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Transport and Hydro d ynamic Model for Ultra-relativistic Heavy Ion Collisions

Transport and Hydro d ynamic Model for Ultra-relativistic Heavy Ion Collisions. Yu-Liang Yan China Institute of Atomic Energy. Collaborators: Yun Cheng (CCNU, China) Dai-Mei Zhou (CCNU, China) Bao-Guo Dong (CIAE, China)

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Transport and Hydro d ynamic Model for Ultra-relativistic Heavy Ion Collisions

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  1. Transport and Hydrodynamic Model for Ultra-relativistic HeavyIon Collisions Yu-Liang Yan China Institute of Atomic Energy Collaborators: Yun Cheng (CCNU, China) Dai-Mei Zhou (CCNU, China) Bao-Guo Dong (CIAE, China) Xu Cai (CCNU, China) Ben-Hao Sa(CIAE, China) L. P. Csernai (UiB, Norway) May. 7 - 13, 2014, CCNU, Wuhan, China

  2. Outline • Introduction • PACIAE model • Hydrodynamic model • Transport and Hydrodynamic hybrid Model (PACIAE+HYDRO+ PACIAE) • Results and Summary

  3. Stages of heavy ion collisions

  4. PACIAE model • The PACIAE model is a parton and hadron cascade model , which is based on PYTHIA. • PYTHIA is a famous model for relativistic hadron-hadron collisions. • ThePACIAE model is composed of (1) Parton initialization (2) Parton evolution (3) Hadronization (4) Hadron evolution

  5. Particle list particle order position and four momentum particle 1 particle 2 particle 3 …… x, y, z, px, py, pz, E of particle 1 x, y, z, px, py, pz, E of particle 2 x, y, z, px, py, pz, E of particle 3 …… Collision list nn collision happens if their least approaching distance collision order collision pair collision time 1 2 3 …… Part. i and j Part. l and m Part. l and n …… col. time for ij col. time forlm col. time forln ……

  6. Sketch for pp simulation inPYTHIA Remnant Initial state radiation a Rescattering ? … h Parton Distribution Function Decay b Final state radiation Remnant Hadronization

  7. PACIAE model 1) Parton Initialization • Nucleus-nucleus collision is decomposed into nucleon-nucleon (NN) collisions. • NN collision is described by the PYTHIA model, and the string fragmentation is switched-off. • The diquarks (anti-diquarks) are broken into quarks (anti-quarks), so the consequence of this NN collision is a partonic final state (quarks, anti-quarks, and gluons, beside a few remnants).

  8. PACIAE model 2) Parton Evolution (Parton Recattering) Only 2→2 process are considered,2 → 2 Leading-Order (LO-) pQCD differential cross sections. (Replaced by the Hydro evolution in the hybrid model.) 3) Hadronization String Fragmentation (SF) model in PYTHIA, and Coalescence model. The coalescence model is used in the hybrid model. 4) Hadron Evolution (Hadron Rescattering) Only and their antiparticles are condsidered, and the usual two-body collision model is used. Reference：Ben-Hao Sa, et al, Comp. Phys. Comm. 183 (2012) 333-346.

  9. Hydrodynamical model Relativistic fluid dynamics (FD) is based on the assumption of local equilibrium and theconservation laws. The MIT bag model is used for the equation of state (EoS). Algorithms for solving the hydrodynamic equations: PIC, SHASTA, and RHHLE etc. Particle in Cell (PIC) method is used in hydro code.

  10. Particle in Cell (PIC) method 1) The baryon charge related marker particles are introduced to represent the motion of the fluid. • The momentum and energy are distributed evenly among the marker particles. • Each marker particle is given an effective velocity. • In a time stepDt, if the marker particle crosses to a new cell, then it transfers the corresponding amount ofbaryon charge, momentum, andenergyfrom the donor cell to the acceptor cell.

  11. Particle in Cell (PIC) method 2) Update the baryon charge, momentum, and energy values. Use the updated values to solve hydrodynamic equations. 3) Proceed thenext time stepof the calculations. Reference： Phys. Rev. C 17 (1978) 2080 Phys. Lett. B 261 (1991) 352

  12. Particle in Cell (PIC) method Initial marker particle position Time step is 100 cycles. Time step is 200 cycles.

  13. Initial state for Hydrodynamic model • There are many initial state models, such as: • perturbative QCD (hard scatterings) plus saturation model, • Glauber-based parametrization method, • color glass condensate inspired model, • effective string rope model, • transport model, etc. In the HYDRO-PACIAE model, the effective string rope model is used to generate initial state. We choose the transport model PACIAE to generate initial state in the new hybrid model.

  14. Physical Quantities in Hydro and PACIAE model Quantities of particlesin PACIAE model Quantities of cells in Hydro 1), Energy density: Ecf 2), Baryon density: n 3), Pressure: p 4), Velocity: vx, vy, vz 5), Temperature and Entropy: T and sq 1), Particle number: N 2), Particle type: KF code 3), Momentum and energy of each particle: E, px, py, pz 4), Coordinates and time of each particle: vx, vy, vz, T

  15. From PACIAE model to Hydro • PACIAE model is Monte Carlo transport model. • Event-by-event fluctuations of the initial state • can naturally included. • The energy, momentum, and baryon number • density are described by three-dimensional • Gaussian distribution.

  16. From Hydro to PACIAE model Case 1: Isochronous transition, t = Constant. Case 2: Transition takes place on the hyperboloid, τ=Constant. Case 3: Realistic and complex condition.

  17. Solutions of Boundary Conditions Cooper-Frye formula Fermi distribution for Quark and anti-quark: Bose distribution for Gluon:

  18. Structure of the hybrid model • Initial stage for hydrodynamic • (effective string rope model (ESRM) • and/or PACIAE model). • 2. Hydrodynamic evolution (Hydro code). • 3. Translate hydro into parton • (Cooper-Frye formula). • 4. Hadronization (PACIAE model). • 5. Hadron rescattering(PACIAE model).

  19. Results of the Hybid model Charged Hadron Pseudorapiditydistribution: Reference：Yu-Liang Yan, et al, J. Phys. G: Nucl. Part. Phys. 40 (2013) 025102

  20. Transverse momentum distribution from Hybrid and PACIAE model

  21. Transverse momentum distribution of pion

  22. Transverse momentum distribution of kaon

  23. Transverse momentum distribution of proton

  24. Elliptic flow from Hybrid and PACIAE model Deformation parameter in PACIAE:

  25. Elliptic flow for pion, kaon, and proton

  26. Summary • Based on the PACIAE and Hydrodynamic model, a hybrid model, ESRM +HYDRO+PACIAE and PACIAE+HYDRO+PACIAE, is established. • The ESRM (or PACIAE)+HYDRO+PACIAE model is a partonic based integrated hybrid model, which can reproduce the experimental data well. • The PACIAE+HYDRO+PACIAE hybrid model can be used to study the partonic degrees of freedom, quark number scaling,and the initial state fluctuations, etc.

  27. Thanks for yourattention!

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