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Hydro+Cascade Model: Hadron Spectra and Elliptic Flow at RHIC

This study explores the hydrodynamic model coupled with a cascade model to analyze hadron spectra and elliptic flow at RHIC. The results show the effects of resonance decays, final interactions, and the role of rescattering in the experimental data. Work is ongoing to refine the parameters, initial conditions, and equation of state.

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Hydro+Cascade Model: Hadron Spectra and Elliptic Flow at RHIC

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  1. 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

  2. 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?

  3. 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.

  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. 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

  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: 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

  8. 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 

  12. 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

  13. BACK UP

  14. 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.

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