Dihadron Azimuthal Correlations in 200 GeV Au-Au and 2 . 76 TeV Pb-Pb Collisions

In a multisource thermal model, we detailedly show dihadron azimuthal correlations for 20–40% and 50–80% in Au-Au collisions at √sNN = 200GeV and over a centrality range from 10–15% to 70–80% in Pb-Pb collisions at √sNN = 2.76TeV. The model can approximately describe the azimuthal correlations of particles produced in the collisions. The p x amplitude of the corresponding source is magnified, and the source translates along the direction. The factor α x , in most cases, increases with the increase of the centrality in Pb-Pb collisions at√sNN = 2.76TeV.


Introduction
An important subject of high energy physics is to discuss the strongly interacting matter and nuclear matter at high temperature and high density by heavy-ion collisions at ultrarelativistic energies [1,2].In the initial stage of the collision, tremendous amounts of energy are accumulated at a finite zone in a short time.Then, they result in the creation of a nearly perfect quark-gluon plasma (QGP), which will undergo the hadronization and freeze-out and will finally produce lots of observed particles [3].As we know, a description of strong nuclear interactions is quantum chromodynamics (QCD).Studying QCD phase transition and properties of quark matter is a main target of heavy-ion collisions at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) [4].But the evolution of the heavy-ion collisions and the production of hadrons are very complicated for us.In general, we can extract the evolution information of the colliding system by analyzing the properties of observable quantities, which contain multiplicity, transverse momentum, polar and elliptic flow, and angular correlation, and so on.
In recent years, a dihadron correlation has been one of the hot topics in particle and nuclear physics.Experimentally, RHIC and LHC have observed or will observe the dihadron azimuthal correlations in proton-proton, protonnucleus, and nucleus-nucleus collisions.Some theoretical investigations [5][6][7][8][9][10] give many valuable and interesting results to explain the ridge phenomena, which were regarded as a contribution from jet-medium interactions.In these works, various models have been proposed.In this paper, we would like to apply a multisource thermal model to discuss azimuthal correlations of dihadron for different associated transverse momentum  assoc  intervals in 20-40% and 50-80%, which are measured in Au-Au collisions at √ NN = 200 GeV [11].For a comparison, we will also use the model to discuss the azimuthal correlations of the dihadron for a wide centrality range in Pb-Pb collisions at √ NN = 2.76 TeV [12].

Dihadron Azimuthal Correlation in the Model and Experiments
As a presupposition in the multisource thermal model [13][14][15], the observed particles are projected isotropically from different or the same coordinates in a system of highenergy collision.The emission coordinates compose a space of emission sources, which are at a local equilibrium state.For the particle pairs, the normal distribution is taken to calculate their spectra [16,17].The two particles may be considered to be from two emission coordinates in one source or two sources.Due to the interaction between the emissions, in momentum space (   ,    ,    ), the particle distribution is given by where   and   denote the amplitude change of the momentum and   and   denote the translational amplitude.By the Monte Carlo method, the particle momentum is where  is the standard deviation.We obtain the formulation of the dihadron correlation, Figures 1 and 2 show dihadron azimuthal correlations for 20-40% and 50-80% in Au-Au collisions at √ NN = 200 GeV.The  assoc  ranges are 0.2-0.8GeV, 0.8-1.4GeV, and 1.4-2.0GeV, respectively.The symbols indicate the experimental data observed in the RHIC [11], and the lines indicate the modeling results.Table 1 shows   and   extracted by fitting the data.The   amplitude of the source increases, and the source translates along a negative direction of the   [6,18,19].For the same centrality, the values of   and |  | increase with the increase of  assoc  intervals [20].For the same  assoc  interval, the values of   for 50-80% are greater than those in 20-40%.It is found that the central 20-40% and 50-80% events both have a single-peak structure.
Figure 3 shows the azimuthal correlations of the pertrigger-particle associated hadrons produced in Pb-Pb collisions at √ NN = 2.76 TeV.The symbols indicate the data measured by the CMS collaboration at the LHC [12], and the lines indicate the modeling results.The rapidity  interval   is 2-4 for trigger particles with   in 3-3.5 GeV and for associated particles with   in 1-1.5 GeV for centralities 10-15%, 15-20%, 20-25%, and 25-30%.The modeling results are in agreement with the data for the four centrality intervals.The values of   and   are listed in Table 1.The   amplitude of the source increases, and the source translates along the negative direction of the   for 10-15%.For the other three centralities, the source translates along the positive direction of the   .In addition, there is a single-peak shape in the figure for the four centrality bins.
Similar to Figure 3, we present the correlations as a function of Δ in Figures 4 and 5.The symbols indicate the data [12] for 30-35%, 35-40%, 40-50%, 50-60%, 60-70%, and 70-80%.The values of   and   are also given in Table 1.The   amplitude of the source is also magnified, and the source translates along the positive   direction for 30-35%, 35-40%, and 40-50% and along the negative   direction for the other centralities.With the increase of the centrality, the value of   increases over a range from 30-35% to 40-50% and decreases from 50-60% to 70-80%.In Figures 3 and 4, there is the single-hump phenomenon.

Conclusion
In a multisource thermal model, we investigate the dihadron azimuthal correlations for 20-40% and 50-80% in Au-Au collisions at √ NN = 200 GeV in the associated transverse momentum  assoc  intervals, 0.2-0.8,0.8-1.4,and 1.4-2.0GeV.As a comparison, we also investigate the azimuthal correlations of particles produced in Pb-Pb collisions at √ NN = 2.76 TeV for trigger particles with   in 3-3.5 GeV and for associated particles with   in 1-1.5 GeV.By comparing the model results with the experimental data, we find that the model can approximately describe the dihadron azimuthal correlations of hadrons produced in Au-Au collisions at 200 GeV and in Pb-Pb collisions at 2.76 TeV.In the calculation, the parameter   is used to characterize the expansion extent of the source in the   direction and the parameter Figure 4: The same as Figure 3, but for 30-35%, 35-40%, 40-50%, and 50-60%.
is used to characterize the source movement along the positive or negative   direction for the different centralities.
The   amplitude of the source is magnified, and the source translates along the   direction.In most cases, the value of   increases with the increase of the centrality in Pb-Pb collisions at √ NN = 2.76 TeV.Moreover, a single-peak structure has been seen in all the figures.For a dihedron, the "trigger" and "associated" particles at final state are projected from the two coordinates in single or two sources formed in the collisions.The interaction between the two emission coordinates leads to the dihadron azimuthal correlation.In the high-energy collisions, the model has successfully described a variety of observables spectra at final state [9,10,13,14], which reveal a multisource phenomenon in the colliding process.Further discussions on the dihadron azimuthal correlations of other different colliding systems using the model will be of interest.

2 AdvancesFigure 1 :
Figure 1: Dihadron azimuthal correlations for 20-40% in Au-Au collisions at √ NN = 200 GeV.The symbols denote the data of the RHIC [11], and the lines are the modeling results.