Anisotropic Flow and Phase transitions,

1
Anisotropic Flow and Phase transitions,and a
little bit on fluctuations/correlations
Sergei Voloshin Wayne State
University, Detroit

• Outline
• Anisotropic flow where to look for a phase
  transition - v1(y) - directed flow wiggle -
  v2(pt) constituent quark number scaling -
  v2(pt) mass splitting and QGP -
  v2(energy,centrality) approaching hydro
  limit - v2/? vs dN/dy/S, any wiggle/step?
• Correlation functions and fluctuations.
• Centrality dependence of ltdpt dptgt and radial
  flow.
• Conclusions

2
Anisotropic flow
Anisotropic flow ? correlationswith respect to
the reaction plane
Term flow does not mean necessarily hydro
flow used only to emphasize the
collectivebehavior ?? multiparticle azimuthal
correlation.

• Note large orbital angular momen-tum in the
  system.
• Parity violation
• Orbital momentum ? particle spin.

Fourier decomposition of single particle
inclusive spectra
Directed flow
Elliptic flow
3
Hydro antiflow, third flow component
Csernai, Rohrich, PLB 458 (1999) 454. Magas,
Csernai, Strottman, hep-ph/0010307
Brachmann, Soff, Dumitru, Stocker, Maruhn,
Greiner Bravina, Rischke , PRC 61 (2000) 024909

Net baryon density
flow
antiflow

• - Strongest at the softest point?
• The same for pions and protons ?

4
Third flow component as the QGP signal
L.P. Csernai, D. Rohrich PRL 458 (1999) 454
Wiggle is present only for the QGP EoS.
This calculations have been done at 11 AGeV.
Would the results change for RHIC?
5
Wiggle from anti-flow development in time.

• J. Brachmann Soff, Dumitru, Stocker, Maruhn,
  Greiner
• Bravina, Rischke,
• PRC 61, 024909 (2000)

6
Wiggle from uRQMD
Rich dependence on the particle type baryons,
antibaryons, mesons
Marcus Bleicher, Horst Stocker PLB 526, (2002)
309-314
7
Anti-flow from shadowing
Anti-flow is developingin more peripheral
collisions
8
Directed flow wiggle in cascade models
R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003
R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu,
PRL
84 (2000) 2803
Baryon stopping
Radial flow ? ltx pxgt gt 0
The wiggle is pronounced only at high energies
wiggle
Does the picture contradict FOPI resultson
different isotope collisions?
9
QM2002
Warning Large systematic errors!
10
Laszlos slide from BNL Flow workshop 03
The slope of v1(eta) at eta0is indeed as in
antiflowscenario, but also the sameas always
for pions at lowerenergies
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PHOBOS, v1(eta)
Qualitatively the samepicture from SPS
energiesto highest RHIC energy.
12
STAR ZDC-SMD
What about ALICE, CMS, do they have something
like that?
13
v1(eta), v1(pt), AuAu_at_62 GeV,different
centralities
Qualitatively the picture is very similar at
different centralities
14
Comparison with models. Centrality dependence
Neither model describes v1(eta) close to
midrapidty
- In order to prove the wiggle one needs
identified particle measurementsand look for the
change of sign of the slope with
energy/centrality. At 62 GeV the errorbars are
too large, we hope to have it such results for
200 GeV data.
15
Elliptic Flow.
Sensitive to early times. (Free streaming kills
? )
16
Elliptic flow as function of

• It is measured vs
• collision energy
• transverse momentum
• centrality
• rapidity
• particle ID

• Integrated values of v2 noticeably increase with
  energy
• The slope of v2(pt) increase slowly
• Most of the increase in integrated v2 comes from
  the increase in mean pt.
• In mid and more central collisions elliptic flow
  is rather well described by hydro model

PHOBOS
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Integrated v2 at different energies
We still have to analyze carefully the centrality
dependence
18
Constituent quark model coalescence
coalescence
fragmentation
S.V., QM2002 D. Molnar, S.V., PRL 2003
Low pt quarks
High pt quarks
In the low pt region density is large and most
quarks coalesce N hadron N quark
In the high pt region fragmentation eventually
wins
Taking into account that in coalescence and in
fragmentation
, there could be a region in quark pt
where only few quarks coalesce, but give
hadronsin the hadron pt region where most
hadrons are produced via coalescence.

• Side-notes
• a) more particles produced via coalescence rather
  than parton fragmentation ? larger mean pt
• ? higher baryon/meson ratio
• ? lower multiplicity per participant

• -gt D. Molnar, QM2004, in progress
• gt Bass, Fries, Mueller. Nonaka Levai, Ko
• gt Eremin, S.V.

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Constiuent quark scaling v2 and RCP

• Constituent quark scaling holds well.
  Deviations are where expected.
• Elliptic flow saturates at pt 1 GeV, just at
  constituent quark scale. An accident?

Gas of constituent quarks deconfinement !?
20
PHENIX const. quark scaling, v2 saturates at
RHIC energy
21
Are they thermalized?
S. Pratt, S. Pal , nucl-th/0409038

• Two pictures correspond to the same v2 of quarks,
  but
• v2(B) 3/2 v2(M) (no thermalization ?)
• v2(B) v2(M) (freeze-out at constant phase
  space density)

• My conclusion constituent quark scaling ?-
  Deconfinement!
• No thermalization (at least in this region of
  pt)
• (Freeze-out at constant density in the
  configuration space)
• The same mechanism at sqrt(s_NN) 200 and 62 GeV.
  
• If thermalized, disappear at LHC??

22
v2(pt) at 200 GeV. Mass splitting.
Data PHENIX, Nucl. Phys. A715, 599, 2003 Hydro
P. Huovinen, P. Kolb, U. Heinz, P. Ruuskanen,
S.V., Phys. Lett. B503, 58, 2001
Mass dependence is rather well reproduced by
hydrodynamical model calculations. Note
dependence on the EoS. But qualitatively such a
mass dependence will be present in any model, for
example, in the constituent quark coalescence
picture (heavier particle ? larger difference in
constituent quark momenta)
23
v2(pt) _at_ 200 and 62 GeV
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Centrality dependence. Hydro and Low Density
limits
Hydro v2 ?
Low Density Limit v2 ? dN/dy / A
Ollitrault, PRD 46 (1992) 229
Heiselberg Levy, PRC C59 (1999) 2716
Hydro P.F. Kolb, et al
SV A. Poskanzer, PLB 474 (2000) 27
LDL
v2 / ?
hydro
(pts are RQMD v2.4)

5 10
b (fm)
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v2/? and phase transitions
Centrality dependence Sorge, PRL 82 2048 (99),
Heiselberg Levy, PRC 59 2716 (99)
Dependence on the particle density in the
transverse plane S.V. A. Poskanzer, PLB
474 (2000) 27
Uncertainties Hydro limits slightly depend on
initial conditions Data no systematic
errors, shaded area uncertainty in centrality
determinations. Curves hand made
Cold deconfinement?
E877 NA49
26
Hydro limits
v2 / ?
Hydro P.F. Kolb, et al

• Questions to address
• is it saturating?- what happens at SPS
  energies? Any wiggle?

27
Cold deconfinement, color percolation?
There is a need for the next generationof this
plot better estimates of epsilon,adding more
data (in particular 62 GeV) It is a real pity
that NA49 measurements have so large systematic
uncertainty. Need detector with better azimuthal
acceptance (could be just a simple extra
detector used to determine the RP) . FT RHIC?
CERN SPS energies b 4 fm RHIC b 7 fm
28
Charm flow (via electron measurements)
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Correlations/fluctuations
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2-particle correlation functions
Distribution of correlated pairs
Distribution of associated particles (2) per
trigger particle (1)
Probability to find a correlated pair
Relation to fluctuations
Fluctuations are determined by the average
valueof the correlationfunction over
momentumregion under study.
31
ltptgt fluctuations observables and observables.
What are the main requirements for a good
observable? -- be sensitive to the physics under
study -- be defined at the theoretical level,
be detector/experiment independent -- have clear
physical meaning -- not to be limited in scope,
provide new venues for further study
32
Multiplicity fluctuations
? - Free from volume fluctuations ? - Fails
at small lt n2 gt
Particle ratios
Charge fluctuations

• ? - lt n n-gt - used multiplicity, subject
• to cuts and acceptance

33
Comparison to PHENIX, Fpt (slide from G.
Westfall (STAR), QM04)
200 GeV AuAuSTAR Cuts ? lt 1.0?? 360?0.1 lt
pt lt 2 GeV
200 GeV AuAuSTAR withPHENIX Cuts ? lt 0.35??
2x90?0.2 lt pt lt 2 GeV
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Elliptic flow contribution to ltdpt dptgt
Shengli Huang (STAR) USTC RHIC Workshop, Hefei,
China , Oct. 2004
Could be better to plot ltdpt dptgt /ltptgt2
35
correlations elongation in ??
All data on ltdpt dptgt are STAR preliminary,
taken from talks of G. Westwall (STAR) at
QM2004 and Nuclear Dynamics WSs 04 and 05
R(??) 1 - ??? ? ltRgt (Y) 1 - 4/3 ? Y,where
Y (??)max/2
Blue dotted lines assume the same ?. Note
difference in slopes (red vs blue) broadening
of R(??) with centrality
36
centrality dependence
At midrapidity, the probability to find a
particle is about 60 larger if one particle has
been already detected.
In a superposition of two independent
collisions,the ratio of the probability that in
a randomly chosen pair both particles are from
the same collision to the probability that two
particles are from different collisions is about
1.66
37
Elementary NN-collision. Correlation functions.
y
rapidity
x
Correlations are due to local charge(s)
conservation, resonances, due to fluctuations in
number of produced strings, e.g. number of
qq-collisions.
ISR
At midrapidity, the probability to find a
particle is about 60 larger if one particle has
been already detected.
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Radial flow ? 2- particle correlations
All particles produced in the same NN-collision
(qq-string) experience the transverse radial
push that is(a) in the same direction (leads
to correlations in phi) (b) the same in magnitude
(? correlations in pt) ? Position-momentum
correlations caused by transverseexpansion
brings totally new mechanism for momentum
correlations, not present in NN-collisions
39
Transverse radial expansion
STAR Collaboration, PRL 92, 112301 (2004)
y
rapidity
x
Blast wave parameterization (Schnedermann,
Sollfrank, Heinz, PRC 48, 2462 (1993), d3n/d3p
e-E/T) of the source at freeze-out
Parameters T-temperature, velocity profile ?t
?r n
Note uniform source densityat r lt R has been
assumed
40
Azimuthal correlations
Figures are shown for particles from the same NN
collision. Dilution factor to be applied!
First and second harmonics of the distribution
on the left
n1, T110 MeV
! - the large values of transverseflow, gt 0.25,
would contradict non-flow estimates in
elliptic flow measurements
No momentum conservation effects has been
included. Those would be important for the
charge independent first harmonic correlations.
41
?? x ?? correlations

• Charge independent correlations particles at
  large rapidities, initially uncorrelated, become
  correlated, as all of them are pushed by radial
  flow in the same direction. For those, one needs
  2d correlations (rapidity X azimuth) Shown
  below hand drawn sketch.

42
Extracting Near-Side Jet Yields
dAu, 40-100
D. Magestro (STAR) Hard Probes 2004
In AuAu, jet-like correlation sits on top of an
additional, approximately flat correlation in ??
STAR preliminary
AuAu, 0-5
3 lt pT(trig) lt 6 GeV2 lt pT(assoc) lt pT(trig)
43
Brief comparison to data
centrality dependence

• Possible reasons for discrepancy
• diffusion, thermalization time
• spatial source profile (not uniform density
  in transverse plane, e.g. cylinder shell)

44
correlation summary
1. Avoid using ratios (n/n-, K/K0,), use
to get rid of
volume fluctuations and be free from
problems related to low multiplicities. 2. If use
normalized variance correct for the efficiency.

1. Transverse radial flow leads to strong
   space-momentum correlation. In combination with
   space correlations between particles created in
   the same NN collision, it leads to
   characteristic two (and many) particlerapidity,
   transverse momentum, and azimuthal correlations.
2. This phenomenon provides a natural (at present,
   qualitative) explanation of the centrality
   dependence of mean pt pseudorapidity/azimuthal
   anglecorrelations. It can be further used to
   study the details of the systemequilibration/ther
   malization and evolution (e.g. thermalization
   time, velocityprofile, etc.)

45
EXTRA SLIDES
46
Rapidity correlations

• How to disentangle initial correlations at the
  parton production stage and obtaineddue to the
  transverse expansion? - Charge dependent and
  charge independent correlations.
• Correlation of conserved charges (Balance
  Functions). In this case the correlationsexisted
  already at the production moment would be
  modified (narrowed) by radial flow.
• Charge independent correlations particles at
  large rapidities, initially uncorrelated, become
  correlated, as all of them are pushed by radial
  flow in the same direction.

47
Initial and freeze-out configurations
Uncertainty particles are at the same
positionat the moment of production, but the
blastwave parameterization is done at freeze-out

• Smearing would depend on the
• thermalization time (which is supposedly small)
• diffusion during the system evolution before
  freeze-out
• non-zero expansion velocity in pp

Should we take it as a possibility to study all
the above effects?
48
AA collision. Single jet tomography.
In this picture, the transverse momentum of the
(same side, large ??) associated particles would
be a measure of the space position the hard
scattering occurred
The plot on the right shows particle
azimuthaldistribution (integrated over all pts)
with respect to the boost direction. In order to
compare with data it should be also convoluted
with jet azimuthal distribution relativeto
radial direction.
49
Sensitivity to the velocity profile
Results for n0.5 and n2 are shown
50
Parity violation study via 3-particle correlations
hep-ph/0406311
a gt 0 ? preferential emission along the angular
momentum The sign can vary event by event,
aQ/N?, where Q is the topological charge,
Q1,2, ?at dN/dy100, a1.
Looking for the effect ofD. Kharzeev,
hep-ph/0406125
Projections on the direction of angular momentum
All effects non sensitive to the RP cancel
out! Possible systematics clusters that flow
projections onto reaction plane
And using only one particle instead of the event
flow vector
note that for a rapidity region symmetric with
respect to the midrapidity v10
51
Ebye and inclusive approaches
Most of the present measurementsare done this way
Would be better, easier to analyze
theoretically. (! Numerically both are very
close)