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Contents. Introduction 3-d Hydrodynamic Model Hydro + Cascade Model Results (hadron spectra, elliptic flow) Summary. Hydro + Cascade Model at RHIC. Duke University, Chiho Nonaka. In Collaboration with Steffen A. Bass (Duke University & RIKEN) October 30, 2004@DNP, Chicago.

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Hydro cascade model at rhic

Contents

  • Introduction

  • 3-d Hydrodynamic Model

  • Hydro + Cascade Model

  • Results (hadron spectra, elliptic flow)

  • Summary

Hydro + Cascade Model at RHIC

Duke University, Chiho Nonaka

In Collaboration with

Steffen A. Bass (Duke University & RIKEN)

October 30, 2004@DNP, Chicago


Introduction
Introduction

  • Hydrodynamic Model at RHIC

Success

Failure?

  • Single particle spectra

  • Elliptic flow

Morita, Muroya, CN and Hirano,

PRC66:054904,2002

Hirano and Tsuda, PRC66

  • HBT

  • Elliptic flow

Morita et al., PRC66

Huovinen et.al, PLB503

Possible solution?


Freeze out final interactions
Freeze-out, Final Interactions

Freeze-out

Thermal model

T = 177 MeV

 = 29 MeV

UrQMD

  • universal Tf for all hadrons in Hydro

  • Tf & 

  • Final interactions

Thermal + radial flow fit

STAR, nucl-ex/0307024

Markert @QM2004

  • Freeze-out is not universal for all hadron spectra.

  • Rescattering and regeneration is important.


Hydro cascade model
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.

Hadronization

UrQMD

  • 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


3 d hydrodynamic model
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


Trajectories on the phase diagram
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)


Parameters
Parameters

  • Initial Conditions

    • Energy density

    • Baryon number density

    • Parameters

    • Flow

      longitudinal: Bjorken’s 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


Hadron spectra i
Hadron Spectra (I)

  • Pure Hydro

    • Central collision

    • Parameters

  • Hydro works well up to PT ~ 2 GeV


Hadron spectra ii
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.


Elliptic flow
Elliptic Flow

  • Pure Hydro

  • Centrality 5-10 %

  • Hydro works well.

Centrality dependence


Elliptic flow ii
Elliptic Flow (II)

  • Hydro + UrQMD

preliminary

  • In UrQMD elliptic flow becomes small ?

  • Shape of elliptic flow as a function of 


Summary
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



Numerical calculation
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.