KET and Quark Number
Scaling of v2
Maya Shimomura!!! University of Tsukuba

Collaborated withYoshimasa Ikeda, ShinIchi Esumi and Yasuo Miake
May, 20, 2010

Exotics from Heavy Ion Collisions

Contents!Introduction• Elliptic Flow (v2)
• Time Evolution!Results• Fundamental Findings of v2 at RHIC
– Scaling of v2• Blast-Wave Model Fit!SummaryMay, 20, 2010

Exotics from Heavy Ion Collisions

Elliptic Flow (v2)
At non central collision

Reaction plane (!)

PyzPz•Small mean free path!
Px•Thermalization

Ｙ•Pressure gradient!

xGeometrical anisotropy

Elliptic flow

Momentum anisotropy

Fourier expansion of the distribution of produced particle angle (#) to reaction plane (!)

v2 is the coefficient of the second term " indicates ellipticity
v2 measurement has been considered as a powerful probe forinvestigating the property of the QGP.
May, 20, 2010

Exotics from Heavy Ion Collisions

Time Evolution
The matter produced in the high energy heavy ion collision is expected to undergo several
stages from the initial hard scattering to the final hadron emission.

tKinematical freeze-out

Hadron gas
Mixed phaseQGP

Chemical freeze-out
Hadronization
Expansion & Cooling

Thermalization
pre-equilibrium
Hard scatterings
Collision

Note whenever the matter interacts each other, v2 could change.

May, 20, 2010

Exotics from Heavy Ion Collisions

WordsNpart --- Number of nucleons participating the collision
Eccentricity ($) --- geometrical eccentricity of participant nucleons- Monte-Carlo simulation with Glauber model- Nucleus formed by wood-Saxon shape- Participant eccentricity which is calculated with long and shortaxis determined by distribution of participants at each collision.
$ vs. Npart

May, 20, 2010

Exotics from Heavy Ion Collisions

Fundamental Findings of v2 at RHIC
•Hydro-dynamical behavior•KET scaling•Quark number scaling
May, 20, 2010

Exotics from Heavy Ion Collisions

v2 explained by hydro model
PRL 91, 182301

v2 at low pT (<~2 GeV/c) can be
explained by a hydro-dynamical
model assuming:" Early thermalization(~0.6 fm/c)

Mass Ordering: v2(!)>v2(K)>v2(p)"Existence of radial flow.
Single particle spectra also indicatesradial flow.
convex shape due to radial flow.
May, 20, 2010

Exotics from Heavy Ion Collisions

PHENIX: Au+Au: PRC 63, 034909 (2004);
p+p: PRC74, 024904 (2006)

KET Scaling
Presented by Yoshimasa IKEDA at spring JPS 2010

Au+Au, %sNN = 200GeV (RUN7)

KET = mT-m0 = !(m02 + pT2) – m0! v2 is similar to proton v2 .
" v2 is near to meson (# or K) rather than baryon (p or !) at mid- pT (= 2 – 5 GeV).
Mass ordering can be seen at low pT. ! scaled by KET
Clearly different between meson and baryon v2.
May, 20, 2010

Exotics from Heavy Ion Collisions

Quark number scaling
Presented by Yoshimasa IKEDA at spring JPS 2010

Au+Au, %sNN = 200GeV (RUN7)

v2(pT) /nquark vs. KET/nquark becomes one curve independent of particle species.

Significant part of elliptic flow at RHIC develops at quark level.
! QGP phase
May, 20, 2010

Exotics from Heavy Ion Collisions

the quark number scaling
everywhere

AuAu 62.4GeV
PHENIX/STAR

Au+Au 200 GeV (Run7)

PHENIX Preliminary#meson (Au+Au 200GeV)

SQM06, M. Oldenburg
QM06, A. Taranenko

Cu+Cu 200GeVSTAR preliminary

Au+Au 200GeV (Run7)v4 (Au+Au 200GeV)

QM09, A. Taranenko

Quark number scaling work out up to KET ~1GeV.
10

quark number scaling at SPS
v2 of p, !, " - C. Alt et al (NA49 collaboration) nucl-ex/0606026 submitted to PRLv2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003)

Pb+Pb at 17.2 GeV, NA49

-A. Tranenko’s talk at QM06

Quark number + KET scaling doesn’t seem to work out at SPS.
No flow at quark level due to nonexistence of QGP ?

May, 20, 2010

Exotics from Heavy Ion Collisions

For a comprehensive understating of the matter and the mechanism of v2 production…

Other scaling of v2•Energy dependence•Eccentricity scaling•Npart scaling

May, 20, 2010

Exotics from Heavy Ion Collisions

Energy dependence
Au+Au 200 vs. 62 GeV
Centrality dependence

Identified particles
v2 vs. pT for &/K/p

PHENIX PRELIMINARY

No significant difference between 200 and 62 GeV.
May, 20, 2010

Exotics from Heavy Ion Collisions

Eccentricity scaling
Au+Au vs. Cu+Cu
Compare v2 normalized by eccentricity ($) in collisions of different size.
0.2<pT<1.0 [GeV/c]phenix preliminary

Eccentricity scaling suggests
early thermalization.
PHOBOS Collaboration
PRL 98, 242302

May, 20, 2010

There is a strong Npart dependence.

Exotics from Heavy Ion Collisions

Npart Scaling
The dependence can be normalized by Npart1/3.

v2 vs. Npart

Dividing by Npart1/3

v2/$ vs. Npartv2/$/Npart1/3 vs. Npart

phenix preliminary

0.2<pT<1.0 [GeV/c]phenix preliminary

v2/eccentricity/Npart1/3 scaling works for all collisionsystems except small Npart at 62 GeV.
- This exception may indicate non-sufficient thermalization region.

May, 20, 2010

Exotics from Heavy Ion Collisions

Universal v2 for identified charged hadrons
Taking all scaling together,! Different Energy and System(AuAu200, CuCu200, AuAu62)! Different Centrality (0-50%)! Different particles (&/ K /p)

45 curves

Scale to one curve.
"2/ndf = 2.1 (with systematic errors)
May, 20, 2010

Exotics from Heavy Ion Collisions

Then, we have a question .
If the matter is thermalized and the pressure
gradient produce the flow, what is the reason forNpart dependence and KET scaling of v2?

Blast Wave Model Fit

May, 20, 2010

Exotics from Heavy Ion Collisions

Blast Wave Fitting for v2 and Spectra
We use this well-known fitting technique to obtain theinformation of the flow velocity and temperature in andout-of plane separately.
Measured spectra weighted by # distribution
Measured pT spectra
1/pT dN/dpTdy

Measured v2

pTpT

Fitting pT distribution in and out-of plane
separately for &/K/p simultaneously by speed of light
blast wave, 'T and Tfo in and out-of plane
are obtained separately.
May, 20, 2010

Exotics from Heavy Ion Collisions

yzx#TRadial flow and KET scaling• Species dependence of v2 can be reproduced by
the Blast-wave model " Radial flow effectMay, 20, 2010

Exotics from Heavy Ion Collisions

Azimuthal dependence of 'T and Tfo• 'T has clear azimuthal dependence.
– Larger velocity @ in-plane• Tfo has small azimuthal dependence.
– Lower temperature @ in-plane

May, 20, 2010

Exotics from Heavy Ion Collisions

Npart Dependence of 'T and Tfo

Tfo and 'T agree between Au+Au and Cu+Cu, especially for the in-plane.
Since v2 is produced by the difference between in and out-of plane,
the modulation of 'T is expected to have important rule to make v2.

May, 20, 2010

Exotics from Heavy Ion Collisions

v2

Eccentricity scaling here !

'2'T2 = (' Tin - ' Tout) / (' Tin + 'Tout) / 2

v2/$

May, 20, 2010

v2/$ vs. Npart

Exotics from Heavy Ion Collisions

Freeze-out Temperature and v2
Tch obtained by statistical model

Dr. M.Konno’s thesis

Tfo depends on Npart (while Tch doesn’t) !
Larger system size ! Lower Tfo ! Steeper spectra ! Larger v2
Why does larger system have lower freeze out temperature ?

May, 20, 2010

Exotics from Heavy Ion Collisions

Freeze-out Temperature and Time
Dr. M.Konno’s thesis

Tch obtained by statistical model

Simple adiabatic expansion model
yspeed of lightzx#TFreeze-out time vs. Npart[Assumption]-Cylindrically expanding-Freeze-out condition: ((t)=R(t)The model explains Npart dependence well !
The times until freeze-out can becalculated by this model. Larger systemtakes more time to freeze-out. !Thismakes lower Tfo

May, 20, 2010

Exotics from Heavy Ion Collisions

Summary• Systematic study of v2 have been done in Au+Au/Cu+Cu at %sNN =62.4/200 GeV.
• v2 values are saturated above 62.4 GeV in Au+Au.
–Local thermalization• v2(pT) follows quark number + KET scaling in Au+Au (200,62GeV) andCu+Cu (200GeV) .
– Flow at quark level " QGP phase• v2(Npart) / $ are same between Au+Au and Cu+Cu at 200 GeV.
– Eccentricity scaling " Early thermalization• v2(pT) /$/Npart1/3 scaling works except for small Npart at 62 GeV.
– Existence of a universal v2 scaling at RHIC
– Exception may indicate non-sufficient thermalization region.

<From Blast-wave fit results with v2 and spectra together>•'2/eccentricity is constant not depending on system size (Npart>40).

•Larger system freezes out later at lower temperature.

– Early thermalization !

– cause the Npart dependence of v2/ $ .
May, 20, 2010

Exotics from Heavy Ion Collisions

Back Up

May, 20, 2010

Exotics from Heavy Ion Collisionsv2 at high pT
Emission
smallLong axis direction
Larger energy loss
Short axis direction
Smaller energy loss

Emissionlarge• Non-zero v2 at high pT• Consistent to Jet suppression scenarios.
May, 20, 2010

Exotics from Heavy Ion Collisions

Energy dependence up to RHIC
FOPI : Phys. Lett. B612, 713 (2005). E895 : Phys. Rev. Lett. 83, 1295 (1999)
CERES : Nucl. Phys. A698, 253c (2002). NA49 : Phys. Rev. C68, 034903 (2003)
STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary.
PHOBOS : nucl-ex/0610037 (2006)

PRL 94, 232302~ 50% increase from SPS to RHIC.
Above 62.4 GeV, v2 seems to be saturated.
! The matter reaches thermal equilibrium state at RHIC.
May, 20, 2010

Exotics from Heavy Ion Collisions

Scaling (others)
QM2006, S. A. Voloshin

QM2006, R. Nouicer• Straight line from SPS to RHIC energy.
• v2 is reaching the hydro limit at central collision ?
LHC and low energy scan may have answer for this !?
May, 20, 2010

Exotics from Heavy Ion Collisions

v2 compared with hydro model at SPS
SPS (%sNN = 17 GeV)
NA49: nucl-ex/0606026 (2007)
Hydro-dynamical model: 1st order phase transition,
Tc=165 MeV, Tf=120 MeV, )0 = 0.8 fm/c

Hydro-dynamical model at SPS: Overestimate v2
May, 20, 2010

Exotics from Heavy Ion Collisions

RatioMay, 20, 2010

Exotics from Heavy Ion Collisions

RatioMay, 20, 2010

Exotics from Heavy Ion Collisions

Back Up
Comparison with Hydro simulation

May, 20, 2010

Exotics from Heavy Ion Collisions

Differential v2 in Au+Au and Cu+Cu Collisions
QGP fluid+hadron gas with Glauber I.C.
Au+Au

Cu+Cu

Same Npart, different eccentricity
Au+Au

Cu+Cu

Same eccentricity, different Npart

May, 20, 2010

Exotics from Heavy Ion Collisions

Comparison with hydro-simulation
Hydro calculations done by Prof. Hirano.

&ref: arXiv:0710.5795 [nucl-th] and Phys. Lett.B 636, 299 (2006)

Au+Au 200GeV

Au+Au 62.4GeV

Hydro should be middle of two data.

Cu+Cu 200GeV

May,20,Au+Au
2010
Exotics
fromHeavyIon Collisions
Theresults agree
wellwithhydrobut Cu+Cu results don’t.

Comparison of v2(data)/$participant to v2(hydro)/$standard&Au+Au 200GeV

Au+Au 62.4GeV

Hydro should be middle of twodata.

Cu+Cu 200GeVThe Au+Au and Cu+Cu
agree
Exotics resultsfrom Heavy Ion
Collisionswell with hydro.

May, 20, 2010

Comparison with hydro-simulation

pCu+Cu 200GeV

Hydro should be middle of two data.
#・・・hydro#・・・hydro#・・・0-10 ％#・・・0-10 ％#・・・10-20％

#・・・10-20％

Normalized by
eccentricities#・・・hydro#・・・hydro#・・・20-30％

#・・・20-30％

v2(data)/$participant for proton doesn’t agree with v2(hydro)/$standard
May, 20, 2010

Exotics from Heavy Ion Collisions

Hydro v2/$ vs. Npart1/3

Fitting lines: dash line v2/$ = a*Npart1/3
solid line v2/$ = a*Npart1/3 + b
May, 20, 2010

Exotics from Heavy Ion Collisions

Rapidity dependence• To repoduce rapidity dependence of v2, needhadronic re-scattering as well as flow at QGP.
May, 20, 2010

Exotics from Heavy Ion Collisions

Multi-strange hadrons
J. H. Chen et., al, Phys. Rev. C74, 064902 (2006)

Y. Liu et., al, J. Phys. G32, 1121 (2006)

October,15, 2009

• Why ?
– # and * are lessaffected by hadronicinteractions– Hadronic interactions
at a later stage do not
produce enough v2

3rd Joint Meeting of APS and JPS40