b in a given centrality bin size at different centralities from the most central to peripheral Au+Au collisions at √ s$_{NN}$ =200 GeV. A discussion is given for the com- parison among the models and STAR data as well as the STAR’s convention of different centrality determina- tion for different measured Δ η points. A prediction for the forward-backward multiplicity correlation in Pb+Pb collisions at √ s$_{NN}$ =5500 GeV is also given. The parton and hadron cascade model, PACIAE [16], is based on PYTHIA [17] which is a model for hadron- hadron ( hh ) collisions. The PACIAE model is composed of four stages: the parton initialization, parton evolu- tion (rescattering), hadronization, and hadron evolution (rescattering). 1. PARTON INITIALIZATION: In the PACIAE model, a nucleus-nucleus collision is decomposed into the nucleon-nucleon collisions based on the collision ge- ometry. A nucleon-nucleon ( NN ) collision is described with the PYTHIA model, where a NN (hadron-hadron, hh ) collision is decomposed into the parton-parton col- lisions. The hard parton-parton collision is described by the lowest-leading-order (LO) pQCD parton-parton cross section [18] with modification of parton distribu- tion function in the nucleon. And the soft parton-parton interaction is considered empirically. The semihard, be- tween hard and soft, QCD 2 → 2 processes are also involved in the PYTHIA (PACIAE) model. Because of the initial- and final-state QCD radiation added to the parton-parton collision processes, the PYTHIA (PA- CIAE) model generates a partonic multijet event for a NN ( hh ) collision. That is followed, in the PYTHIA model, by the string-based fragmentation scheme (Lund string model and/or Independent Fragmentation model), thus a hadronic final state is reached for a NN ( hh ) collision. However, in the PACIAE model the above fragmentation is switched off temporarily, so the result is a partonic multijet event (composed of quark pairs, diquark pairs and gluons) instead of a hadronic final state. If the diquarks (anti-diquarks) are split forcibly into quarks (anti-quarks) randomly, the consequence of a NN ( hh ) collision is its initial partonic state composed of quarks, anti-quarks, and gluons. 2. PARTON EVOLUTION: The next stage in the PACIAE model is the parton evolution (parton rescat- tering). Here the 2 → 2 LO-pQCD differential cross sections [18] are employed. The differential cross section of a subprocess ij → kl reads where the factor K is introduced considering the higher order pQCD and non-perturbative QCD corrections as usual, α$_{s}$ stands for the strong (running) coupling con- In the theoretical calculation it is convenient to define the centrality by impact parameter b$_{i}$ . The mapping relation between centrality definition in theory and ex- periment In our calculations the default values given in the PYTHIA model are adopted for all model parameters except the parameters K and b$_{s}$ (in the Lund string frag- mentation function). K =3 is assumed and b$_{s}$ =6 is tuned to the PHOBOS data of charged particle multiplicity in 0-6% most central Au+Au collisions at √ s$_{NN}$ =200 GeV [22], as shown in Tab. I. 4. HADRON EVOLUTION: After hadronization the rescattering among produced hadrons is dealt with the usual two-body collision model. Only the rescattering among π, k, p, n, ρ ( ω ) , Δ , Λ , Σ , Ξ , Ω , J/ Ψ and their an- tiparticles are considered in the calculations. An isospin averaged parametrization formula is used for the hh cross section [19, 20]. We also provide an option for the con- stant total, elastic, and inelastic cross sections ( σ NN tot = 40 mb, σ πN tot = 25 mb, σ kN tot = 35 mb, σ ππ tot = 10 mb) and the assumed ratio of inelastic to total cross section of 0.85. More details of hadronic rescattering can see [21]. 3. HADRONIZATION: The parton evolution stage is followed by the hadronization at the moment of partonic freeze-out (no any more parton collision). In the PA- CIAE model, the Lund string fragmentation model and phenomenological coalescence model are supplied for the hadronization of partons after rescattering. The Lund string fragmentation model is adopted in this paper. We refer to [16] for the details of the hadronization stage. With the total and differential cross sections above the parton evolution (parton rescattering) can be simulated by the Monte Carlo method. The total cross section of the parton collision, i + j , then reads where ˆ s , ˆ t , and ˆ u are the Mandelstam variables. Since it diverges at ˆ t =0 one has to regularize it with the parton color screen mass µ stant. Taking the process q 1 q 2 → q 1 q 2 as an example one has 2 II. THE PACIAE MODEL III. CALCULATIONS AND RESULTS b$_{i}$ = √ gb max i , b max i = R$_{A}$ + R$_{B}$, (6) dσ$_{ij}$ → kl d ˆ t = K πα 2 s ˆ s ∑ ij → kl , (2) σ$_{ij}$ (ˆ s ) = ∑ k,l ∫ 0 − ˆ s d ˆ t dσ$_{ij}$ → kl d ˆ t . (5) ∑ q$_{1}$q$_{2}$ → q$_{1}$q$_{2}$ = 4 9 ˆ s 2 + ˆ u 2 ( ˆ t − µ $^{2}$)$_{2}$. (4) ∑ q$_{1}$q$_{2}$ → q$_{1}$q$_{2}$ = 4 9 ˆ s 2 + ˆ u 2 ˆ t 2 , (3)