# Presentation: 527982

## Duke University
Chiho Nonaka

**Chiho Nonaka**

***Recombination plus Fragmentation Model at RHIC:****** –****** ******Elliptic Flow***

- in Collaboration with
- R. J. Fries (Minnesota), B. Muller (Duke), S. A. Bass (Duke & RIKEN)
- and M.Asakawa (Osaka)

- PRL90,202303(2003), PRC68,044902(2003) ,
- PLB587,73(2004), PRC69, 031902(2004)

- July 23, 2004@Taos

**Notes:**
I would like talk about  ‘’Study of the Finite Density State based on SU(2) Lattice 
QCD’’.

## Outline

**Introduction**
- Motivation
- Experimental data
**Hadronization mechanism **
- Recombination + Fragmentation Model
**Elliptic Flow**
- Comparison with experimental data
- PT dependence, impact parameter dependence
- Quark number scaling
- v2 for resonances
- v2 for exotic particles
- v2 at SPS
**Summary**

## Motivation

** ****Anisotropy of collective flow**

-  Thermalization
-  Equation of state

-  Sensitive to initial geometry

- RHIC

## Quark Number Scaling in v2

- PHENIX : PRL 91 (2003) 182301

- (STAR : PRL91 (2004) 052302_)_

## Quark Number Scaling in v2

** ****Hadronization from **
**                       ****recombination**
-  number of constituent quark

- Voloshin, NPA715(2003)379
- Molnar and Voloshin, PRL91 (2003)092301
- Lin and Molnar, PRC68 (2003) 044901
- Greco and Ko, PRC68 (2003) 034904
- Our group, PRC68,044902(2003) ,
-                   PLB587,73(2004)

- P. Sorensen

## Recombination + Fragmentation Model

**Recombination at moderate *****P*****T**
- Recombination occurs
-      in an instant.
- The parton spectrum is
**           **shifted to higher pT in the hadron
-            spectrum.
- Entropy and energy conservation
- No gluon dynamics
**Fragmentation at high *****P*****T**
- The parton spectrum has a power law tail (quarks and gluons) from pQCD.
- The parton spectrum is shifted to lower pT in the hadron spectrum.

## Elliptic Flow 

** ****Elliptic flow is sensitive to initial geometry**

** ****Total elliptic flow**

- At moderate *P*T
- recombination

- At high *P*T
- fragmentation

-  Pressure gradient
-  Collision plane >
-   Perpendicular plane

*r*(*p*t):  relative weight of the recombination contribution in spectra

-  Energy loss
-  Perpendicular plane >
-   Collision plane

## Elliptic Flow 

-  *v*2 of baryons saturates at a higher value
-   than for mesons.
-  At high *P*T, *v*2 is dominated by   fragmentation.
-   *v*2 of baryon and meson is identical.

- PLB587,73(2004)

## Comparison with Hydrodynamical Model

*Comparison with Hydrodynamical Model*

-  # of valence quarks

- Universal *v*2 curve

-  Low *P*T

-  Intermediate *P*T

-  High *P*T

-  Mass effect

-  Fragmentation

-  Saturation feature

- (Blast wave model)

-  **Hydrodynamical Model**

**Model**

-  **Recombination + Fragmentation**

- mass effect ?
-      recombination ?

## Impact Parameter Dependence

- STAR:nucl-ex/0407007

** ****Peripheral Collisions**

- ?

- Shuryak,PRC66,027902(2002)
- X-N.Wang, nucl-th/0305010

## Brief Summary

*Brief Summary*

*Elliptic Flow*

## v2 for resonance particles

-  QGP resonances:
-     hadronizing QGP, no rescattering
-  HG resonances:
-     hadron final stage, h-h rescattering

- Key:
-   v2 is additive for composite particles

- Final Interactions
- freeze-out process

## v2 for exotic particles 

- compact 5 quark state ?
- K-N molecular state ?

** ****Structure of exotic particles**

- At intermediate PT , there are measurable
- differences (up to 20 %) between them.

- n=5 scaling

- K

- N

- 5q

## Elliptic Flow at SPS ( I )

**Hadrons in QGP?**

- Shuryak@QM2004

-  Lattice QCD
-     Bielefeld group, Asakawa-Hatsuda and
-      Umeda et al.

- Ex.

## Elliptic Flow at SPS ( II )

*Elliptic Flow at SPS ( II )*

-  Fragmentation mechanism
-   should be negligible.

-   Assumption
-   Thermalization is achieved.

- Quark number scaling is broken down !

## Summary  

-  Hadronization Mechanism

-  Elliptic Flow *–* Useful tool *–*

- PT

- Hydro(Thermal)

- Recombination

- Fragmentation