling number of quarks
v2 after scaling fall on
same curve
partonic level v2
v2 already formed in the
partonic phase for hadrons
made of light quarks (u,d,s)

8. Φ meson v2 φ v2 is important mass dependence ? v2(p) ~ v2(φ)
Quark number scale ?
　=> number of quarks = 2
saturate around 2.0 GeV/c
like π,K v2
Current φ v2 has large error
=>consistent with hydro model
& quark coalescence model

9. Electron v2 electron sources ; photonic --- hadronic decay
(π0,η, etc.)
non-photonic --- heavy flavor
decay (c)
=> give us charm flow info.
v2non-γe = {(1+RNP)v2e - v2γe} }/RNP
RNP ; phonic / non-photonic
v2γe; phonic e v2
converter ; experimentally determined
with/without converter
cocktail ; simulation
Non photonic
signal
Photonic b.g.
Experimentally determined
[electron analysis ; 2/17 15:05-15:40 ]
Experimentally determined
simulation
photonic e v2
simulation
inclusive e v2

10. Non-photonic electron v2
pT dependence non-γ e v2
low pT ; increasing with pT
high pT ; small energy loss ?
B contribution ?
Compared with quark
coalescence model prediction.
with/without charm quark flow
(Greco, Ko, Rapp: PLB 595 (2004) 202)
Below 2.0 GeV/c ;
consistent with charm quark
flow model.
indicate charm quark flow 1 1 2 3

11. Charm v2 estimate from non-γ e v2
Estimate charm v2 with non-γ e v2
Assuming several v2 shape for
D meson v2
Dv2(pT) = api * pi v2
Dv2(pT) = aK * kaon v2
Dv2(pT) = ap * proton v2
Calculate D -> e
chi-squared test with
“measured” non-photonic electron v2
find chi-squared “a”
Calculate charm v2 from
the D v2 with N.Q.S
D meson v2
Decay
Decay
electron v2

12. Charm quark v2 (private analysis)
mass effect for N.Q.S
v2M (pT) = v21 (R1 pT) + v22 (R2pT)
Ri = mi / mM
(mi ; effective mass of quark i)
(Phys.Rev. C68 (2003)
Zi-wei & Dence Molnar)
v2π(pT) ~ 2*v2q(1/2pT)
v2D(pT) ~ v2u (1/6*pT) + v2c (5/6*pT)
u quark v2
My model case
Rapp prediction
Charm quarkv2
- charm v2 shape same as light quark
- D meson made quark coalecence 2
DNP/JPS ?
Light quark v2
Private analysis !
Mass effect in partonic level ?

13. Photon v2 direct photon provide very early time information
[Photon production mechanism]
thermalization
Hadronisation
Direct photon
thermal photon ; v2>0
Bresmsrahlung ; v2<0
prompt photon
v2=0
Hadron decay
Direct phhadro
Hadron decay
Photon production mechanism
direct photon provide very early time information
high pT
prompt photon dominant
prompt photon ; binary scale (no energy loss)
high pT ; expect v2 = 0

14. Direct photon v2 Trend ; v2 seems like smaller @ most central
R*direct photon v2
R * direct photon v2
Trend ; v2 seems like most central
=> bremsstrahlung main source pT < 4.0 GeV/c ?
direct photon high pT < 10 GeV/c coming soon !

15. Summary for identified v2
Identified hadrons (π,K,p,Λ,φ ---)
low pT consistent with hydro model
=> early time thermalization
v2 scale number of quarks (quark coalescence)
=> partonic level flow
non-photonic electron
consistent with charm flow model
=> charm quark flow
direct photon
Trend ; v2 seems like most central
　 => bremsstrahlung main source pT < 4.0 GeV/c ?

16. Energy & System size dependence

17. v , 130 & 200 GeV
Phys. Rev. Lett. 94,
very similar 62.4, 130 & 130 GeV at same Npart
same 62.4 GeV & 200 GeV

18. Energy dependence ; Softening EOS @ RHIC
130
62.4
200
AGS
SPS
RHIC
62.4 GeV
Phys. Rev. Lett. 94,
v2 √sNN = 62.4 ~ 200 GeV
　　 => indicate “softening” of EOS

19. Cu+Cu results Hydrodynamical behavior @ Cu+Cu collisions ?
Hirano et al., nucl-th/
Large v2 has been measured
Hydrodynamical Cu+Cu collisions ?
What’s the scaling laws of v2 between Au+Au & Cu+Cu ?

20. v2 is scaled by system size (A) linearly ?
AMPT : v2 scale system size ; v2 (Cu+Cu) ~ 0.3 * v2(Au+Au)
AMTP prediction --- v2 (Cu+Cu) = 0.3 * v2 (Au+Au)
PHENIX Preliminary
v2 (Cu+Cu) ~ 0.8 * v2(Au+Au)
v2 doesn’t scale system size (A) linearly

21. Eccentricity scaling Hydro ; v2 scales with eccentricity
Eccentricity ; relate to geometry of overlap
region x Y
(1) v2(cent,pT) divide by v2(cent) ; v2(pT,cent)/v2(cent)
v2(cent) = ∫v2(pT,cent)dpT ~ ε
(2) v2 divide by eccentricity (ε) ; v2/<ε>

22. Eccentricity scailing v2 @ Au+Au & Cu+Cu
v2 Cu+Cu fall on same
curve after eccentricity scailing
Eccentricity works well

23. dN/dη& RAA @ Au+Au & Cu+Cu
200 GeV
PHOBOS
Cu+Cu
Preliminary
(PHOBOS)
Cu+Cu
Preliminary
15-25%, Npart = 61
Au+Au
Au+Au
45-55%, Npart = 56
dN/dη & Au+Au & Cu+Cu --- very similar at same Npart

24. v2 scales with Npart ? v2 @ Au+Au & Cu+Cu ;
PHOBOS
PHOBOS
Au+Au & Cu+Cu ;
very different same at Npart
is very similar
at same Npart
< εpart >; taking into account
fluctuation in <ε>
Image ; same Npart Au+Au & Cu+Cu
Cu+Cu
Au+Au
Image ; same Npart Au+Au & Cu+Cu

25. Summary for energy & system size dependence
Energy dependence
same 62.4 GeV, 130 GeV and 200 GeV
=> indicate “softening” of EOS
System size dependence (Au+Au v.s. Cu+Cu)
v2 doesn’t scale with system size (A)
Eccentricity scailing well works
Npart scaling between Au+Au & Cu+Cu

26. Outlook Detector update @ PHENIX new reaction plane detector
=> good reaction plane resolution
(reduce error bar)
silicon vertex detector
=> direct measurement of D meson
Future v2 PHENIX
High pT v2 with smaller error (non-γ e & direct photon, etc・・・)
J/ψ v2
D meson v2, etc ・・・

27. Back Up

28. “experimentally” determined !
Converter method
Separate non-photonic & photonic e v2 by using
Non-converter run & converter run
Non-converter ; Nnc = Nγ+Nnon-γ
Converter ; Nc = R *Nγ+Nnon-γ
(1+RNP)v2nc = v2γ + RNPv2non-γ
(R +RNP) v2c = R v2γ + RNPv2non-γ
v2non-γ(non-photonic) & v2γ(photonic) is
“experimentally” determined !
RNP；non-photonic/photonic
R --- ratio of electrons with & without converter (measured)
RNP --- non-photonic/photonic ratio (measured)
v2nc --- inclusive e v2 measured with non-converter run (measured)
　v2c --- inclusive e v2 measured with converter run (measured)

29. Cocktail method Determined photonic electron v2 with simulation
Then subtract it from electron v2 measured
with non-converter run
dNe/d = dNpho.e /d + dNnon-pho.e /d
v2non-γ = {(1+RNP) v2 - v2γ} } / RNP
measured
RNP；non-photonic/photonic
measured
calculate
From F. Kajihara
Clear non-photonic signal !
S/B > 1 in pT>1.5 GeV/c
RNP --- non-photonic/photonic ratio
experimentally determined
v2 --- inclusive electron v2 (without converter)
v2γ --- photonic electron v2
calculated from pi0 (pion) v2
From F. Kajihara

30. Chi2 map & D meson v2 v2 D = a * pi v2 v2 D = a * kaon v2
v2 D = a * proton v2
v2 D = a * D v2 (y_T scailing)