Report

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) 10th Workshop on QCD Phase Transition and Relativistic Heavy-ion Physics, Aug. 8 - 10, 2013, Chengdu. 1 Outline • Introduction • PACIAE model • Hydrodynamic model • Connecting the PACIAE and Hydrodynamic model • Transport and Hydrodynamic hybrid Model (PACIAE+HYDRO+ PACIAE) • Results and Summary 2 Stages of heavy ion collisions 3 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. – The PACIAE model is composed of (1) Parton initialization (2) Parton evolution (3) Hadronization (4) Hadron evolution 4 PACIAE model 1) Parton Initialization a) Nucleus-nucleus collision is decomposed into nucleonnucleon (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). 5 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 p, n, , k , , , , ( ), J / 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. 6 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. 7 Particle in Cell (PIC) method The baryon charge related marker particles are introduced to represent the motion of the fluid. 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. 8 Particle in Cell (PIC) method Initial marker particle position Time step is 100 cycles. Time step is 200 cycles. 9 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. 10 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. Ecf ( x, y, z ) ( x x p ) ( y y p ) [ z ( z z p )] 2 N exp{ 2 2 2 2 } 11 From Hydro to PACIAE model Case 1: Isochronous transition, t = Constant. d (1,0,0,0) Case 2: Transition takes place on the hyperboloid, τ=Constant. d (1,0,0, v ) Case 3: Realistic and complex condition. d differentin each cell 12 Solutions of Boundary Conditions Cooper-Frye formula E dN f ( x , p ) p d i 3 d p Fermi distribution for Quark and anti-quark: gi 1 f i ( i ) (2)3 e ( i ) / T 1 Bose distribution for Gluon: gi 1 f i ( i ) (2)3 e ( i ) / T 1 13 Structure of the hybrid model 1. Initial stage for hydrodynamic (PACIAE model). 2. Hydrodynamic evolution (Hydro code). 3. Translate hydro into parton (Cooper-Frye formula). 4. Hadronization (PACIAE model). 5. Hadron rescattering (PACIAE model). 14 Results of the Hydro-PACIAE model Charged Hadron Pseudorapidity distribution: Reference：Yu-Liang Yan, et al, J. Phys. G: Nucl. Part. Phys. 40 (2013) 025102 15 Transverse momentum distribution from Hybrid and PACIAE model 16 Elliptic flow from Hybrid and PACIAE model Deformation parameter in PACIAE: rp2 y2 x2 p C r , r , rp 2 4 y x2 17 Summary • Based on the PACIAE and Hydrodynamic model, a hybrid model, PACIAE+HYDRO+PACIAE, is established. • The 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. 18 Thanks for your attention! 19