Hydro + Cascade Model at RHIC

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Presentation transcript:

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

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 universal Tf for all hadrons in Hydro Freeze-out Tf &  Final interactions Thermal + radial flow fit Thermal model T = 177 MeV  = 29 MeV UrQMD STAR, nucl-ex/0307024 Markert @QM2004 Freeze-out is not universal for all hadron spectra. Rescattering and regeneration is important.

Hydro + Cascade Model Hydro + hadron transport model Key: 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. Full 3-d Hydrodynamics EoS 1st order phase transition QGP + excluded volume model Hadronization UrQMD ( Improved) Cooper-Frye formula (Reco) Final interactions Monte Carlo t fm/c

3-d Hydrodynamic Model Hydrodynamic equation Coordinates 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 Lagrangian hydrodynamics Discretized grids move along the expansion of the fluid; therefore, we can perform The calculation at all stages on the lattice points which we prepare under the initial Condisions. Flux of fluid

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 Initial Conditions Equation of State Hydro UrQMD 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) Pure Hydro Hydro works well up to PT ~ 2 GeV Central collision Parameters Hydro works well up to PT ~ 2 GeV

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 Pure Hydro Centrality 5-10 % Centrality dependence Hydro works well. Centrality dependence

Elliptic Flow (II) Hydro + UrQMD preliminary In UrQMD elliptic flow becomes small ? Shape of elliptic flow as a function of 

Summary Hydro + Cascade Model Work in progress 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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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.