# Presentation: 510446

## Anisotropic Flow 

- It must be something!
-  Fully  Artistic!
- - Art’s playground
- for many years
- - Fun for everyone!

- Anisotropic Flow

- 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.

*             ****Sergei A. Voloshin ***
*Wayne State University, Detroit, Michigan*

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## 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 pt’s.
- 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

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## Anisotropic flow

- Newer trend: “event anisotropy”

- Anisotropic flow  correlationswith respect to the reaction plane

- 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)

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## How to characterize anisotropic flow?

- Advantages:
- - Describes different kind of anisotropies in a common way
- - Possibility to fully correct the results    compare directly with theory and other experiments

- S.V., Y. Zhanghep-ph/9407282
- Z.Phys. C70 (1996) 665

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## 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.

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## 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

- 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 ~ **R****A****/****γ**
*Initial transverse size* of the system ~ **R****A**
*Freeze-out time* (could be up to a several **R****A**)

- 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

- Collide Au+Au, 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 !

- PRD 46 (1992) 229

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## 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

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## Directed flow “wiggle” in cascade models

- Snellings, Sorge, S.V., F. Wang, Nu Xu,  PRL 84 (2000) 2803

- Baryon stopping

- “wiggle”

- The wiggle is pronounced only at high energies

- Does the picture contradict FOPI resultson different isotope collisions?

- Snellings, Poskanzer, S.V., nucl-ex/9904003

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## Hydro: “antiflow”, “third flow component”

- Net baryon
-  density

- Csernai, Rohrich, PLB 458 (1999) 454.
- Magas, Csernai, Strottman, hep-ph/0010307

- Brachmann, Soff, Dumitru, Stocker, Maruhn, Greiner
- Bravina, Rischke ,  PRC 61 (2000) 024909

**flow**

**antiflow**

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## 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?

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## Interplay of radial and anisotropic (directed) flow

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

- High pt particles areproduced mostly in the redregion; low pt particles – in the blue region

- Solid lines: non-relativistic case

- 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

- S.V., PRC 55 (1997) 1630

- The effect is larger for larger mass

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## Fitting the real data

- S.V and E877, Nucl Phys. A638, 455c (1998)

- Directed flow of protons in Au+Au collisions
- at Elab=11.4 GeV,  2.6 < y < 2.8

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## Coalescence I. E877 light nuclei flow.

- What is needed for the equation aboveto work?
- “Rare” process
- B=const 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.

- S.V and E877, Nucl Phys A638 (1998) 455c
- E877 PRC 59(1999) 884

- Note v1 values  > 0.5  there must be other non-zero harmonics!

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## Resonances

- S.V and E877, Nucl Phys. A638, 455c (1998)

- X. Dong, S. Esumi, P.Sorensen, N.Xu,Z. Xu, PLB 597(2004)328

- Nonaka, Müller, Asakawa, Bass, Fries PRC 69(2004)031902R

- Elliptic flow:

- Note: one of the examples of “non-thermal”
- interpretation of blast wave formulae

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## Elliptic flow. General properties.

- 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

- 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

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## Sensitivity to “early times”

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

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## When the elliptic flow is formed

- XZ-plane  -  the reaction plane

- Sensitive to the physics of constituent interactions (needed to converts space to momentum anisotropy) at early times (free-streaming kills the initial space anisotropy)

- The characteristic time scale of 2-4 fm is similar in any model: parton cascade, hydro, etc.

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## Low density limit

- (called “collisionless” in the original paper of Heiselberg and Levy)
- Below - my own derivation of Heiselberg’s results

- 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

- Heiselberg & Levy, PRC _59_ (1999) 2716

- Note:
- (x-vt) changes very little over the entire history

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## First hydro calculations

- 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.

- J.-Y. Ollitrault, PRD 46 (1992) 229

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## Centrality dependence

- S.V. & A. Poskanzer, PLB _474_ (2000) 27

- “HYDRO limit”

- Ollitrault:

- Heinz et al.:

- Points – RQMD, dashed curve - (b)

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## v2/ and phase transitions

- After original ideas of : Sorge, PRL _82_ (1999) 2048,   Heiselberg & Levy, PRC _59_ (1999) 2716

- LDL

- HYDRO

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## More on “hydro limits”

- Minimum in v2/ due to softening of the EoS at phase transition

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## v2/ and phase transitions

- 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”

- E877   NA49

- “Cold” deconfinement?

- What to expect for different nuclei, Cu+Cu?
- First guess would be:

- ... but there is no such factor in the LDL:

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## Centrality dependence. Hydro + RQMD.

- LH8  latent heat = 0.8 GeV/fm^3
- Pt slope parameters are about 20% larger
-  in hydro compared to data

**       ****400          600           800****                              **dN**ch**/dy

- Teaney, Lauret, Shuryak nucl-th/0110037

- - v**2** increases with dN/dy
- - Centrality dependence – close to data

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## v2(pt) dependence. Blast wave model.

**v****2****(p****t****)  -**** **Houvinen, Kolb, Heinz, Ruuskanen, S.V., PLB 503 (2001) 58

**v****2****(p****t****)  -**** **STAR Collaboration,   PRL 87 (2001) 182301

- Parameters:
-   T – temperature
-  * *****0** - radial expansion rapidity
-   ****2 **- amplitude of azimuthal    variation in expansion rapidity

- 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.

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## 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

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## v2(pt). “Mass splitting”. Dependence on the EoS.

- “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)

- P. Huovinen, P. Kolb, U. Heinz, P. Ruuskanen, S.V., PLB503, 58, 2001;

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## Constituent quark model + coalescence

- Only in the intermediate region (rare processes) coalescence can be described by:

- 

- 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.

- 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:

- coalescence                                          fragmentation

- Low pt quarks

- High pt quarks

- S.V., QM2002
- D. Molnar, S.V., PRL 2003

- Side-notes:
- a) more particles produced via coalescence rather than  parton fragmentation  larger mean p**t**...
-    higher baryon/meson ratio
-    lower multiplicity per “participant”

- -> D. Molnar, QM2004
- > Bass, Fries, Müller, Nonaka; Levai, Ko; ...
- > Eremin, S.V.

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## Elliptic flow due to jet quenching

-  Gyulassy, Vitev & Wang, PRL _86_ (2001) 2537

- R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003

- Easier “escape” in the
*x* direction
- “in-plane” particle
- emission

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## Elliptic flow in absorption model

- Hard shell      ==  box density profile (+) extreme quenching
-                                             E. Shuryak, nucl-th/0112042
- Hard sphere   ==     -”-  (+) realistic quenching
- Woods-Saxon ==  WS density profile  (+) realistic quenching

**L**

- Probability to “escape”:

- STAR, PRL 93 (2004) 252301

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## 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

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## Hanbury Brown – Twiss interferometry of an 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

- _Let us measure the geometry of anisotropic source!_

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## Hanbury Brown – Twiss interferometry of an anisotropic source

- Same parameters fit R() and v(pT,m)

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## azHBT

- S.V. LBNL 1998 annual report # R20http://ie.lbl.gov/nsd1999/rnc/RNC.htm

- RQMD v 2.3, AuAu @ RHIC

- In this picture at high energies /high pt, the relative differencebetween out-of-plane size and in-plane size only increases.

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## azHBT-2

**IPES initial conditions**, U. Heinz, P. Kolb PL B542 (2002) 216

- Note “out-of-phase” Rside modulations for k=0 case.
- Should we try very low
- kT at RHIC?

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## Do different particles freeze-out at the same place?

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## Non-identical 2-particle correlations

- S.V., R. Lednicky, S. Panitkin, Nu Xu, PRL 79 (1997) 4766

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## 2-particle correlations wrt RP

*x* – azimuthal angle, transverse
- momentum, rapidity, etc.

- J. Bielcikova, P. Wurm, K. Filimonov
- S. Esumi, S.V.,  PRC, 2003

- “a” == “trigger particle”

- CERES, PRL 92(2004)032901

- Selection of one (or both) of particles in- or out- of the reaction plane “distorts” the RP determination

- Approach: - “remove” flow contribution- parameterize the shape of what is left
- - study RP orientation dependence of the parameters

- STAR, PRL 93 (2004) 252301

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## Parity, CP- violation, global polarization...

- Observing parity (CP) violation with
- anisotropic flow techniques

- Kharzeev, Pisarski, Tytgat, PRL 81 (1998) 512
- Kharzeev, Pisarski, PRD 61 (2000) 111901

- S.V. PRC 62 (2000) 044901

- S.V. PRC 70 (2004) 057901

- Parity violation

- Global polarization

- “Oriented” DCC

- Asakawa, Minakata, Müller, nucl-th/0212070

- Negative elliptic flow of neutral pions

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## How one would measure flow?

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## Flow induced correlations

- E877, PRL 73, 2532 (1994)

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## “Differential flow”. First observation of v2 > 0

- Distribution of hits in the silicon pad detector wrt RP
- determined by calorimeters.

- E877, PRC 55 (1997) 1420

- n – n-th harmonic Event Plane

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## End of the ideal world:  “Non-flow”,  flow fluctuations, ...

- “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:

- Flow  ******       **** ******** “**non-flow”

- 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.

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## 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

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## EXTRA

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## Mixed harmonic technique or 3-particle correlations

- a > 0  preferential emission along the angular momentum
- The sign can vary event by event, a~Q/N, where Q is  the topological charge, |Q|=1,2,...
- at dN/dy~100, |a|~1%.

- And using only one particle instead of the event flow vector

- projections onto reaction plane

- Projections on the direction
- of angular momentum

-  note that for a rapidity region symmetric with respect to the midrapidity v1=0

- hep-ph/0406311

- All effects non sensitive to the RP
- cancel out!
- Possible systematics:
- clusters that flow

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## Anti-flow from shadowing

- Anti-flow is developingin more peripheral collisions

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## Wiggle from uRQMD

- Marcus Bleicher, Horst Stocker
- PLB 526, (2002)  309-314

- “Rich” dependence on the particle type: baryons, antibaryons, mesons

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## Flow due to absorption. v2, v4; e2, e4

- b/2RA

- V2

- Flow due to absorption. v2, v4; e2, e4

- See also: nucl-th/0310044
-  A. Drees, H. Feng, J. Jia

- <cos(4)> would behave quite differently (sign, etc.)

- WS density,finite absorption

- Surface emission limit,hard sphere

- Not clear what should be used for  4

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