Anisotropic Flow

1
Anisotropic Flow
Sergei A. Voloshin Wayne State
University, Detroit, Michigan
Disclaimer - Not a real review this is an
introductionto Anisotropic Flow terminology,
physics,analysis techniques, achievements and
problems, current status of the art. - Many of
the most recent results will bediscussed in the
original talks at this School. - Apologies for
not mentioning many good papers on the subject.
This talk is based mostly on works where I
participated and know the best.

• It must be something!
• Fully Artistic!
• - Arts playground
• for many years
• - Fun for everyone!

2
Outline
Part I. Physics 1. Introduction.
Definitions. 2. Directed flow - Physics of
the wiggle - Blast wave parameterization
- Coalescence I. Directed flow of light
nuclei 3. Elliptic flow - General
properties. Early times - Low Density and
Hydro Limits - Phase transition -
Blast wave. Mass splitting - Coalescence
II. Constituent quarks. Resonances.
- Elliptic flow at high pts. 4. Anisotropies
and asymmetries - Femtoscopy of anisotropic
source - High pt, 2-particle correlations
- Global polarization, Parity violation 5.
Can we measure it? - correlations induced by
flow - Non-flow. Flow fluctuations
Part II. Methods and Results 1. Non-flow
estimates - From the resolution plot
- Azimuthal correlations in pp and AA 2.
Multiparticle correlations - 4-particle
cumulants. Methods. - Non-flow and flow
fluctuations - Mixed harmonics. 3-particle
correlations. - Distributions in q-vector
- Detector effects 3. Main results -
Reaching the hydro limit - Mass splitting
- Constituent quark scaling - Elliptic
flow at high pt - v1 and higher harmonics
- other 4. Conclusion
3
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. Newer trend event anisotropy
Note large orbital angular momen-tum in the
system !
No symmetry between x and -x,except
midrapidity Symmetry between y and and -y
(Otherwise parity violation)
4
How to characterize anisotropic flow?
S.V., Y. Zhanghep-ph/9407282 Z.Phys. C70 (1996)
665
Advantages - Describes different kind of
anisotropies in a common way - Possibility to
fully correct the results ? compare directly
with theory and other experiments
5
Definitions, continued

• Terminology
• harmonics, not multipoles (dipole, etc.required
  to describe 2d or 3d distributions)
• v2 in pp collisions is almost 100
• event anisotropy at high pt, elliptic flow at
  low pt

Anisotropic flow ? correlationswith respect to
the reaction plane
The situation with definitions is more
complicated with two particle spectra measured
with respect to the reaction plane. One way
parameterize, consider parameter dependence on
pair orientation relative to the reaction plane.
6
Why are we interested in anisotropic flow?
Short answer to learn more about system
properties, evolution dynamics, hadronization
Anisotropic flow as a measure of interactions
in the system. Example Does hydrodynamic model
works? 1992 paper of J.-Y. Ollitrault
PRD 46 (1992) 229

• Collide AuAu, is it enough to create QGP?
• Is the system dense enough? What are the Quark
  Gluon densities?
• Does the system equilibrate?
• What is the initial Temperature?

To answer these questions we need to study the
system early in the collision - hard (rare)
probes J/Psi, jets, dileptons, - anisotropic
flow !
Before discussing how the anisotropic flow let
us set some time scales (in the center of mass
frame) Passing time the time two nuclei pass
each other RA/? Initial transverse size of the
system RA Freeze-out time (could be up to a
several RA)

• Directed flow is predefined at passing time, as
  at this moment the initial geometry of the
  system being set.
• Elliptic flow is mostly defined at the time scale
  of the initial size of the system for two
  reasons
• This is the time required for a fast particle to
  traverse the system
• The time after which the spatial anisotropy
  diminish

7
Qualitative features of anisotropic flow.

• Let us try to catch the possible physics
• Can we describe flow assuming some properties of
• the collective motion.
• Directed flow does it look like particle
  emission from
• Moving source?
• Screened source (shadowing)?
• Elliptic flow
• Surface emission?
• Anisotropically expanding source?
• Rescattering?

• Among others, a few pictures will be discussed in
  more detail
• Blast wave parameterization
• Low Density Limit
• Coalescence

8
Directed flow wiggle in cascade models
Snellings, Poskanzer, S.V., nucl-ex/9904003
Snellings, Sorge, S.V., F. Wang, Nu Xu, PRL 84
(2000) 2803
Baryon stopping
The wiggle is pronounced only at high energies
wiggle
Does the picture contradict FOPI resultson
different isotope collisions?
9
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
10
Third flow component as the QGP signal
L.P. Csernai, D. Rohrich PRL 458 (1999) 454
The wiggle is present only for the QGP EoS.
This calculations have been done at 11 AGeV.
Would the results change for RHIC?
11
Interplay of radial and anisotropic (directed)
flow
S.V., PRC 55 (1997) 1630
Solid lines non-relativistic case
High pt particles areproduced mostly in the
redregion low pt particles in the blue region

• Interplay of three velocities
• Thermal velocity
• Radial expansion mean velocity
• Anisotropic (modulation in radial expansion)

Note! Similar formalism can be achieved with
totallydifferent interpretation (not requiring
thermalization), where the role of Temperature
plays mean pt change due to scattering Radial
flow velocity mean radial component of
particlevelocityAnisotropic flow velocity the
modulation in the above
The effect is larger for larger mass
12
Fitting the real data
S.V and E877, Nucl Phys. A638, 455c (1998)
Directed flow of protons in AuAu collisions at
Elab11.4 GeV, 2.6 lt y lt 2.8
13
Coalescence I. E877 light nuclei flow.
S.V and E877, Nucl Phys A638 (1998) 455c E877 PRC
59(1999) 884

• What is needed for the equation aboveto work?
• Rare process
• Bconst only if the configuration space density
  does not depend on theorientation wrt RP
• Note! The coalescence picture itself can
  havemuch larger region of applicabilitythan the
  equation above. We/I just do notknow how to
  describe coalescence in thecase of not rare
  processes.

E877 conclusion Configuration space density
increases in the direction of flow.
Note v1 values gt 0.5 ? there must be other
non-zero harmonics!
14
Resonances
S.V and E877, Nucl Phys. A638, 455c (1998)
Note one of the examples of non-thermal interpr
etation of blast wave formulae
X. Dong, S. Esumi, P.Sorensen, N.Xu,Z. Xu, PLB
597(2004)328
Elliptic flow
Nonaka, Müller, Asakawa, Bass, Fries PRC
69(2004)031902R
15
Elliptic flow. General properties.
Elliptic flow must vanish if initially the system
was created symmetric. Then, at small
eccentricities, v2?
e -- initialization of energy density s
initialization ofentropy density
Other similar/same quantities Ollitrault
?s Heiselberg ? Sorge A2 Shuryak s2

• Note
• - it is not at all trivial what should be used
  (if any) for higher harmonics (no simple form)
• - s2 parameter in the Blast Wave fit (below) to
  v2(pt), in general, is a different parameter
• -- do not confuse initial and final state
  anisotropy

16
Sensitivity to early times

• The sensitivity is due to two reasons
• Decrease in spatial anisotropy
• Decrease in spatial particle density.

17
When the elliptic flow is formed
Sensitive to the physics of constituent
interactions (needed to converts space to
momentum anisotropy) at early times
(free-streaming kills the initial space
anisotropy)
XZ-plane - the reaction plane
The characteristic time scale of 2-4 fm is
similar in any model parton cascade, hydro, etc.
18
Low density limit
(called collisionless in the original paper of
Heiselberg and Levy) Below - my own derivation of
Heiselbergs results
Heiselberg Levy, PRC 59 (1999) 2716
Change in the particle flux is proportional to
the probability for the particle to interact.
Integrations over a) particle emission point b)
Over the trajectory of the particle (time) with
weight proportional to the density of other
particles --scattering centers
Particle density at time t assuming free
streaming
Note (x-vt) changes very little over the entire
history
19
First hydro calculations
J.-Y. Ollitrault, PRD 46 (1992) 229
In hydro, where mean free path is by assumption
much less than the size of the system,there is
no other parameters than the system size (may
enter time scales, see below). Then elliptic flow
must follow closely the initial eccentricity.
20
Centrality dependence
S.V. A. Poskanzer, PLB 474 (2000) 27
Points RQMD, dashed curve - ?(b)
HYDRO limit
Ollitrault
Heinz et al.
21
v2/? and phase transitions
After original ideas of Sorge, PRL 82 (1999)
2048, Heiselberg Levy, PRC 59 (1999) 2716
LDL
HYDRO
22
More on hydro limits
Minimum in v2/? due to softening of the EoS at
phase transition
23
v2/? and phase transitions
S.V. A. Poskanzer, PLB 474 (2000) 27
What to expect for different nuclei,
CuCu? First guess would be
but there is no such factor in the LDL
Cold deconfinement?
E877 NA49
Uncertainties Hydro limits slightly depend on
initial conditions Data no systematic
errors, shaded area uncertainty in centrality
determinations. Curves hand made
24
Centrality dependence. Hydro RQMD.
Teaney, Lauret, Shuryak nucl-th/0110037

1. 400 600 800
   dNch/dy

LH8 ? latent heat 0.8 GeV/fm3 Pt slope
parameters are about 20 larger in hydro
compared to data
- v2 increases with dN/dy - Centrality dependence
close to data
25
v2(pt) dependence. Blast wave model.
v2(pt) - Houvinen, Kolb, Heinz, Ruuskanen, S.V.,
PLB 503 (2001) 58
Parameters T temperature ?0 - radial
expansion rapidity ?2 - amplitude of azimuthal
variation in expansion rapidity
v2(pt) - STAR Collaboration, PRL 87 (2001)
182301

• Note
• The possibility different interpretation of the
  parameters (other than hydro-like)
• The possibility of different realization of the
  parameter s2. There is no strictcorrespondence
  between this parameter and the shape of the
  source at freeze-out.

26
How much s2 matters?
- model fits data well - shape (s2 parameter)
agrees with the interferometry measurements (see
below) under assumption that flow velocity field
is normal to the surface
27
v2(pt). Mass splitting. Dependence on the EoS.
P. Huovinen, P. Kolb, U. Heinz, P. Ruuskanen,
S.V., PLB503, 58, 2001
Mass splitting is stronger for the QGP
EoS. But qualitatively such a mass dependence
will be present in any model, for example, in the
constituent quark coalescence picture (discussed
below) (heavier particle ? larger difference in
constituent quark momenta)
28
Constituent quark model coalescence
coalescence
fragmentation
S.V., QM2002 D. Molnar, S.V., PRL 2003
Low pt quarks
High pt quarks
Only in the intermediate region (rare processes)
coalescence can be described by
?
In the low pt region the 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
• gt Bass, Fries, Müller, Nonaka Levai, Ko
• gt Eremin, S.V.

29
Elliptic flow due to jet quenching
R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003
Gyulassy, Vitev Wang, PRL 86 (2001) 2537

• Easier escape in the
• x direction
• in-plane particle
• emission

30
Elliptic flow in absorption model
STAR, PRL 93 (2004) 252301
L
Probability to escape
Hard shell box density profile ()
extreme quenching
E. Shuryak, nucl-th/0112042 Hard
sphere -- () realistic
quenching Woods-Saxon WS density profile ()
realistic quenching
31
New possibilities

• Anisotropies and asymmetries
• HBT with respect to the reaction plane
• Non-identical particle correlations with respect
  to the reaction plane
• High pt 2-particle correlation wrt reaction plane
• Global polarization in AA
• Parity violation

32
Hanbury Brown Twiss interferometry of an
anisotropic source
Let us measure the geometry of anisotropic source!
Proposed S.V. W. Cleland, PRC 53 (1996) 896
PRC 54(1996) 3212 Further technique developments
U. Wiedemann, U. Heinz, M. Liza First attempt to
measure D. Miskowiec, E877, QM 95 First and
subsequent real measurements M. Lisa et al.,
E895, STAR
33
Hanbury Brown Twiss interferometry of an
anisotropic source
Same parameters fit R(f) and v2(pT,m)
34
azHBT
S.V. LBNL 1998 annual report R20http//ie.lbl.g
ov/nsd1999/rnc/RNC.htm
RQMD v 2.3, AuAu _at_ RHIC
In this picture at high energies /high pt, the
relative differencebetween out-of-plane size and
in-plane size only increases.
35
azHBT-2
Note out-of-phase Rside modulations for k0
case. Should we try very low kT at RHIC?
IPES initial conditions, U. Heinz, P. Kolb PL
B542 (2002) 216
36
Do different particles freeze-out at the same
place?
37
Non-identical 2-particle correlations
S.V., R. Lednicky, S. Panitkin, Nu Xu, PRL 79
(1997) 4766
38
2-particle correlations wrt RP
J. Bielcikova, P. Wurm, K. Filimonov S. Esumi,
S.V., PRC, 2003
x azimuthal angle, transverse momentum,
rapidity, etc.
CERES, PRL 92(2004)032901
Approach - remove flow contribution-
parameterize the shape of what is left - study RP
orientation dependence of the parameters
Selection of one (or both) of particles in- or
out- of the reaction plane distorts the RP
determination
a trigger particle
STAR, PRL 93 (2004) 252301
39
Parity, CP- violation, global polarization
Kharzeev, Pisarski, Tytgat, PRL 81 (1998)
512 Kharzeev, Pisarski, PRD 61 (2000) 111901
Observing parity (CP) violation with anisotropic
flow techniques
Parity violation
S.V. PRC 62 (2000) 044901
S.V. PRC 70 (2004) 057901
Global polarization
Oriented DCC
Asakawa, Minakata, Müller, nucl-th/0212070
Negative elliptic flow of neutral pions
40
How one would measure flow?
41
Flow induced correlations
E877, PRL 73, 2532 (1994)
42
Differential flow. First observation of v2 gt 0
E877, PRC 55 (1997) 1420
Distribution of hits in the silicon pad detector
wrt RP determined by calorimeters.
?n n-th harmonic Event Plane
43
End of the ideal world Non-flow, flow
fluctuations,
Flow ? ? non-flow
Non-flow azimuthal correlations of any other
originexcept the correlation with respect to the
reaction plane. It combines the possible
contributions from resonance decay, inter and
intra jet correlations, etc.
An example
Effect of flow fluctuations
Other possibilities fro flow fluctuations
fluctuation in theinitial geometry, in
multiplicity at the same geometry, etc.
Each one by itself presents little problem, but
taken at the same time, it is the major problem
we fight during the last years.
44
Part I. The End.
Part II. Methods and Results 1. Non-flow
estimates - From the resolution plot
- Azimuthal correlations in pp and AA 2.
Multiparticle correlations - 4-particle
cumulants. Methods. - Non-flow and flow
fluctuations - Mixed harmonics. 3-particle
correlations. - Distributions in q-vector
- Detector effects 3. Main results -
Reaching the hydro limit - Mass splitting
- Constituent quark scaling - Elliptic
flow at high pt - v1 and higher harmonics
- other 4. Conclusion
45
EXTRA
46
Mixed harmonic technique or 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.
Projections on the direction of angular momentum
projections onto reaction plane
All effects non sensitive to the RP cancel
out! Possible systematics clusters that flow
And using only one particle instead of the event
flow vector
note that for a rapidity region symmetric with
respect to the midrapidity v10
47
Anti-flow from shadowing
Anti-flow is developingin more peripheral
collisions
48
Wiggle from uRQMD
Rich dependence on the particle type baryons,
antibaryons, mesons
Marcus Bleicher, Horst Stocker PLB 526, (2002)
309-314
49
Flow due to absorption. v2, v4 e2, e4
See also nucl-th/0310044 A. Drees, H. Feng, J.
Jia
Surface emission limit,hard sphere
V2
Such absorption corresponds to suppression for
inclusive yield in central collisionsabout
factor of 4-5
WS density,finite absorption
b/2RA
Not clear what should be used for ?4
ltcos(4?)gt would behave quite differently (sign,
etc.)