# Presentation: 190571

## Spectra and Flowfrom Full 3DHydro+Cascade Model 

- Tetsufumi Hirano
- Institute of Physics, University of Tokyo

- References:
- T.Hirano and M.Gyulassy, Nucl.Phys.A **769**(2006)71.
- T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B **636** (2006)299.

- Workshop “How perfect is this matter?”
- in 2006 RHIC & AGS annual users’ meeting

## OUTLINE

- Dynamical modeling in heavy ion collisions (hydro+cascade)
- Results from OUR hydro + cascade model
- Discussion on hadronic dissipation
- Summary

## A Bigger Picture

- Proper time

- Transverse momentum

**CGC**

**Geometric Scaling**

**Shattering CGC**

**Hydrodynamics**
**viscosity?**
**non chem. eq.?**

**Parton energy loss**
**Inelastic**
**Elastic**

**Hadronic**
**cascade**

**Low p****T**

**High p****T**

**Recombination**
**Coalescence**

**“****DGLAP region”**

**(N)LOpQCD**

- Before collisions

- Parton
- production
- Pre-
- equilibrium

- “Perfect” fluid
- QGP or GP

- Dissipative
- hadron
- gas

**Fragmentation**

**Interaction**

**Intermediate p****T**

**Instability?**
**Equilibration?**

## Ideal QGP Fluid + Dissipative Hadron Gas Models

|  | (1+1)D with
Bjorken flow | (2+1)D with
Bjorken flow | Full (3+1)D |
| --- | --- | --- | --- |
| UrQMD | A.Dumitru et al., PLB460,411(1999); PRC60,021902(1999);S.Bass and A.Dumitru, PRC61,064909(2000). | 
N/A | C.Nonaka and S.Bass, 
nucl-th/0510038. |
| RQMD | 
N/A | D.Teaney et al., PRL86,4783(2001), nucl-th/0110037;
D.Teaney,             nucl-th/0204023. | 
N/A |
| JAM | 
N/A | 
N/A | TH, U.Heinz, D.Kharzeev, R.Lacey, and Y.Nara, PLB636,299(2006). |

- hydro

- cascade

## What needed (practically) for Dynamical Modeling in Heavy Ion Collisions

- Man Power
- Modeling
- Coding
- Computing Power
- Consistency of Results
- Comparison among groups
- Need benchmark calculations?
- Not exclusive, but supplementary
- Maintenance of Codes
- UrQMD: UrQMD collaboration (Frankfurt)
- 3D hydro (Lagrange): C.Nonaka (Nagoya)
- JAM: Y.Nara (Frankfurt)
- 3D hydro (Euler): T.Hirano (Tokyo)

- Previous talk

- Current talk

## (CGC +)QGP Hydro+Hadronic Cascade

- 0

*z*

*t*

- (Option)
- Color Glass
- Condensate

- sQGP core
- (Full 3D
- Ideal Hydro)

- Hadronic
- Corona
- (Cascade,
- JAM)

- TH et al.(’05-)

- 0.6fm/c

## Hydro Meets Data for the First Time at RHIC: “Current” Three Pillars

-  Perfect Fluid (s)QGP Core
- Ideal hydro description of the QGP phase
- Necessary to gain integrated v2
-  Dissipative Hadronic Corona
- Boltzmann description of the hadron phase
- Necessary to gain enough radial flow
- Necessary to fix particle ratio dynamically
-  Glauber Type Initial Condition
- Diffuseness of initial geometry

- TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)

- A Lack of each pillar leads to discrepancy!

## (1) Glauber and (2) CGC Hydro Initial Conditions Which Clear the First Hurdle 

- Glauber model
-    Npart:Ncoll = 85%:15%
- CGC model
-    Matching I.C. via e(x,y,)

- Centrality dependence

- Rapidity dependence

## pT Spectra for identified hadronsfrom QGP Hydro+Hadronic Cascade

- Caveat: Other components such as recombination and
- fragmentation should appear in the intermediate-high pT regions.

- dN/dy and dN/dpT are o.k. by hydro+cascade.

## v2(Npart) from QGP Hydro + Hadronic Cascade

- _Glauber_:
-  Early thermalization
-  Mechanism?
- _CGC_:
-  No perfect fluid?
-  Additional viscosity
- is required in QGP

- Importance of better understanding of initial condition

- Result of JAM: Courtesy of M.Isse

- TH et al.(’06)

## Large Eccentricity from CGC Initial Condition

*x*

*y*

- Pocket formula (ideal hydro):
-  v2 ~ 0.2 @ RHIC energies

- Ollitrault(’92)

- Hirano and Nara(’04), Hirano et al.(’06)
- Kuhlman et al.(’06), Drescher et al.(’06)

## v2(pT) for identified hadronsfrom QGP Hydro + Hadronic Cascade

- Glauber type initial condition

- CGC initial condition

- Mass dependence is o.k.

- v2(model) > v2(data)

- 20-30%

- 20-30%

## v2() fromQGP Hydro + Hadronic Cascade

- Glauber-BGK

- CGC

## Discussions: Hadronic Dissipation

- Hybrid Model:
- QGP Fluid + Hadronic Gas  + Glauber I.C.
- Hydro Model:
- QGP Fluid + Hadronic Fluid + Glauber I.C.

- ComparisonTry to draw
- information on hadron gas

- _Key technique in hydro_:
- Partial chemical equilibrium in hadron phase
- Particle ratio fixed at Tch
- Chemical equilibrium changes dynamics.
-                          TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

## Hydro ~ Hydro+Cascade for Protons

- Tth ~ 100 MeV
- Shape of spectrum
- changes due to
- radial flow rather
- than hadronic
- dissipation for
- protons.

- radial flow

## Opposite Behavior for Pions

- Hadronic Fluid
- (pdV work)

- Hadronic Gas
- (Viscous pressure)

- Green line:

- Teaney(’03)

- Caveat:
- Transverse expansion
- Non-scaling solution

## Hadronic Dissipation Suppresses Differential Elliptic Flow

- Difference comes from dissipation only in the hadron phase

- Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and M.Gyulassy (’06))

- Relevant parameter: s
-                       Teaney(’03)
- Dissipative effect is not so
- large due to small expansion
- rate (1/tau ~ 0.05-0.1 fm-1)

## Mass Splitting Comes from the Late Hadronic Stage

- Proton

- Pion

- Pion: Generation of v2
- in the hadronic stage
- Proton: Radial flow effects
-                       Huovinen et al.(’01)

- Mass splitting itself
- is not a direct signature
- of perfect fluid QGP.

## v2() fromQGP Hydro + Hadronic Cascade

- Suppression due to
- hadronic dissipation

- Glauber-BGK

## Excitation Function of v2

- Hadronic Dissipation
- is huge at SPS.
- still affects v2 at RHIC.
- is almost negligible at LHC.

## Summary

- An answer to the question, “Whether Perfect Fluid QGP is discovered”, depends on relatively unknown details of the initial state.
- Perfect fluid QGP or CGC?
- Hadronic dissipative (rescattering) effects after hadronization of QGP fluids are considered through a hadron cascade model.
- Many discrepancy between ideal hydro and data can be interpreted by hadronic dissipation.

## Source Function from 3D Hydro + Cascade

- Blink: Ideal Hydro, Kolb and Heinz (2003)
- Caveat: No resonance decays in ideal hydro

- How much the source function
- differs from ideal hydro
- in Configuration space?

## Non-Gaussian Source?

- x

- y

- px=
- 0.5GeV/c

## v2(pT) from Hydro: Past, Present and Future

- _2000 (Heinz, Huovinen, Kolb...)_
- Ideal hydro w/ chem.eq.hadrons
- _2002 (TH,Teaney,Kolb...)_
- +Chemical freezeout
- _2002 (Teaney...)_
- +Dissipation in hadron phase
- _2005 (BNL)_
- “RHIC serves the perfect liquid.”
- _2004-2005 (TH,Gyulassy)_
- Mechanism of v2(pT) slope
- _2005-2006(TH,Heinz,Nara,...)_
- +Color glass condensate
- _Future_
- “To be or not to be (consistent
- with hydro), that is THE question”
-                            -- anonymous

- History of differential elliptic flow
- ~History of development of hydro
- ~History of removing ambiguity in hydro

- 20-30%

- XXXXXXXXXXXXXX

- ?????????????????

- XXXXXXXXXXXXXX

## Viscosity from a Kinetic Theory

- See, e.g. Danielewicz&Gyulassy(’85)

- For ultra-relativistic particles, the shear viscosity is

_*Ideal*_ hydro:
-   0
- shear viscosity  0

- Transport cross section

## Viscosity and Entropy

- 1+1D Bjorken flow Bjorken(’83)
- Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)...

- (Ideal)

- (Viscous)

- Reynolds number

*** *: shear viscosity (MeV/fm2), *s *: entropy density (1/fm3)

- where

**/*s* is a good dimensionless measure
- (in the natural unit) to see viscous effects.

*R*>>1
- Perfect fluid

- Iso, Mori, Namiki (’59)

## Why QGP Fluid + Hadron Gas Works?

- TH and Gyulassy (’06)

- !

- Absolute value of viscosity

- Its ratio to entropy density

- Rapid increase of entropy density can
- make hydro work at RHIC.
- Deconfinement Signal?!

*** *: shear viscosity, *s *: entropy density

- Kovtun,Son,Starinets(’05)

## Temperature Dependence of /s

- We propose a possible scenario:

- Kovtun, Son, Starinets(‘05)

- Danielewicz&Gyulassy(’85)

- Shear Viscosity in Hadron Gas

- Assumption: /s at Tc in the sQGP is 1/4

- No big jump in viscosity at Tc!

## Digression

- (Dynamical) Viscosity :
-    ~1.0x10-3 [Pa s]  (Water 20°C)
-    ~1.8x10-5 [Pa s]  (Air 20°C)
- Kinetic Viscosity :
-    ~1.0x10-6 [m2/s]  (Water 20°C)
-    ~1.5x10-5 [m2/s]  (Air 20°C)

- [Pa] = [N/m2]

- Non-relativistic Navier-Stokes eq. (a simple form)

- Neglecting external force and assuming incompressibility.

- water > air  BUT   water < air