Elliptic%20Flow%20measurements%20at%20RHIC

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Elliptic Flow measurements at RHIC

Arkadij Taranenko
Nuclear Chemistry Group SUNY Stony Brook, USA
Helmholtz International Summer School Dense
Matter In Heavy Ion Collisions and Astrophysics
Dubna , Russia, July 14-26,
2008
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Phase diagram (QCD) and RHIC
How one can probe this new state of matter
(QGP)?
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One want to see a probe (phenomena) which is

• Exist only in Heavy-Ion Collisions (HIC)
• Provides reliable estimates of pressure
  pressure gradients
• Can address questions related to thermalization
• Gives insides on the transverse dynamics of the
  medium
• Provides access to the properties of the medium
  EOS, viscosity , etc
• Well calibrated measured at Ganil (MSU), SIS,
  AGS, SPS energies

Elliptic Flow in Heavy-Ion Collisions
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Elliptic Flow measurements from RHIC to SIS

Arkadij Taranenko
Nuclear Chemistry Group SUNY Stony Brook, USA
Helmholtz International Summer School Dense
Matter In Heavy Ion Collisions and Astrophysics
Dubna , Russia, July 14-26,
2008
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Squeeze-Out - First Elliptic flow signal in
HIC
Diogene, M. Demoulins et al., Phys. Lett. B241,
476 (1990)
Plastic Ball, H.H. Gutbrod et al., Phys. Lett.
B216, 267 (1989)
Reaction plane
Reaction Plane
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KAOS
Cheuk-Yin WONG , Physics Letters, 88B, p 39
(1979) Sergei Voloshin, Y. Zhang, Z. Phys.
C70,(1996), 665
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Small Elliptic flow, Large Elliptic Flow?
SIS
V2 -0.2 ? ROUT/IN 2 ( two times more particles
emitted out-of-plane than in the plane )
1- 2 V2
N(900) N(2700)
ROUT/IN

N(00) N(1800)
1 2 V2
RHIC
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Where to stop or If Elliptic Flow is very large
To balance the minimum a v4 gt (10v2-1)/34 is
required v4 gt 4.4 if v225
STAR, J. Phys. G34 (2007)
V4V22 VnV2n/2
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Excitation function of elliptic flow Do we
understand it ?
RHIC
GANIL/MSU
SPS
AGS
SIS

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At E/A lt 100 MeV attractive nuclear mean field
potential rotating system of projectile and
target
Low energy heavy-ion collisions E/A25 MeV
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Excitation function of elliptic flow 0.4-10
GeV(SIS/AGS) energies
Passage time 2R/(ßcm?cm) Expansion time R/cs
cscvdp/de - speed of sound ( time for the
development of expansion perpendicular to the
reaction plane)
AGS
SPS
SIS
Delicate balance between 1) Ability of pressure
developed early in the reaction zone to affect a
rapid transverse expansion of nuclear matter 2)
Passage time for removal of the shadowing of
participant hadrons by projectile and target
spectators

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If the passage time is long compared to the
expansion time (spectator blocking) ? squeeze-out
Azimuthal anisotropy in momentum space
(elliptic flow)
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In-plane elliptic flow (due to pressure gradient)
at high beam energies.
Azimuthal anisotropy in momentum space
(elliptic flow)
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Interplay of passage/expansion times
Passage time 2R/(ßcm?cm) Expansion time R/cs
cscvdp/de - speed of sound
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(KAOS Z. Phys. A355 (1996) (E895) - PRL 83
(1999) 1295
Squeeze-out Mechanism
Particle emitted in the center-of-mass of the
system and moving in a transverse direction with
velocity vT will be shadowed by spectators during
the passage time tpass2R/(ßcm?cm) simple
geometry estimate? vTtpass/2 gt R-b/2 or
vT gt (1-b/2R) (ßcm?cm)
V2 will increase with vT and impact parameter b
Squeeze-out contribution reflects the ratio
cs/(ßcm ?cm)
cscvdp/de - speed of sound
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Elliptic Flow_at_ SIS/AGS
Low Energy Squeeze-out
High Energy In-plane
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Determination of the Equation of State of dense
matter from collective flow of particles
P. Danielewicz, R. Lacey, W.G. Lynch, Science 298
(2002) 1592
elliptic flow
dN/dF ? (1 2v1 cosF 2v2 cos2F)
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Prologue Constraints for the Hadronic EOS
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Elliptic flow at RHIC
Longitudinal and transverse expansion gt no
influence of spectator matter at midrapidity
Passage time 0.15 fm/c
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Significant Energy Density is produced in AuAu
collisions at RHIC
Thermalization
PRL87, 052301 (2001)
eccentricity
time to thermalize the system (t0 0.2 - 1 fm/c)
eBjorken 5 - 15 GeV/fm3
e drives pressure gradients which result in flow.
Substantial elliptic flow signals should be
present for a variety of particle species !
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Fine Structure of Elliptic Flow at RHIC
Substantial elliptic flow signals are observed
for a variety of particle species at RHIC.
Indication of rapid thermalization?
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Mass ordering of v2 and ideal fluid
hydrodynamics
PHENIX PRL 91, 182301 (2003)
STAR PRC 72, 014904 (2005)
pTlt1.8 GeV ( 99 of all particles)
Flavor dependence of v2(pT) enters mainly
through mass of the particles ? in hydro all
particles flow with a common velocity !!! v2
results are in a good agreement with the
predictions of ideal relativistic hydrodynamics (
rapid thermalization tlt 1fm/c and an extremely
small ?/s ) ? small viscosity ? Large cross
sections Large cross sections ? strong
couplings
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Elliptic Flow ultra-cold Fermi-Gas

• Li-atoms released from an optical (laser) trap
  exhibit elliptic flow analogous to what is
  observed in ultra-relativistic heavy-ion
  collisions
• Interaction strength among the atoms can be tuned
  with an exteranl magnetic field (Feshbach res)
• Elliptic flow is a general feature of strongly
  interacting systems?

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Hadron Gas ?
Clearly the system is not a hadron gas.
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Elliptic flow at SPS and ideal hydrodynamics
CERES
Different picture than at RHIC!?
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Intermediate pT range Meson vs Baryon

• Intermediate pT (2lt pTlt5 GeV/c)
• elliptic flow v2(pT) saturates and tends to
  depends on the particle species-type ( meson
  vs baryon)
• Suppression pattern (RCP or RAA) is different
  meson/baryon effect
• p/p ratio more (anti-)protons than
• pions at intermediate pT ( 2-5 GeV)

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Transverse kinetic energy scaling
Scaling breaks
mT m
Baryons scale together
Mesons scale together


PHENIX Phys. Rev. Lett. 98, 162301 (2007)

• Elliptic flow scales with KET up to KET 1 GeV
• Indicates hydrodynamic behavior?
• Possible hint of quark degrees of freedom become
  more apparent
• at higher KET

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KET Quark number Scaling
PHENIX Phys. Rev. Lett. 98, 162301 (2007)
v2 /nq vs KET/nq scaling works for the full
measured range with deviation less than 10 from
the universal scaling curve!
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KET Number of constituent Quarks (NCQ) scaling
Centrality dependence

• Scaling seems to hold well for different
  centralities up to 60 centrality

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KET/n scaling and beam energy dependence AuAu
(62.4-200 GeV)

STAR Collaboration Phys. Rev. C 75(2007) 054906

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KET/n scaling and system size (AuAu/CuCu)
KET/n scaling observed across different
colliding systems

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v4 Scaling

• The similar scaling for v4 is found recently at
  PHENIX.
• Compatible with partonic flow picture.

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KET/n Scaling tests at SPS
C. Blume (NA49) QM2006 talk
V2 vs KET/n scaling breaks at SPS? the
statistical errors are too large one need to
measure v2 of f meson at SPS
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Elliptic flow of f meson and partonic
collectivity at RHIC.

• f meson has a very small s for interactions
  with non-strange particles
• f meson has a relatively long lifetime (41
  fm/c) -gt decays outside the fireball
• Previous measurements (STAR) have ruled out the
  KK- coalescence as f meson production mechanism
  -gt information should not be changed by hadronic
  phase
• f is a meson but as heavy as baryons (p, ? )
• m(f)1.019 GeV/c2 (m(p)0.938 GeV/c2
  m(?)1.116 GeV/c2) -gt very important test for v2
  at intermediate pt ( mass or meson/baryon
  effect?)

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v2 of f meson and partonic collectivity at
RHIC
nucl-ex/0703024
v2 vs KET is a good way to see if v2 for the
f follows that for mesons or baryons v2 /n vs
KET/n scaling clearly works for f mesons as well
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Multi-strange baryon elliptic flow at RHIC (STAR)
Elliptic flow of multistrange hadrons (f, ? and ?
) with their large masses and small hadronic s
behave like other particles ? consistent with
the creation of elliptic flow at partonic level
before hadron formation
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Elliptic flow of D meson
Measurements of elliptic flow of non-photonic
electrons (PHENIX)
Measurements and simulations Shingo Sakai
(PHENIX) (See J. Phys G 32, S 551 and his
SQM06,HQ06, QM06 talks for details )
Simulations for D meson v2(pt)

• All non-photonic electron v2 (pT lt 2.0 GeV/c)
  were assumed to come from D decay
• D-gt e, Pt spectrum constrained by the data
• Different assumptions for the shape of D meson
  v2(pt) pion,kaon and proton v2(pt) shapes

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Elliptic flow of D meson Scaling test
Heavy-quark relaxation time tRgtgt tL tR (Mhq
/T)tL 8 tL for Mhq 1.4 GeV and T165 MeV
The D meson not only flows, it scales over the
measured range
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Elliptic Flow at RHIC energies

• For a broad range of reaction centralities
  (impact parameters) elliptic flow at RHIC
  energies (62.4-200 GeV) depends only (?) on
  transverse kinetic energy of the particle KET
  and number of valence quarks nq ?

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KET/n Scaling tests for Ideal Hydro
Why Ideal hydro works so bad after close look? -
In ideal hydro ( ? 0 !!! )
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Elliptic flow at RHIC and ideal fluid
hydrodynamics
From PHENIX White Paper Nucl. Phys. A757 (2005)
184
Rapid Thermalization ?
For pT lt1.5 GeV/c V2(pT) and pT spectra of
identified hadrons are in a good agreement with
the predictions of ideal relativistic
hydrodynamics ( rapid thermalization tlt 1fm/c
and an extremely small ?/s ) ? small viscosity
? Large cross sections Large cross sections ?
strong couplings
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T. Hirano Highlights from a QGP Hydro Hadronic
Cascade Model
Hadronic dissipative effects on elliptic flow and
spectra
AuAu200
Adapted from S.J.Sanders (BRAHMS) _at_ QM2006
b7.2fm
0-50
hadronic - late viscosity
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What is the lowest viscosity at RHIC?
Shear viscosity ( ? ) how strongly particles
interact and move collectively in a body system.
In general, strongly interacting systems have
smaller (?) than weakly interacting. But, (?/s)
has a lower bound in standard kinetic theory
?(nltpgt?)/3 , where n - proper density , ltpgt-
average total momentum, ? momentum degradation
transport mean free path. The uncertainty
principle implies ?gt1/ltpgt , for relativistic
system, the entropy density (s4n) and (?/s) gt
1/12 (?/s) gt 1/12 from Dissipative Phenomena
in Quark-Gluon Plasmas P. Danielewicz, M.
Gyulassy Phys.Rev. D31, 53,1985.
KSS bound (?/s) gt 1/4p
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Constraining h/s with PHENIX datafor RAA v2 of
non-photonic electrons
Phys. Rev. Lett. 98, 172301 (2007)

• Rapp and van Hees Phys.Rev.C71034907,2005
• Simultaneously describe PHENIX RAA(E) and v2(e)
  with diffusion coefficient in range DHQ (2pT)
  4-6
• Moore and Teaney Phys.Rev.C71064904,2005
• Find DHQ/(h/(ep)) 6 for Nf3
• Combining
• Recall ep T s at mB0
• This then gives h/s (1.5-2)/4p
• That is, within factor of 2-3 of conjectured
  lower bound

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Estimation of h/s from RHIC data

• Damping (flow, fluctuations, heavy quark motion)
  h/s
• FLOWHas the QCD Critical Point Been Signaled by
  Observations at RHIC?, R. Lacey et al.,
  Phys.Rev.Lett.98092301,2007 (nucl-ex/0609025)
• The Centrality dependence of Elliptic flow, the
  Hydrodynamic Limit, and the Viscosity of Hot
  QCD, H.-J. Drescher et al., (arXiv0704.3553)
• FLUCTUATIONS Measuring Shear Viscosity Using
  Transverse Momentum Correlations in Relativistic
  Nuclear Collisions, S. Gavin and M. Abdel-Aziz,
  Phys.Rev.Lett.97162302,2006 (nucl-th/0606061)
• DRAG, FLOW Energy Loss and Flow of Heavy Quarks
  in AuAu Collisions at vsNN 200 GeV (PHENIX
  Collaboration), A. Adare et al., to appear in
  Phys. Rev. Lett. (nucl-ex/0611018)

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Viscosity Information from Relativistic Nuclear
Collisions How Perfect is the Fluid Observed at
RHIC?, P. Romatschke and U. Romatschke, Phys.
Rev. Lett. 99172301, 2007

• Calculation2nd order causal viscous hydro
• (Glauber ICs

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T. Hirano Hydro Cascade
QGP viscosity or hadronic viscosity both ?
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Key Future Test
W baryon (sss) is a stringent test due to the
large mass and OZI suppressed hadronic
interactions.
Small deviations from scaling will yield insights
on novel hadronization process.
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Viscosity-to-entropy ratio
minimum bias AuAu, vs200 GeV
Hydrodynamic scaling
Partonic fluid
Lower bound of ?/s1/4p in the strong coupling
limit (P.Kovtun et al. PRL 94 (2005) 111601)
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Eccentricity Calculation
Coalescence/recombination and KET
J.Jia and C. Zhang, Phys. Rev. C 75 (2007)
031901(R)
If one modify the momentum conservation relation
into kinetic energy conservation relation in the
coalescence formula one will get
2v2,q
2 v2,q ( KET/2 )
mesons
V2,M(KET)
12v22,q
KET/2
3v2,q3v32,q
3 v2,q(KET/3)
baryons
V2,B(KT)
16v22,q
KET/3
Problem with conventional quark coalescence
models is energy violation ( 2? 1, 3? 1 channels
). What to do with it?
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Quark Coalescence based on a Transport Equation
L. Ravagli and R. Rapp http//arxiv.org/abs/070
5.0021

• Resonance formation in quark-(anti)quark
  scattering as the dominant channel for meson
  production at RHIC Energy ( 4-momentum )
  conservation satisfied via a finite G.
• Is it a way to solve the problem?

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Constituent Quark Number Scaling (QNS) of v2

• Simple models of hadronization by
  coalescence/recombination of constituent quarks,
  which only considers the momentum distribution of
  quarks and allows quarks with the same pT to
  coalesce into hadrons ? relate quark and hadron
  v2
• v2p v2h(pT/n)/n,
• n is the number of quarks in the hadron
• Models imply
• v2 is developed before hadrons form ( at
  partonic level )

Coalescence/recombination of constituent quarks
can explain both meson/baryon nature of
suppression factors and v2 at intermediate
pt Greco, Ko, Levai Muller, Nonaka,
BassHwa,Yang Molnar, Voloshin
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v2(pT/n)/n QNS scaling close look

• With higher statistics v2 measurements, fine
  structure
• in QNS is observed
• pTgt2GeV/c QNS scaling only works at 20 level
• pTlt2GeV/c QNS scaling breakes badly with
  systematic dependence on the hadron mass it
  undershoots the v2 values of light mesons and
  overshoots the v2 values of heavy baryons

Imperfections of coalescence/recombination
approach? Wrong scaling variable?
Can one get a unified description of hadron
production and elliptic flow at low and
intermediate pT ?
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The idea to use collective flow to Probe the
properties of nuclear matter is long-standing
U
M.I. Sobel, P.J. Siemens, J.P. Bondorf, an H.A.
Bethe, Nucl. Phys. A251, 502 (1975)
G.F. Chapline, M.H. Johnson, E. Teller, and M.S.
Weiss, PRD 8, 4302 (1973)
E. Glass Gold et al. Annals of Physics 6, 1 (1959)
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Summary

• Universal scaling of the flow of both mesons and
  baryons (over a broad transverse kinetic energy
  range) via quark number scaling observed.
• Development of elliptic flow in the
  pre-hadronization phase demonstrated
• Outlook mechanism of hadronisation at RHIC,
  what is the range of (?/s) at RHIC?

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Jet Quenching at RHIC
Strong quenching of jets, observed in central
AuAu collisions ? Evidence of the extreme energy
loss of partons traversing matter containing a
large density of color charges
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Elliptic flow at RHIC
Z

• The probe for early time
• The dense nuclear overlap is ellipsoid at the
  beginning of heavy ion collisions
• Pressure gradient is largest in the shortest
  direction of the ellipsoid
• The initial spatial anisotropy
• evolves (via interactions and density
  gradients ) ? Momentum-space anisotropy
• Signal is self-quenching with time

Reaction plane
Y
X
Pz
Py
Px