Hydro Cascade Model at RHIC

1
Hydro Cascade Model at RHIC
Duke University, Chiho Nonaka

• In Collaboration with
• Steffen A. Bass (Duke University RIKEN)
• October 30, 2004_at_DNP, Chicago

2
Introduction

• Hydrodynamic Model at RHIC

Success
Failure?

• Elliptic flow

• Single particle spectra

Morita, Muroya, CN and Hirano, PRC66054904,2002
Hirano and Tsuda, PRC66

• HBT

• Elliptic flow

Morita et al., PRC66
Huovinen et.al, PLB503
Possible solution?
3
Freeze-out, Final Interactions

• universal Tf for all hadrons in Hydro

• Freeze-out

• Tf ?

• Final interactions

Thermal radial flow fit
STAR, nucl-ex/0307024
Markert _at_QM2004

• Freeze-out is not universal for all hadron
  spectra.
• Rescattering and regeneration is important.

4
Hydro Cascade Model
Bass and Dumitru, PRC61,064909(2000) Teaney et
al, nucl-th/0110037

• Hydro hadron transport model
• Key
• Freeze-out condition ex. Chemical and kinetic
  freeze-out
• Final interactions

Hirano and Tsuda, PRC66(2002)054905
Treatment of freeze-out in transport model is
determined by mean free path.
UrQMD
Hadronization

• Full 3-d Hydrodynamics
• EoS 1st order phase transition
• QGP excluded volume model

( Improved) Cooper-Frye formula (Reco)
Final interactions
Monte Carlo
t fm/c
5
3-d Hydrodynamic Model

• Hydrodynamic equation
• Baryon number density conservation
• Coordinates
• Lagrangian hydrodynamics
• Tracing the adiabatic path of each
• volume element
• Effects of phase transition of observables
• Algorithm
• Focusing on conservation law

Flux of fluid
6
Trajectories on the Phase Diagram

• Lagrangian hydrodynamics

temperature and chemical potential of volume
element of fluid
effect of phase transition
C.N et al., Eur. Phys.J C17,663(2000)
7
Parameters

• Initial Conditions
• Energy density
• Baryon number density
• Parameters
• Flow
• longitudinal Bjorkens Solution
• Equation of State
• 1st order phase transition
• QGP phase (Bag model), mixed phase,
• hadron phase (up to 2GeV)
• (excluded volume model)
• Bag constant
• Hydro UrQMD

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Hadron Spectra (I)

• Pure Hydro
• Central collision
• Parameters

• Hydro works well up to PT 2 GeV

9
Hadron Spectra (II)

• Hydro UrQMD

• Many pions are produced in UrQMD.
• Low PT resonances
• High PT interactions
• Transition temperature is too low.

• PT slope becomes flatter.
• Extra radial flow in UrQMD

The initial condition for Hydro UrQMD Is
different from that for pure hydro.
10
Elliptic Flow

• Pure Hydro

• Centrality 5-10
• Hydro works well.

Centrality dependence
11
Elliptic Flow (II)

• Hydro UrQMD

preliminary

• In UrQMD elliptic flow becomes small ?
• Shape of elliptic flow as a function of ?

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Summary

• Hydro Cascade Model
• Hadron Spectra, elliptic flow
• Effect of resonances, final interactions in
  experimental data
• Work in progress
• Parameter
• Initial Conditions
• EoS (QCD critical point) ,CN and Asakawa
  nucl-th/0410078
• Parton Cascade Model
• Hadronization mechanism
• Recombination Fragmentation model, Duke
  Group

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BACK UP
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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.