Correlation Functions And Cumulants Of Proton, Anti-proton Multiplicity Distributions In Au+Au Collisions At RHIC Energies From AMPT Model

Quantum Chromodynamic predict that the quarks confined in hadrons will be deconfined at high enough energies, and formed quark gluon plasma. At low tem-perature and large baryon chemical potential region, the process from the hadronic matter to quark gluon plasma is called first phase transition. The end point of the first order phase transition line is the critical point of QCD. One of the main goals of the high energy nuclear collisions is to explore the phase structure of the strong-ly interacting hot and dense nuclear matter. The correlation length(?) diverges at the critical point. Theoretical result from the Hadron Resonance Gas (HRG) model and the first principle Lattice QCD shows the high-order susceptibility (cumulants) of conserved charges are related to the correlation length, they may have non-monotonic behavior and sign changes.Recent theoretical study shows the cumulant is related to the correlation func-tions, and is believed the cumulant mix correlations with different order, and it's argued that the correlation functions could provide a cleaner information on possible non-trivial dynamics in heavy-ion collisions. Based on the proton correlation study,it's found that the STAR data at (?)=7.7GeV contain significant positive four-particle correlation and at (?)=19.6GeV the fourth cumulant is dominated by a negative two-particle correlation. However, the anti-proton yield is increase with the energy increasing, the contribution of anti-proton can not be ignored as the energy increases.In order to understand the contribution of anti-proton in correlation functions,we calculate the net-proton correlation functions and mix correlation functions with the contribution of anti-proton is taken into consider. It's first time the contribu-tion of anti-proton is taken into account in calculating the correlation functions. In central collision, two-particle correlation is clearly the dominant contribution at low energies(< 39GeV), the contribution of three-particle correlation and four-particle correlation should be considered at high energies. the result of correlation functions proton and net-proton result indicated the anti-proton should be taken into account,especially at high-order correlation function. the contribution of anti-proton should be take into consider as the increased energies, especially at peripheral central. Mix correlation functions result shows the proton correlation is the dominant contribu-tion for n-order correlation at low energies, anti-proton and mix-correlation play a comparable role in high energies.Finally, we compared the results of from model with those in RHIC/STAR ex-perimental. The comparison between model and STAR experiment result indicate the non-monotonic energy dependence for the net-proton ??2 at the most central Au+Au collisions measured by the STAR experiment cannot be described by the AMPT model. The model results provide us baselines and qualitative estimates about the non-critical background contributions to the fluctuations observables in heavy-ion collisions...