# Presentation: 751920

## PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC energies

*** ***

***                    ******Quark Matter 2006***
***           ******November  13-20, Shanghai, China***

***Nuclear Chemistry Group     SUNY Stony Brook, USA***

**PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC energies**

**for the PHENIX Collaboration**

## Why Elliptic Flow ?

**The probe for early time**
**The dense nuclear overlap is ellipsoid at the beginning of heavy ion collisions**
**Pressure gradient is largest in the shortest direction of the ellipsoid**
**The initial spatial anisotropy**
**      ****evolves (via interactions and density gradients ) ******** Momentum-space anisotropy**
**Signal is self-quenching with time**

- _Reaction plane_

- X

- Z

- Y

- Px

- Py

- Pz

## PHENIX Elliptic Flow Data

***Detailed differential measurements now available for ******π******, K, p, ******φ******, d, D******  ***

## PHENIX Elliptic Flow Data  (Posters)

- Energy and System Size dependence of Elliptic flow at RHIC (AuAu/CuCu at 62.4-200 GeV) in the poster of **Maya Shimomura**:
- “Measurement of Azimuthal Anisotropy for High Pt charged hadrons at RHIC-PHENIX”.
- Poster 38, Room 104 Wind Energy Room

- Differential Elliptic flow measurements at forward rapidities in the poster
- of **I. J. Choi** : “Inclusive single muon flow for Au+Au collisions at 200 GeV in the PHENIX experiment at RHIC”
- Poster 13, Room 104 Wind Energy Room

## RHIC Elliptic Flow Data

**RHIC Elliptic Flow Data**

- PHENIX : PRL 91,  (2003)

## Universal Scaling  of Elliptic Flow at RHIC

***ε******(b,A) ******– integral elliptic flow of charged hadrons****** ***

***At midrapidity  v******2****** (pt,M,b,A)/n~****** F(KE******T******/n)*******ε******(b,A)? ***

***KE******T ****** ******- transverse kinetic energy****** ***

***n ******– number of quarks****** ****** ***

## Elliptic flow: eccentricity scaling

**Ideal hydro is scale invariant:**
**  ****v2(pt,b,A)/v2(b,A)~v2(pt)**
**v2(b,A)/****ε****(b,A)~const**
- “Integrated v2 reflects momentum anisotropy of bulk matter and saturates within the first 3-4 fm/c just after collision” (Gyulassy,Hirano  Nucl.Phys.A769:71-94,2006)
- In hydro models integrated v2 is proportional to the eccentricity

**Bhalerao, Blaizot, Borghini, Ollitrault : **
**Phys.Lett.B627:49-54,2005*** *

## Eccentricity scaling and system size

**v****2**** scales with eccentricity**
**and across system size**

*Scaling test*

**nucl-ex/0608033**

**nucl-ex/0608033**

**k ~ 3.1+/-0.2  obtained from data**

**New PHENIX article on the scaling properties of elliptic flow: ****nucl-ex/0608033**

- For Au+Au collisins the eccentricity from Glauber model ε=k v2(centrality)

## Sound speed & Eccentricity scaled v2  

**Sound speed & Eccentricity scaled v****2  **

**Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005*** *

**Eccentricity scaled v2 has a relatively strong dependence on sound speed**

## Sound speed & Eccentricity scaled v2  

**c****s**** ~ 0.35 ±** **0.05**
**(c****s****2 ****~ 0.12), so****ft EOS**

- v2/ε for <pT> ~ 0.45 GeV/c

- See nucl-ex/0608033 for details

**An effective  EOS is harder than that for the hadron **
**gas but softer than that for high temperature QGP ******** no strong first order phase transition**

**Sound speed & Eccentricity scaled v2**

## Transverse kinetic energy scaling

**Scaling breaks**

-  Elliptic flow scales with KET up to KET ~1 GeV
-  Indicates hydrodynamic behavior
-  Possible hint of quark degrees of freedom become apparent
-   at higher KET

**Baryons scale together**

**Mesons scale together**

**PHENIX preliminary**** **

-                   = mT – m

**Transverse kinetic energy scaling**

**New PHENIX article on the scaling properties of elliptic flow: ****nucl-ex/0608033**

## Quark number Scaling 

-  Apparent Quark number scaling
-  Hadron mass scaling at low KET (KET < 1 GeV) is preserved.

**Quark number Scaling**

**New PHENIX article on the scaling properties of elliptic flow: ****nucl-ex/0608033**

**Consistent with quark degrees of freedom in the initial flowing matter**

## NCQ (pT/n) scaling  compared to KET /n

-  KET/n scaling works for the full measured range with deviation less than 10% from the universal scaling curve
-  NCQ- scaling works only at 20% level for pt>2 GeV/c and breakes below with clear systematic dependence on the mass

**PHENIX Preliminary**

- NCQ- Scaling

## KET/n scaling across collision centralities

**KE****T****/n scaling across collision centralities**

**KE****T****/n**** **** scaling observed across centralities**

## KET/n scaling and  system size (AuAu/CuCu)

**KE****T****/n scaling and  system size (AuAu/CuCu)**

## Elliptic flow of φ meson and partonic collectivity at RHIC. 

-   **φ**** meson** has a **very ****small ****σ** for interactions with non-strange particles
-  **φ**** meson** has a relatively **long lifetime (~41 fm/c)**  -> decays outside the fireball
-  **φ**** is a meson** but **as heavy as baryons** (p, Λ ) :
- m(φ)~1.019 GeV/c2 ;  (m(p)~0.938 GeV/c2: m(Λ)~1.116 GeV/c2) -> very important test for v2 at intermediate pt ( mass or meson/baryon effect?)

## v2 of  φ  meson  and partonic collectivity at RHIC 

***v******2****** vs KE******T****** – is a good way to see if  v******2******  for the ******φ****** follows ***
***that for mesons or baryons***
***v******2***** *****/n vs KE******T******/n  scaling clearly works for ******φ****** ******mesons as well***

## Elliptic flow of D meson 

***The D meson not only flows, it scales over the measured range****** ***

**expected D meson v2 from non-photonic electron v2 (pT < 2.0 GeV/c)**

**Simulations: Shingo Sakai (PHENIX)**
**(See SQM2006, HQ2006 Talks and proceedings for details)**

**See Talk of Shingo Sakai  (Parallel 2.1 , Sat 3:20 pm )**

## Shear viscosity to entropy density ratio estimate

- From R. A. Lacey et al. submitted to PRL (**nucl-ex/0609025** )

** ****PHENIX estimate of  ****η****/s from the comparison of  the measured **
**RAA and v2 of non-photonic electrons with models:  ****η****/s ****~(1.5-3)/4****π****, see**
**Talk of Shingo Sakai  (Parallel 2.1 , Sat 3:20 pm )**

- (η/s) ~ (1.2-2.5)/4π

## Elliptic Flow at SPS (Pb+Pb at 158 GeV, NA49)

**The statistical errors are too large  to make any statement about the scaling of elliptic flow at SPS energies**

- V2 of K0  (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003)

- v2 of p, π, Λ -  C. Alt et al (NA49 collaboration) nucl-ex/0606026 submitted to PRL

## Summary

**Scaling predictions of perfect fluid hydrodynamics for the elliptic  flow coefficient v****2**** tested and validated **
**Development of elliptic flow in the pre-hadronization phase demonstrated**
**Scaling of D meson v****2**** compatible with full thermalization of the **
**       ****charm quark observed.**
**Universal scaling of the flow of both mesons and baryons (over a broad transverse kinetic energy range) via quark number scaling observed. **
** ****Scaled flow values allow constraints for several transport coefficients.**
**Outlook:**** ****we need to find the range where scaling holds and where it  breakes****.**
- .

**Results compatible with a plasma having essentially **
**perfect liquid-like properties**

## Elliptic flow of resonance particles 

- Signal + Background

- Background

- Before subtraction

- After subtraction

- Elliptic flow of resonance particles

*Using the  robust method for study the elliptic flow of resonance particle developed by *_[N. ](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Borghini,%20N.%22)__[Borghini](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Borghini,%20N.%22)_* and  *_[J.Y. ](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Ollitrault,%20J.Y.%22)__[Ollitrault](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Ollitrault,%20J.Y.%22)_* (****Phys.Rev.C70:064905,2004)**** **  *