# Presentation: 934926

## Space-time Evolution of Bulk QCD Matter at RHIC

- HQ2006

- Chiho NONAKA
*Nagoya University*

- In collaboration with Steffen A. Bass (Duke University & RIKEN BNL)

**Contents**
- Introduction
- Hydrodynamic models at RHIC
- Freezeout process, finite state interactions
- 3D hydro+UrQMD
- Results
- Single particle spectra, elliptic flow
- Summary

## Hydrodynamic Models at RHIC 

- Success of Perfect Hydrodynamic
-      Models at RHIC
- Single particle spectra
-                 Huovinen, Kolb, Heinz, Hirano, Teaney,
-                 Shuryak, Hama, Morita, .......
- Strong elliptic flow
-      Strong coupled (correlated) QGP

- at mid rapidity

- Huovinen et.al, PLB503

## Freezeout process in Hydro

-  Difference between chemical and thermal freezeout

- Heinz,NPA

**Possible solutions:**
-  Partial chemical equilibrium (PCE)
-     Hirano, Kolb, Rapp
-  Hydro + Micro Model
-    Bass, Dumitru, Teaney, Shuryak

- Single freezeout temperature?

-  chemical freezeout
-   statistical model
-    *T*ch ~170 MeV
-    hadron ratio
-  thermal freezeout
-   hydro
-    *T*f  ~ 110~140 MeV

**Notes:**
Usually In hydrodynamic model only thermal freezeout process is included.
This thermal freezeout temperature is around from 110 MeV  to 140 MeV.  
However 
From a statistical model, the chemical freezeout temperature is obtained. 
This temperature is around 170 MeV which is close to critical temperature. 
This facts suggests that there are two freezeout temperature, that is to say. 
Chemical freezeout temperature and thermal freezeout temperature. 

For introduction of two suggested freezeout temprature, there are possible 
Solutions. One is the introduction fo partical chemical equilibrium. 
The other one is a construct of a hybrid model, hydro + Micro Model. 
Chemical freezeout temeprature is determined 170 MeV based on statistical model. 

## Final State Interactions

- 2. In UrQMD final state interactions are included correctly.

- Markert @QM2004

## 
Hadron phase: viscosity effect
Freezeout process:
Chemical freezeout & thermal freezeout
Final state interactions
3D-Hydro +UrQMD

- Hadron phase: viscosity effect
- Freezeout process:
- Chemical freezeout & thermal freezeout
- Final state interactions
- 3D-Hydro +UrQMD

*Key:*

- Bass and Dumitru, PRC61,064909(2000)
- Teaney et al, nucl-th/0110037

-   Treatment of freezeout is determined by mean free path.
-   Brake up thermalization: viscosity effect

*3D-Hydro + UrQMD Model*

*T**C*:critical temperature* **** T**SW*:* *Hydro  UrQMD

## 3-D Hydrodynamic Model 

- Relativistic hydrodynamic equation
- Baryon number conservation
- Coordinates
- Lagrangian hydrodynamics
- Tracing the adiabatic path of
-      each volume element
- Effects of phase transition on observables
- Computational time
- Easy application to LHC
- Algorithm
- Focusing on the conservation law

- Flux of
- fluid

- energy momentum tensor

- Lagrangian hydrodynamics

## Parameters

*Parameters*

- Initial Conditions
- Energy density
- Baryon number density
- Flow
- Switching temperature

*T*SW=150  [MeV]

*v*T=0

*v*L=Bjorken’s solution);

***Different from Pure Hydro !***

|  | hydro | Hydro+
UrQMD |
| --- | --- | --- |
| 0(fm) | 0.6 | 0.6 |
| max(GeV/fm3) | 55 | 40 |
| nBmax(fm-3) | 0.15 | 0.15 |
| 0, | 0.5, 1.5 | 0.5, 1.5 |

- longitudinal direction

- transverse plane

## PT spectra 

*P*T spectra at central collisions

## PT Spectra (Pure Hydro)

*T*f=110 MeV
- normalization of* K* and *p*:
- ratio at *T*chem
- Heinz and Kolb, hep-ph/0204061

## Rapidity Distribution

- Impact parameter dependence of rapidity distributions

## Centrality Dependence

- Impact parameter dependence of *P*T

## PT Spectra for Strange Particles

## Reaction Dynamics 

- At mid rapidity

- Slope becomes steeper

## Final State Interactions 

- p, : flatter, pion wind
- : small cross section

## <PT> vs mass

- At mid rapidity

## v2 in hadron phase ?

- Quark number scaling of v2

*v*2: early stage
-      of expansion

## Reaction Dynamics in v2  I

## Reaction Dynamics in v2 II

- Hydro+decay
-    ~ Hydro@*T*SW
*v*2 grows in hadron
-  phase a bit.
*v*2 builds up in QGP
-                              phase.

## Summary

- We present the 3-D hydrodynamic +cascade model
- 3-D Hydrodynamic Model
- Single particle distribution
- Centrality dependence
- Elliptic flow
- Low Tf : single spectra, elliptic flow, hadron ratios
-          Necessity of improvement of freezeout process in Hydro
- 3-D Hydro + UrQMD
- Single particle distribution
- Centrality dependence
- Elliptic flow
- Different initial conditions from pure Hydro
- Hadron ratios Switching temperature from Hydro to UrQMD
- Reaction dynamics in UrQMD
- ,small cross section,  v2:improvement at forward/backward 
- Work in progress
- EoS dependence: ex. lattice QCD
- Switching temperature dependence

## Backup

## Parameters

*Parameters*

- Initial Conditions
- Energy density
- Baryon number density
- Parameters (pure hydro)
- Flow
- Equation of State
- 1st order phase transition
-      Bag Model + Exclude volume model
- Freezeout Temperature

*T*f=110  [MeV]

*v*T=0

*v*L=Bjorken’s solution);

***Different from hydo + UrQMD !***

- longitudinal direction

- transverse plane

**Notes:**
Factorize 

## PT Spectra

- Tf=110 MeV
- normalization of K and p:
- ratio at Tchem
- Heinz and Kolb, hep-ph/0204061

**Notes:**
We fix the initial condition from pion PT spectra. 

## Rapidity distribution

## b dependence of PT spectra

## V2 vs PT

- Elliptic Flow

- b=4.5 fm

- b=6.3 fm

- b=4.5 fm: consistent with experimental data
- b=6.3 fm: proton  overestimate

## v2 vs 

-  Forward/backward rapidity: overestimate
-  Pure hydro is valid around mid rapidity.

- 3-15 %

- 15-25 %

## Step2. 3-D Hydro + UrQMD

## v2 vs PT

## v2 vs 

## Relativistic Heavy Ion Collision  & Hydrodynamic models
Schematic sketch

- Schematic sketch

**initial conditions**
- parametrization
- color glass
-  condensate...

**equation of states**
- bag model
- lattice QCD...

**freezeout process**
- chemical equilibrium
- partial chemical
-  equilibrium
- cascade model...

*Hydrodynamic Model at RHIC*

- t

- QGP production

- hadron phase

- phase transition

**hydrodynamical **
**expansion**

- freeze-out

- hadronization

- thermalization

- collision

- Hydro Model

## Introduction 1 

*Introduction 1 *

- Success of Ideal Hydrodynamic Models at RHIC

-  Strong elliptic flow
-  strong coupled QGP

- Huovinen et.al, PLB503

- Single particle spectra
-   *P*T spectra up to ~ 2GeV
-   Huovinen, Kolb, Heinz, Hirano, Teaney,
-    Shuryak, Hama, Morita, .......

- Nonaka and Bass

- at mid rapidity

## Introduction 2 

- Success of Ideal Hydrodynamic Models at RHIC

- Discrepancy at large :
- Insufficient  thermalization?
- Mean free path
- Viscosity effect?

***However...***

- Elliptic flow as a function of 

- Hirano and Tsuda, PRC66

*freezeout*
*viscosity*

## V2 vs multiplicity 

- NA49:PRC68,034903(2003)

*SPS*

## Hydrodynamic Models

- PT  spectra

- PHENIX:Nucl.Phys. A757 (2005) 184

- Au + Au                   GeV

- 

-  hadron ratio
-  CE       
-  PCE       
-  RQMD   

## Hydrodynamic Models

- Elliptic Flow

- PHENIX:Nucl.Phys. A757 (2005) 184

- Au + Au                   GeV

- 

-  CE     
-  PCE      
-  RQMD  

## Hydrodynamic Models

- PT  spectra

- Elliptic Flow

- PHENIX:Nucl.Phys. A757 (2005) 184

- Au + Au                   GeV

- 

- 

| Ref. | Initial Cond. 
(GeV/fm3)or  s(fm-3) | fm/c | Latent heat
(GeV/fm3) | Hadronic stage | Tf (MeV) |
| --- | --- | --- | --- | --- | --- |
| [1] | 23()(eWN) | 0.6 | 1.15 | CE | 120 |
| [2] | 110(s)(0.75sWN+0.25sBC) | 0.6 | 1.15 | PCE | 100 |
| [3] | 35()(eBC) | 0.6  | 1.7 | PCE | 100,120,140 |
| [4] | 16.7()(sWN) | 1.0 | 0.8 | RQMD | ~100 |

- [1]Huovinen et.al., PLB(130) [2]Kolb et.al. PRC, [3]Hirano et.al.PRC(130), [4]Teaney et al.

## Trajectories on the Phase Diagram

- Lagrangian hydrodynamics

- C.N et al., Eur. Phys.J C17,663(2000)

- (ix,iy,iz)

- effect of
- phase transition

- transverse plane

## Numerical Calculation 

- Step 1.
- Step 2.
- Step 3.

- Coordinates move in parallel
- with baryon number current
- and entropy density current.

- local velocity:

- from hydro eq.

- temperature and chemical potential

- CPU time is almost
- proportional of # of lattice points.

**Notes:**
Brief explanation of numerical calculation 

## Summary 1

- Pure hydro with single freezeout temperature
-     Hadron ratio
-     Elliptic flow at forward/backward rapidity

## Distribution of # of Collisions

## f distribution

***=*0

***=*2.2

***=*3.2

## f distribution

*b=2.4 *fm

*b=4.5 *fm

*b=6.3 *fm

- at mid rapidity

## Distribution of # of Collisions

- finite b:
-  dN/ncoll becomes small
-  steep drop

## f distribution

## Reaction Dynamics in f  (M)

## Reaction Dynamics in f  (B)

## xf  Distribution 

## Reaction Dynamics I

## Reaction Dynamics II

## Reaction Dynamics IV

## xf  Distribution  II

## Future task

- Model :
- Initial conditions
- Realistic initial conditions
- Early thermalization  < 1 fm/c
- From color field
- Hard sector
- Dynamical effect on jets
- Jet correlations
- Observables:
- Electromagnetic probe
- NA60 In + In collisions
- Hadronic states in medium
- Chiral symmetry restoration and deconfinement
- HBT puzzle ?
- The 3-D hydro + cascade model provides a possible solution?

## Soft + Hard

**Soft**

**Hard**

-  Full 3-d Hydrodynamic Model
-   QGP formation, EoS

-  Micro. transport (PCM)
-  Hard scattering & jet production
-  Propagation of jet in medium,
-   energy loss

-   First schematic attempt

- t fm/c

- coupled hydro + PCM calculation

- Hirano & Nara
- PRC66:041901,2002,
- PRL91:082301,2003

**Hadronization**

- Fragmentation

- Improved
- Cooper-Frye
- formula
- (Reco)

**Final**
**Interactions**

-  Dynamical effect on jets
-  Jet correlations

## NA60(QM2005) 1

## NA60(QM2005) 2

## HBT Puzzle 

- Heinz and Kolb, hep-ph/0204061

- Morita, Muroya, Nonaka and Hirano,
- Phys.Rev.C66:054904,2002

- Experimental data:

- Expansion time is very short &
- Flash like particle emission

## Possible Solution to HBT Puzzle

*Possible Solution to HBT Puzzle*

- Super Cooling ?   Csernai et al, PLB551(2003)121
- Viscosity ?             Teaney, nucl-th/0301099
- x-t correlation ?
-    Lin @Collective Flow and QGP properties

**AMPT(a multi-phase transport model):**
-    strong and positive xout-t correlation term **Hydro:**
-     initial negative xout-t correlation

- From
- hydro model

- Hydro:

- Data:

**Notes:**
Super Cooling
1st order phase transition lead to long life time -> R_out/R_side becomes large.
Hadronization from supercooled QGP coincided with flash-like particle emission

## Hydro vs. Hydro + UrQMD

- Hadron Interactions

- y

-   decrease
-  K,p increase
-  proton earn large PT