Anisotropic flow: Quark Matter 2006 a few selected topics

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Anisotropic flow Quark Matter 2006 (a few
selected topics)

• Raimond Snellings

What are the consequences for anisotropic flow at
the LHC?
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Anisotropic Flow

• Anisotropic flow azimuthal correlation with the
  reaction plane
• clean signal of final-state reinteractions
• Unavoidable consequence of thermalization
• Natural description in hydrodynamic language,
  however when we talk about flow we do not
  necessary imply (ideal) hydrodynamic behavior
• Non-flow contribution to vn from azimuthal
  correlations between particles not due to their
  correlation with the reaction plane (HBT,
  resonances, jets, etc)

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The EoS pressure and energy density
F. Karsch and E. Laermann, arXivhep-lat/0305025

• Pressure gradient, dp/de generates collective
  flow
• At the phase transition e changes faster than p,
  smallest value of dp/de so called softest point
• Flow is sensitive to the details of the EoS!

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RHIC the first 3 years
RHIC Scientists Serve Up Perfect Liquid New
state of matter more remarkable than predicted --
raising many new questions April 18, 2005
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The perfect liquid
HYDRO Kolb, Sollfrank, Heinz, PRC 62 (2000)
054909
STAR PRL 86, 402 (2001)
P.F. Kolb et al., PLB 500 (2001) 0012137

• A strongly interacting, approximately thermalized
  system which for more central collisions behaves
  consistent with ideal fluid behavior!

v24 130 GeV
Zhixu Liu
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Viscosity and parton cascade
D. Molnar and P. Huovinen, PRL94012302,2005
D. Teaney PRC68034913,2003

• Viscosity needs to be small
• Parton cascades need huge opacities
• Partially solved by coalescence
• Microscopic picture responsible for large v2
  still not understood

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The perfect liquid

• Particles flow with a common velocity
• The most compact representation of the strong
  radial flow and its azimuthal variation
• Best described by QGP (soft!!) EoS!?

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Selected QM2006 topics

• High statistics results from PHOBOS, PHENIX and
  STAR for different beam energies and species,
  forward rapidity results from BRAHMS to test the
  perfect liquid behavior
• kET, mT-m, and v2/NCQ scaling
• Elliptic flow of the phi meson
• Early freeze-out?
• Eccentricity scaling
• Fluctuations
• Non-flow
• Higher harmonics v4/v22

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RHIC Elliptic Flow Data
Arkadij Taranenko for the PHENIX collaboration
Substantial elliptic flow signals are observed
for a variety of particle species at RHIC.
Indication of rapid thermalization?
PHENIX PRL 91, (2003)
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Universal Scaling of Elliptic Flow at RHIC
Arkadij Taranenko for the PHENIX collaboration
At midrapidity v2 (pt,M,b,A)/n F(KET/n)e(b,A)?
e(b,A) integral elliptic flow of charged
hadrons
KET - transverse kinetic energy
n number of quarks
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NQ and mT scaling
Star Preliminary, Y. Bai QM 2006

• Number of Quark and mT-m0 scaling holds for all
  centralities!

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Hydro Motivated Fit
STAR Phys. Rev. Lett. 87, 182301 (2001)
More extended approach in F. Retiere and M.A.
Lisa Phys.Rev.C70044907,2004
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Different b and T?
F. Retiere and M.A. Lisa, Phys.Rev.C70044907,2004

T 100 MeV, r2 0.05
r00.9, r2 0.05

• Light particle v2(pt) very sensitive to
  temperature
• Heavier particles v2(pt) more sensitive to
  transverse flow

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Identified particle v2
The STAR Collaboration, Phys. Rev. Lett. 87
(2001) 182301

• The largest effect in the v2(pt,m) is the radial
  flow and for light particles T
• However, the other parameters and the interplay
  with the radial flow are part of the tools to
  determine what the physics is which is pushing
  the matter!

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Different b and T?

• If the radial flow and temperature are different
  enough the scaling will be broken!

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Elliptic flow of f meson and partonic
collectivity at RHIC.
Arkadij Taranenko for the PHENIX collaboration

• f meson has a very small s for interactions
  with non-strange particles
• f meson has a relatively long lifetime (41
  fm/c) - decays outside the fireball
• 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) - 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
Arkadij Taranenko for the PHENIX collaboration
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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f meson from STAR and PHENIX

• The f meson follows the systematics from the
  other particle both at intermediate pt ant at
  lower pt (limited range unfortunately)
• Main contribution to the radial flow and elliptic
  flow from the pre-hadronic stage?

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Eccentricity scaling and system size
Arkadij Taranenko for the PHENIX collaboration
New PHENIX article on the scaling properties of
elliptic flow nucl-ex/0608033
Scaling test
nucl-ex/0608033
For AuAu collisions the eccentricity from
Glauber model ek v2(centrality)
k 3.1/-0.2 obtained from data
nucl-ex/0608033
v2 scales with eccentricity and across system size
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The perfect liquid?
S.Voloshin and A. Poskanzer, PLB 474 (2000) 27

• In the low density limit v2 is driven by e and
  dN/dy
• In ideal hydrodynamics driven by the (averaged)
  velocity of sound, v2/e constant

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The perfect liquid?

• Measured v2/e still depends on dN/dy
• At RHIC in-between LDL and ideal hydrodynamics
• Establishing where the LHC data point lay is
  crucial

S. Voloshin, QM2006
Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909
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Non-flow, fluctuations and e
fluctuations
see S. Voloshin QM2006
Measuring the cumulants of different order
provides constraints on fluctuations and
non-flow.
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Non-flow, fluctuations and e
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Non-flow, fluctuations and e
!!
M. Miller and RS, arXivnucl-ex/0312008
Ratio v24/v22 sensitive to the
fluctuations! For mid-central collisions
fluctuations compatible with fluctuations in e
!! Non-flow should give a constant g2 which is
incompatible with the data
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Is our first RHIC snapshot in focus?
Lets focus on the spatial distribution of the
interaction points of participating nucleons
for the same b, these interaction points will
vary from event-to-event
Y0
AuAu
AuAu
Y0
and thus the relevant eccentricity for elliptic
flow also varies event-by-event
From PHOBOS _at_ Quark Matter 2005 ? explored much
further since then
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Does using make a difference?
YES
200 GeV
Increasingly important for smaller systems
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Average v2/ in CuCu and AuAu
Participant Eccentricity
Standard Eccentricity
200 GeV
200 GeV
CuCu
CuCu
AuAu
AuAu
arXivnucl-ex/0610037, submitted to PRL
arXivnucl-ex/0610037, submitted to PRL
unifies average v2 in CuCu and AuAu
Related work Miller, Snellings, Zhu, Bleicher,
Stöcker
Voloshin, Poskanzer, PLB 474 27 (2000)
Heiselberg, Levy, PRC 59 2716, (1999)
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The perfect liquid?

• Measured v2/e still depends on dN/dy
• At RHIC in-between LDL and ideal hydrodynamics
• Establishing where the LHC data point lay is
  crucial

S. Voloshin, QM2006
Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909
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v2/e

• The measured v2 values by PHOBOS, PHENIX and STAR
  agree rather well
• PHENIX shows that by dividing by all curves
  collapse
• They do not calculate e
• They use v2 is proportional to e
• They claim from earlier measurements that v2/e
  constant
• is this well motivated?
• PHOBOS and STAR show that v2/e scales with 1/S
  dN/dy
• They calculate e using Glauber and show that for
  reconciling different systems epart2 is
  essential
• Is e from Glauber the correct scaling variable?

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Eccentricity from Glauber and CGC

• If the initial condition is more like CGC, v2/e
  from the data would be much lower
• Breaking the perfect fluid agreement!
• v2/e(CGC) would seem to even stronger depend on
  centrality!

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consistency with other methods
v24 agrees with q-fit results non-flow does
not have to be invoked difference between v22
and v24 apparently dominated by fluctuations
For discussion of fluctuations and cumulants see
R. Snellings nucl-ex/0312008 and talk by S.
Voloshin
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Fluctuations in participant eccentricity
What magnitude of fluctuations are expected?
Quantify with s(epart)/
Expect large dynamical fluctuation in the
participant eccentricity
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New Analysis event-by-event v2 measurement
200 GeV AuAu

• Utilize Full Phase space coverage of PHOBOS
  (h
• Detailed modeling of detector response,
  statistical fluctuations and multiplicity
  dependence.
• Method is described in arXivnucl-ex/0608025
• Measure v2 on an event-by-event basis.
• Take e-by-e result and average to compare to our
  other results.

measured event-by-event is in agreement with
both hit and track based PHOBOS results.
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New Result v2 and epart Fluctuations
s(v2)/ and s(epart)/ in 200 GeV AuAu
Collisions
band 90 CL
PHOBOS v2 result
PHOBOS epart prediction
MC with nofluctuations
Magnitude of v2 fluctuations is in agreement with
epart fluctuations
Poster by Burak Alver and talk by Constantin
Loizides
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Non-flow (still) matters!
non flow!

• At intermediate pt the centrality dependence can
  even change order

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Non-flow (still) matters!
S. Voloshin, QM2006
STAR preliminary
CuCu 200 GeV v2FTPC FTPC h 2.9 3.9

• Even when using correlations between the TPC and
  FTPC (Dh 2) still signs of non-flow at larger
  pt

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Energy dependence of v2(pt)

• What is the reason for this similar behavior?
• Are the individual contributions from the
  different particles also so similar (naïve
  expectations are somewhat larger flow and
  different relative contribution from the various
  (mass) particles as function of pt)?

PHENIX
PHENIX arXivnucl-ex/0411040

• For charged particles PHENIX observes similar
  v2(pt) at 62 and 200 GeV while the difference
  with 17 GeV (CERES) is much bigger

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Energy dependence of v2(pt)

• v2(pt) increases between 10-15 from SPS to RHIC

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BRAHMS rapidity dependence
BRAHMS preliminary
?3
?
?0
K
p
No strong indication of rapidity dependence, the
strong rapidity dependence on the integrated v2
is more or less explained by the mean pT.
Meson/baryon splitting might be different between
y0 and y3, if statistical significance is
improved.
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The perfect liquid?
Yuting Bai, QM2006

• v4 /v22 a detailed probe of ideal hydro behavior
  and related to the degree of thermalization!
• Data points are above the model predictions,
  however due to the systematic uncertainty from
  non-flow we can not exclude the models yet

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Sound speed Eccentricity scaled v2
Arkadij Taranenko for the PHENIX collaboration
See nucl-ex/0608033 for details
v2/e for 0.45 GeV/c
cs 0.35 0.05 (cs2 0.12), soft EOS
An effective EOS is softer than that for high
temperature QGP, but does not reflect a strong
first order phase transition, where Cs0 during
an extended hadronization period
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The QCD EoS and Cs

• Test the effect of four different EoS qp is
  lattice inspired, Q has first order phase
  transition, H is hadron gas with no phase
  transition and T a smooth parameterization
  between hadron and QGP phase

Pasi Huovinen, arXivnucl-th/0505036
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v2(m,pt) and the softest point
Pasi Huovinen, arXivnucl-th/0505036

• EoS Q and EoS T (both have significant softening)
  do provide the best description of the magnitude
  of the mass scaling in v2(pt)
• The lattice inspired EoS (EoS qp) in ideal hydro
  does as poorly as a hadron gas EoS!

• Elliptic flow as function of pt and mass very
  sensitive to EoS (particular the heavier
  particles)
• Before we can draw conclusions about the EoS much
  more work needed in theory (test different EoS,
  influence viscosity, hadronic phase)

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Summary

• More than 20 talks about anisotropic flow!
• Lot of high statistic results
• Starting to address in more detail fluctuations
  and non-flow and trying to say something about
  EoS
• Still many important questions to answer
• What are the initial conditions and in particular
  the initial eccentricity?
• Is most of the collective motion (including the
  radial flow) build up during the partonic phase?
• What is the energy dependence of v2(pt)?

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Viscosity/entropy versus T
Csernai, Kapusta and McLerran arXivnucl-th/060403
2
Hirano and Gyulassy arXivnucl-th/0506049

• Important to quantitatively calculate the effect
  of viscosity on v2
• Would reduce further the elliptic flow

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The perfect liquid?
Adapted from S.A. Voloshin and A.M. Poskanzer,
Phys.Lett.B474 27-32 (2000) 9906075

• Different centrality dependence between hydro
  (proportional to e and peaks around b12 fm) and
  low density limit (peaks around b8 fm)
• Data peaks around b 10 fm (in between LDL and
  hydrodynamics)
• Expect the value of v2 to peak more peripheral
  for higher (LHC) energies

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Elliptic flow at the LHC
T. Hirano
D. Teaney, J. Lauret, E.V. Shuryak,
arXivnucl-th/0011058 Phys. Rev. Lett 86, 4783
(2001).

• The higher the beam energy the more dominant the
  QGP contribution becomes

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First RHIC non-flow estimates
K.H. Ackermann et al (STAR), Phys. Rev. Lett 86,
402 (2001)
RS (STAR), Nucl. Phys. A 698, 193 (2002)
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HIJING estimates of LHC non-flow
Random subevents
h subevents
h gap larger 1
b

• Non-flow in HIJING depends on subevent definition
  and kinematic cuts
• Estimated non-flow in magnitude is comparable to
  RHIC estimates

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Flow and non-flow in ALICE
E. Simili, ALICE QM2006 poster
non-flow (HIJING) fit
LDL fit
dN/dy estimate from Armesto, Salgado, Wiedemann
- hep/ph0407018
hydro

• LDL fit based on CGC dN/dy estimate and v2/e
  extrapolation
• Hydro lines based on hard and soft EoS
• Estimated nonflow is an issue for the centrality
  dependence study but not for the mid-central
  collision range
• With real data better studies will be based on
  cumulant methods

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Non flow matters v4
v4 from 3 particle correlations i,j,k
nonflow contributes if i and j are correlated by
nonflow and j and k are correlated by flow

• Uncertainties on are small, however they
  quickly become significant at larger pt

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Non-flow matters!
Yuting Bai, QM2006

• Charged particle v2 from four particle cumulant
  are measured up to 10 GeV at 200GeV.
• For AuAu at 200 GeV still significant v2 above 6
  GeV/c
• Theoretical large flow values at large pt still
  poorly understood
• Microscopic picture at low-pt also still not
  complete