# Presentation: 016099

## Scaling of Anisotropic Flow in the Picture of Quark Coalescence

- Markus D. Oldenburg
- for the STAR Collaboration

- Hot Quarks 2004

- July 23, 2004

## Outline

- Introduction
- Meson-Baryon Scaling of Elliptic Flow v2(pt)
- Scaling of Higher Harmonics of Anisotropic Flow
- Summary and Outlook

## RCP of Strange Hadrons

- RCP of Strange Hadrons

-  Two groups (2<pt<6GeV/c): - K0s, K, K*,   mesons - , , 	  baryons
-  dependence on number of constituent quarks
-  limited to pt < 6GeV/c?
-  hadron production from quark coalescence?

## Anisotropic Flow

- Look at peripheral collisions
- Overlap region is not symmetric in coordinate space
- Almond shaped overlap region
- Larger pressure gradient in x-z plane than in y-direction

- Spatial anisotropy  Momentum anisotropy
- Interactions among constituents transform the initial spatial anisotropy into an (observed) momentum anisotropy
- Process quenches itself → sensitive to early times in the evolution of the system
- sensitive to the equation of state

- Perform a Fourier decomposition of the momentum space particle distributions in the    x-y plane
- vn is the n-th harmonic Fourier coefficient of the distribution of particles with respect to the reaction plane
- v1: “directed flow”
- v2: “elliptic flow”

## Scaled strange particle v2(pt)

- Hadronization via quark coalescence:
- v2 of a hadron at a given pt is the partonic v2 at pt/n scaled by the # of quarks (n).

**D. Molnar, S.A. Voloshin: Phys. Rev. Lett. 91, 092301 (2003)**
**V. Greco, C.M. Ko, P. Levai: Phys. Rev. C68, 034904 (2003) **
**R.J. Fries, B. Muller, C. Nonaka, S.A. Bass: Phys. Rev. C68, 044902 (2003)**
**Z. Lin, C.M. Ko: Phys. Rev. Lett. 89, 202302 (2002) **

-  Shown to work for K0s&
-   (PRL 92, 052302 (2004))
-  Works also for other   	particles
-  v2s ~ v2u,d ~ 7%

**200 GeV**

**preliminary**

## Number of constituent quark scaling of v2(pt) 

- KS and Lambda from published STAR data **(PRL 92, 052302 (2004))****.**
- K± and Cascade are preliminary STAR measurements            (K. Schweda, J. Castillo and J. Amonett).
- Pion and proton from published PHENIX data **(Nucl. Phys. A715, 599 (2003))**.
- Polynomial fit to all species except pions.

**200 GeV**

**preliminary**

## Elliptic Flow v2(pt) at low pt

-  v2(pt) and mass dependence is reproduced by hydrodynamical model calculations
-  Hydro model implicitly assumes local thermal equilibrium and is sensitive to the EOS

**Pion, neutral Kaon and Proton data taken from PHENIX: **
**Nucl. Phys. A715, 599 (2003)**
**Hydro: P. Huovinen et al., Phys. Lett. B503, 58 (2001)**

**200 GeV**

**preliminary**

## Higher harmonics

-  strong potential to constrain model calculations
-  sensitive to the dynamical evolution of the system
-  initial conditions of hydro influence magnitude and 	even the sign of vn

## Scaling of higher harmonics

- Voloshin, Kolb, Chen, Ko, and Lin

- Assuming coalescence of quarks:

- Assuming scaling for quarks:

- vnq = (v2q)(n/2)

- for mesons

- for baryons

- for mesons

- for baryons

## v4(pt) and v6(pt) @ 200 GeV

-  utilizing large elliptic flow to estimate the reaction plane
-  sizeable v4
-  v6=0 within errors

-  v4 and v6 scale like v22 resp. v23

- PRL 92, 062301 (2004)

**200 GeV**

## v4/v22 scaling

- v4/v22 scaling

- 1.2

- Mean is definitely larger than 1.

**200 GeV**

## v4(centrality) @ 200 GeV

- PRL 92, 062301 (2004)

**200 GeV**

## v4(pt) of pions @ 62.4 GeV

-  v4 scales approximately as v22  as a function of pt

**STAR preliminary**

**62.4 GeV**

- Analysis done by Yuting Bai

## Scaling of higher harmonics

- Assuming coalescence of quarks:

- for mesons

- for baryons

- Experimental value is 1.2 → v4q is greater than zero!

- Assuming scaling for quarks:

- for mesons

- for baryons

- Experimental value is 1.2       →** **v4q is even greater than simple parton scaling indicates.

- vnq = (v2q)(n/2)

## Summary and Outlook

- Meson-baryon scaling of v2 at intermediate pt works (except for pions).
- consistent with hadronization via quark coalescence
- We seem to see anisotropic flow of partons in this pt region!
- v2(pt) and mass dependence below 1 GeV/c are well reproduced by hydro calculations. (No contradiction to scaling argument at intermediate pt!)
- The higher harmonics v4 and v6 @ 200 GeV were measured and a scaling with v22 was observed.
- Pions show similar scaling properties of v4 @ 62.4 GeV.
- v4q is greater than simple coalescence models with scaling for quarks would predict.
- Studies @ 62.4 GeV for v2 and higher harmonics for different particle species are under way.
- 200 GeV data of run IV will allow detailed studies on anisotropic flow to test coalescence.