On Correlation Functions of Two Particles at RHIC and LHC Energies

The multi-source thermal model is used in this paper to analyze the long-range azimuth correlation in deutron-gold (d+Au) collisions at center-of-mass energy per nucleon pair √sNN=200 GeV measured by the PHENIX Collaboration at the relativistic heavy ion collider (RHIC), and the short-range pseudorapidity correlation in high multiplicity event in proton-proton (p+p) collisions at center-of-mass energy √s=0.9, 2.36, 7 TeV measured by the CMS Collaboration at the large hadron collider (LHC). The modeling results are in approximately agreement with the experimental data in error ranges. Four parameters are used in the analysis of long-range azimuth correlation, which show that the parameters describe the change trend of ridge structure. The ridge structure is related to the collective effect, hydrodynamic flow effect, transverse momentum and signal of particle pair, and so forth. Three parameters are used in the analysis of the short-range pseudorapidity correlation in high multiplicity event in small system, which show that the parameters σ and c₃ are related to collision energy. Large collision energy results in strong correlation due to close distance between particles.