# Presentation: 183775

## Anisotropic Flow

- Raimond Snellings

## What have we learned from elliptic flow so far? According to:

- U. Heinz: Resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (arXiv:hep-ph/0109006).
- E. Shuryak: Probably the most direct signature of QGP plasma formation, observed at RHIC (arXiv:nucl-th/0112042).
- L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (arXiv:hep-ph/0202025).
- M. Gyulassy: _The_ most powerful probe of the QGP equation of state: the mass dependence of v2; One of the three lines of evidence for the QGP at RHIC (arXiv:nucl-th/0403032).

- Raimond Snellings; Trento 2004

## Outline

- Elliptic flow:
- v2 at low pt, the dependence on particle mass and its relation to freeze-out parameters in a hydro motivated picture
- Some uncertainties related to the measurement
- What are the changes from SPS to RHIC energies?

- Raimond Snellings; Trento 2004

## Elliptic flow of the bulk

- Coordinate space configuration anisotropic (almond shape) however, initial momentum distribution isotropic (spherically symmetric)
- Only interactions among constituents generate a pressure gradient, which transforms the initial coordinate space anisotropy into a momentum space anisotropy (no analogy in pp)
- Multiple interactions lead to thermalization -> limiting behavior ideal hydrodynamic flow

- Raimond Snellings; Trento 2004

## Time evolution

- Elliptic Flow reduces spatial anisotropy -> self quenching

- SCIENCE Vol: 298 2179 (2002)

- Hydro calculation: P. Kolb, J. Sollfrank and U.Heinz

- Raimond Snellings; Trento 2004

## Main contribution to elliptic flow develops early in the collision 

- Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45

- Raimond Snellings; Trento 2004

## Non-central heavy-ion collisions: coordinate system

- Raimond Snellings; Trento 2004

## Integrated Elliptic Flow

**Integrated Elliptic Flow**

- First time in Heavy-Ion Collisions a system created which at low pt is in quantitative agreement with ideal hydrodynamic model predictions for v2 up to mid-central collisions

- PHOBOS: Phys. Rev. Lett.** 89**, 222301 (2002)** **

- STAR: Phys. Rev. Lett. **86**, 402 (2001)

- PHENIX: Phys. Rev. Lett. 89, 212301 (2002)

- RQMD

- Raimond Snellings; Trento 2004

## Identified particle v2 

- Typical pt dependence for different masses
- Heavy particles more sensitive to velocity distribution (less effected by thermal smearing) therefore put better constrained on EOS

- STAR

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## Hadron Cascade

- UrQMD: Marcus Bleicher and Horst Stocker,arXiv:hep-ph/0006147

- Magnitude off in v2 and different scale in pt

- Raimond Snellings; Trento 2004

## v2(pt,mass)

**v****2****(p****t****,mass)**

- All particles reasonably described at low-pt with common set of parameters
- PHENIX (squares) and STAR agree well

- STAR, PHENIX preliminary

- Raimond Snellings; Trento 2004

## Everything flows?

**p****T**** [GeV/c]**

- M. Kaneta (PHENIX) QM2004

- J. Castillo (STAR) QM2004

- What about charm?

- Raimond Snellings; Trento 2004

## Reaction plane determination

- Anisotropic flow ≡ azimuthal correlation with the reaction plane
- Experimentally the reaction plane r is _unknown_
- Can introduce “non-flow” contributions

- Raimond Snellings; Trento 2004

## Determining the reaction plane

- Raimond Snellings; Trento 2004

## Event plane resolution

- Event plane resolution  N * v22
- Most non flow contributions v2 1/N
- Kovchegov and Tuchin: N = Nwounded
- Non flow contribution will be constant in this variable. Dashed red line estimate of non-flow in first STAR flow paper

- STAR, PRL 86, (2001) 402, Nucl. Phys. A698 (2002) 193

- Raimond Snellings; Trento 2004

## Elliptic flow as a function of centrality

- STAR Nucl. Phys. A698 (2002) 193

- Non-flow considerable for central and peripheral events

- Raimond Snellings; Trento 2004

## Calculating flow using multi particle correlations

- Assumption all correlations between particles due to flow
- Non-flow correlation contribute order (1/N), problem if vn≈1/√N

- Non-flow correlation contribute order (1/N3), problem if vn≈1/N3⁄4

- N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906

- Raimond Snellings; Trento 2004

## Higher moments

- <v2n> ≠ <v2>n

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## Integrated v2 from cumulants

- A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020

- About 20% reduction from v2{2} to v2{4}
- v2{4} ≈ v2{6}

- Raimond Snellings; Trento 2004

## The possible fluctuation contribution

- “standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities

- M. Miller and RS, arXiv:nucl-ex/0312008

- Raimond Snellings; Trento 2004

## Integrated v2 from cumulants

- A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020

- About 20% reduction from v2{2} to v2{4}
- v2{4} ≈ v2{6}

- Raimond Snellings; Trento 2004

## How does it compare to data?

- M. Miller and RS, arXiv:nucl-ex/0312008

- Raimond Snellings; Trento 2004

## Non-flow or fluctuations?

- M. Miller and RS, arXiv:nucl-ex/0312008

- NA49: Phys.Rev. C68 (2003) 034903

- N. Borghini, P.M. Dinh, J-Y Ollitrault: Phys. Rev. C 63 (2001) 054906

- Raimond Snellings; Trento 2004

## Uncertainties

- Non-flow and fluctuations expected in general to both contribute
- At mid-central collisions (20-60%) the estimated effect is about 10%. IMO best estimate of the true flow are in between (v2{2}+v2{4})/2 and v2{4}

- Raimond Snellings; Trento 2004

## Elliptic flow at lower energies

- P. Kolb, J. Sollfrank,  and U. Heinz, Phys. Rev. C.  C62 054909 (2000).

- Increase of about 50% in v2 from top SPS to top RHIC energy

- Raimond Snellings; Trento 2004

## Hydrodynamics + RQMD

- D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett  86, 4783 (2001).

- Raimond Snellings; Trento 2004

## Energy dependence

- At low energies pions, at RHIC charged hadrons. This makes a difference, this figure approximates the excitation plot of h-

- Raimond Snellings; Trento 2004

## v2(pt) SPS-RHIC

**v****2****(p****t****) SPS-RHIC**

- Integrated v2 depends on slope and <pt>
- <pt> pions 17 GeV ≈ 400 MeV/c, 130 GeV charged particles <pt> ≈ 500 MeV/c

- NA49: Phys. Rev. C68 (2003) 034903; CERES: Phys. Rev. Lett. 92 (2004) 032301

- Raimond Snellings; Trento 2004

## Similar or very different?

- arXiv:nucl-ex/0305001

- Raimond Snellings; Trento 2004

## Similar or very different??

- Note: only statistical errors plotted

- Raimond Snellings; Trento 2004

## Similar or very different?

- Raimond Snellings; Trento 2004

## Summary

- Consistent measurements of elliptic flow at RHIC from PHENIX, PHOBOS and STAR
- Elliptic flow for all measured particles at low-pt well described by boosted thermal particle distributions
- Smooth increase in elliptic flow from SPS to RHIC. Detailed measurements of identified particle v2(pt) by the RHIC experiments (or perhaps SPS data not presented yet) will provide a clearer picture
- At intermediate centralities (20-60%) I estimate not more than 10% uncertainty in the integrated elliptic flow values
- At RHIC the large elliptic flow is not described by hadronic models; strong (partonic) interactions at early stage of the collision are needed
- From comparisons with ideal hydro calculations early thermalization deduced (is this the only possibility? what is the freedom in EOS? What about HBT?)

- D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett  86, 4783 (2001).

- Raimond Snellings; Trento 2004

## Backup

- Raimond Snellings; Trento 2004

## Elliptic flow; excitation function

- Raimond Snellings; Trento 2004

## Hydro + Jet Quenching?

- X.-N. Wang: nucl-th/0305010

- T. Hirano and Y. Nara: nucl-th/0307015

- Coupling of hydro and parton energy loss gives a reasonable description of the data and also has a mass dependence at higher-pt

- Raimond Snellings; Trento 2004

## Flow (radial, directed and elliptic)

- Only type of transverse flow in central collision (b=0) is transverse flow.
- Integrates pressure history over complete expansion phase

- Elliptic flow, caused by anisotropic initial overlap region (b > 0).
- More weight towards early stage of expansion.

- Directed flow, sensitive to earliest collision stage (pre-equilibrium, b > 0)

- Raimond Snellings; Trento 2004

## v1 predictions (QGP invoked)

- J. Brachmann et al., Phys. Rev. C. 61 024909 (2000)

- L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454

- Raimond Snellings; Trento 2004

## v1 predictions (more general, QGP interpretation not necessary)

- R.S., H. Sorge, S.A. Voloshin, F.Q. Wang, N. Xu: Phys. Rev. Lett 84 2803 (2000)

- M. Bleicher, H. Stocker: Phys. Lett. B 526 (2002) 309 (UrQMD)

- Raimond Snellings; Trento 2004

## Directed flow at the SPS (NA49)

- NA49: Phys.Rev. C68 (2003) 034903

- Raimond Snellings; Trento 2004

## First measurement of v1 at RHIC

- A. Tang, M. Oldenburg, A. Poskanzer, J. Putschke, RS, S. Voloshin

- Confirms v2 is in-plane at RHIC
- Suggestive of limiting fragmentation picture
- Consistent with theory predictions
- The data with current statistics shows no sign of a wiggle (also does not exclude the magnitude of the wiggle as predicted

- Raimond Snellings; Trento 2004

## Is there boost invariance?PHOBOS v2()

- average over
-  all centrality
- (Npart ~200)

- PHOBOS: Phys. Rev. Lett.** 89**, 222301 (2002)** **

- Raimond Snellings; Trento 2004

## Elliptic flow at higher pt, extracted using multi-particle correlations

- Significant *v**2* up to ~7 GeV/c in pt as expected from jet quenching. However at intermediate pt the magnitude is unexpectedly large

- A. Tang (STAR) QM 2004

- Raimond Snellings; Trento 2004

## Early freeze-out in a blast wave approach

**Early freeze-out in a blast wave approach**

- Low-pt measurements and comparison to full dynamical calculations important for drawing a conclusion !!!!

- STAR, PHENIX preliminary

- Raimond Snellings; Trento 2004