Discrepancy between hadron matter and quark-gluon matter in net charge transfer fluctuation

A parton and hadron cascade model, PACIAE, is employed to investigate the net charge transfer fluctuation within $|\eta|$=1 in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV. It is turned out that the observable of net charge transfer fluctuation, $\kappa$, in hadronic final state (HM) is nearly a factor of 3 to 5 larger than that in initial partonic state (QGM). However, only twenty percent of the net charge transfer fluctuation in the QGM can survive the hadronization

Quark-Gluon-Plasma (QGP) phase transition expected to be existing in the relativistic nucleus-nucleus collisions.Following [3] the observable is employed to describe the net charge transfer fluctuation.In the above equation the net charge transfer deviation, D u , reads where the net charge transfer, u, is defined by where the Q F (η) (Q B (η)) is referred to the net charge in forward (backward) region of η and the N ch stands for the charge multiplicity accounted according to the charge of particle.
The κ is argued to be a measure of the local unlike-sign charge correlation length [2] and the charge correlation length in QGP phase (in quark-gluon matter, QGM) is expected to be much smaller than the one in hadronic matter (HM) because the charge unit is 1/3 and 1 in QGM and HM [4,5,6], respectively.
In [2] a neutral cluster model was used first and the hadronic transport models of HIJING [7], RQMD [8], and UrQMD [9] were employed then to study the net charge transfer fluctuation.The results from above hadronic transport models could be summarized as follows: 1.The discrepancy among them is not obvious from each other.2. The κ(η = 1) calculated in interval of |η| < 1 is equivalent to the net charge fluctuation at η = 1 and is close to the STAR datum [10] of ∼ 0.27 ± 0.02 (cited from [2] directly) in Au + Au collisions at √ s N N =130 GeV. 3. The κ(η) does not strongly depend on the centrality.
A parton and hadron cascade model, PACIAE, is employed in this letter investigating the net charge transfer fluctuation, κ, within |η| < 1 both in the early partonic stage (QGM) and in the hadronic final state (HM) in Au + Au collisions at √ s N N =200 GeV.As expected the later results are quite close to the results in HIJING, RQMD, and UrQMD.However the former results are smaller than the later one by a factor of 3 to 5. Unfortunately, the κ in QGM seems to be hard to survive the hadronization.
As the simplified version of PACIAE model has been published in [11] and a nice bit of detailed description has been given in [12], here we just give a brief introduction for PACIAE model.In the PACIAE model a nucleus-nucleus collision is decomposed into nucleon-nucleon collisions.The nucleons in a nucleus is distributed randomly according to Wood-Saxon distribution.A nucleon-nucleon collision is described by the Lowest-Leading-Order (LLO) pQCD parton-parton hard interactions with parton distribution function in a nucleon and by the soft interactions considered empirically, that is so called "multiple mini-jet production" in HIJING model [7].However, in PACIAE model that is performed by PYTHIA model [13] with string fragmentation switched-off.Therefore, the consequence of nucleus-nucleus collision is a configuration of q (q), diquark (anti-diquark), and g, besides the spectator nucleons and beam remnants [13].The diquark (anti-diquark) is forced to split into qq (q q) randomly.
So far we have introduced the partonic initialization of nucleus-nucleus collision in PA-CIAE model, what follows is then parton evolution (scattering).To the end, the 2→2 LLO pQCD differential cross section [14] is used.Of course, that must be regularized first by introducing the color screen mass.The total cross section of parton i bombarding with j could then be calculated via a integral over the squared momentum transfer in a subprocess ij → kl and a summation over partons k and l.With above differential and total cross sections the parton scattering can be simulated by Monte Carlo method.As of now, only 2→2 processes are involved, among them there are six elastic and three inelastic processes [14].
As for the hadronization we first assume that the partons begin to hadronize when the interactions among them have been ceased (freeze-out).They could hadronize by either fragmentation model [15,16] or coalescence model [17,18].What the fragmentation models included here are the Field-Feynman model, i. e.Independent Fragmentation (IF) model [15] and Lund string fragmentation model [16].However, the program built in [13] is employed for the implementation of fragmentation model.On the contrary, we do write a program for coalescence model ourselves.
The hadron evolution (hadronic rescattering) is modeled as usual two body collisions and is copied directly from a hadron and string cascade model LUCIAE [19].There is no need to say more about the hadronic rescattering referring to [19] if necessary.Since we are not aimed to reproduce the experimental date but to study the physics of net charge transfer fluctuation, we do not adjust model parameters at all.In the calculations the IF model [15] is adopted for hadronization and the net charge transfer fluctuation is counted in the interval of |η| <1.The simulated results by default PACIAE model are indicated with "HM w/ QGM" (HM with QGP assumption), since the hadronic final state is evolved from partonic initial state.If the simulation is ended up at the stage of partonic scattering and the net charge transfer fluctuation is counted over partons only, the results will be referred to as "QGM".In that calculation it is assumed that the gluon does not contribute to the net charge but it does contribution to charge multiplicity by 2/3 as assumed in [20,21].If the simulation is ended up at the stage of partonic scattering and both the partons and beam remnants (hadrons) are counted in net charge transfer fluctuation the corresponding results are then symboled as "QGM w/ remnant".It should be mentioned here that the spectator nucleons do not affect the net charge transfer fluctuation in |η| <1.A calculation where the string fragmentation in PYTHIA is switched-on and followed directly by the hadronic rescattering is referred to as "HM", since in this simulation only hadronic transport is taken into account, like in HIJING, RQMD, UrQMD, and JPCIAE [22].
One sees in this figure that the κ of "HM w/ QGM" reproduces nicely the STAR datum and the κ of "HM" is a bit larger than the STAR datum at η=1.The trend of κ varying with η, both in "HM" and "HM w/ QGM", is similar to the ones in HIJING, RQMD, UrQMD (cf.Fig. 5 in [2]).On the contrary, the κ of "QGM" keeps nearly constant, like the charge fluctuation as function of rapidity interval in QGM in thermal model [4] and in transport model [21].It is interesting to see that the κ in "HM" is larger than κ in "QGM" by a factor of 3 to 5 from upper η to the lower η.The discrepancy between κ in "HM" and in "HM w/ QGM " amounts ∼ 20% in the average, that means that the probability of net charge transfer fluctuation in QGM surviving hadronization can be estimated to be ∼ 20% either.In Fig. 2 the centrality dependence of κ(η) is given both for "HM" and "QGM" (solid and open symbols, respectively) for 0-5, 30-40, and 70-80% central Au + Au collisions at √ s N N =200 GeV.Both of the κ(η) in "HM" and in "QGM" do not strongly depend on the centrality which is consistent with the results in hadronic transport models HIJING, RQMD, and UrQMD (cf.Fig. 5 in [2]).
We compare the κ(η) in "QGM" to the one in "QGM w/ remnant" in Fig. 3 for 0-5% most central Au+Au collisions at √ s N N =200 GeV.One sees in this figure that the influence of beam remnants upon the κ(η) in "QGM" amounts ∼35% in average.This influence does not change the status of big difference between κ in "HM" and in "QGM" shown in Fig. 1.In summary, a parton and hadron cascade model, PACIAE, is employed investigating the net charge transfer fluctuation within |η|=1 both in partonic initial state and in hadronic final state for a range centralities of Au + Au collisions at √ s N N =200 GeV.In the hadronic final state (κ in "HM") the observable of net charge transfer fluctuation, κ, turns out to be nearly a factor of 3 to 5 larger than the κ in partonic initial state (κ in "QGM").However, the κ in "QGM" is hard to survive the hadronization, the survival probability amounts ∼ twenty percent.
Finally, the financial support from NSFC (10475032) in China are acknowledged.
FIG.2: κ as a function of η within |η| < 1 in a range centralities of the Au + Au collisions at √ s N N =200 GeV.