1. 1 Transport and Hydrodynamic 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) Xu Cai (CCNU, China) Ben-Hao Sa (CIAE, China) L. P. Csernai (UiB, Norway) May. 7 - 13, 2014, CCNU, Wuhan, China

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

3. 3 Stages of heavy ion collisions

4. 4 –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. –The PACIAE model is composed of (1) Parton initialization (2) Parton evolution (3) Hadronization (4) Hadron evolution PACIAE model

5. 5 Particle list particle orderposition and four momentum particle 1 particle 2 particle 3 …… x, y, z, p x, p y, p z, E of particle 1 x, y, z, p x, p y, p z, E of particle 2 x, y, z, p x, p y, p z, E of particle 3 …… Collision list collision ordercollision pair 1 2 3 …… collision time Part. i and j Part. l and m Part. l and n …… col. time for ij col. time for lm col. time for ln …… nn collision happens if their least approaching distance

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

7. 7 1) Parton Initialization a)Nucleus-nucleus collision is decomposed into nucleon- nucleon (NN) collisions. b)NN collision is described by the PYTHIA model, and the string fragmentation is switched-off. c)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). PACIAE model

8. 8 3) Hadronization 4) Hadron Evolution (Hadron Rescattering) String Fragmentation (SF) model in PYTHIA, and Coalescence model. The coalescence model is used in the hybrid model. Only and their antiparticles are condsidered, and the usual two-body collision model is used. 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.) Reference ： Ben-Hao Sa, et al, Comp. Phys. Comm. 183 (2012) 333-346.

9. 9 Hydrodynamical model Relativistic fluid dynamics (FD) is based on the assumption of local equilibrium and the conservation 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. 10 1) The baryon charge related marker particles are introduced to represent the motion of the fluid. Particle in Cell (PIC) method a)The momentum and energy are distributed evenly among the marker particles. b)Each marker particle is given an effective velocity. c)In a time step  t, if the marker particle crosses to a new cell, then it transfers the corresponding amount of baryon charge, momentum, and energy from the donor cell to the acceptor cell.

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

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

13. 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. 14 Quantities of cells in Hydro Quantities of particles in PACIAE model 1), Particle number: N 2), Particle type: KF code 3), Momentum and energy of each particle: E, p x, p y, p z 4), Coordinates and time of each particle: v x, v y, v z, T 1), Energy density: E cf 2), Baryon density: n 3), Pressure: p 4), Velocity: v x, v y, v z 5), Temperature and Entropy: T and sq Physical Quantities in Hydro and PACIAE model

15. 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. 16 Case 1: Isochronous transition, t = Constant. Case 2: Transition takes place on the hyperboloid, τ=Constant. Case 3: Realistic and complex condition. From Hydro to PACIAE model

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

18. 18 1. 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). Structure of the hybrid model

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

20. 20 Transverse momentum distribution from Hybrid and PACIAE model

21. 21 Transverse momentum distribution of pion

22. 22 Transverse momentum distribution of kaon

23. 23 Transverse momentum distribution of proton

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

25. 25 Elliptic flow for pion, kaon, and proton

26. 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. 27 Thanks for your attention!