Research Article  Open Access
Dihadron Azimuthal Correlations in 200 GeV AuAu and 2.76 TeV PbPb Collisions
Abstract
In a multisource thermal model, we detailedly show dihadron azimuthal correlations for 20–40% and 50–80% in AuAu collisions at GeV and over a centrality range from 10–15% to 70–80% in PbPb collisions at TeV. The model can approximately describe the azimuthal correlations of particles produced in the collisions. The amplitude of the corresponding source is magnified, and the source translates along the direction. The factor , in most cases, increases with the increase of the centrality in PbPb collisions at TeV.
1. 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 heavyion 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 quarkgluon plasma (QGP), which will undergo the hadronization and freezeout 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 heavyion collisions at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) [4]. But the evolution of the heavyion 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 protonproton, protonnucleus, and nucleusnucleus collisions. Some theoretical investigations [5–10] give many valuable and interesting results to explain the ridge phenomena, which were regarded as a contribution from jetmedium 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 intervals in 20–40% and 50–80%, which are measured in AuAu collisions at 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 PbPb collisions at TeV [12].
2. Dihadron Azimuthal Correlation in the Model and Experiments
As a presupposition in the multisource thermal model [13–15], 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 AuAu collisions at GeV. The ranges are 0.2–0.8 GeV, 0.8–1.4 GeV, and 1.4–2.0 GeV, 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 intervals [20]. For the same 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 singlepeak structure.

(a)
(b)
(c)
(a)
(b)
(c)
Figure 3 shows the azimuthal correlations of the pertriggerparticle associated hadrons produced in PbPb collisions at 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 singlepeak shape in the figure for the four centrality bins.
(a)
(b)
(c)
(d)
Similar to Figure 3, we present the correlations as a function of 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 singlehump phenomenon.
(a)
(b)
(c)
(d)
(a)
(b)
3. Conclusion
In a multisource thermal model, we investigate the dihadron azimuthal correlations for 20–40% and 50–80% in AuAu collisions at GeV in the associated transverse momentum intervals, 0.2–0.8, 0.8–1.4, and 1.4–2.0 GeV. As a comparison, we also investigate the azimuthal correlations of particles produced in PbPb collisions at 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 AuAu collisions at 200 GeV and in PbPb 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 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 PbPb collisions at TeV. Moreover, a singlepeak 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 highenergy 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.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This work is supported by the National Natural Science Foundation of China under Grant nos. 11247250 and 11005071, and the National Fundamental Fund of Personnel Training (no. J1103210).
References
 L. Adamczyk, J. K. Adkins, G. Agakishiev et al., “Energy dependence of moments of netproton multiplicity distributions at RHIC,” Physical Review Letters, vol. 112, Article ID 032302, 2014. View at: Publisher Site  Google Scholar
 G. Antchev, P. Aspell, I. Atanassov, and et al, “Double diffractive crosssection measurement in the forward region at the LHC,” Physical Review Letters, vol. 111, Article ID 262001, 2013. View at: Publisher Site  Google Scholar
 B. Abelev, J. Adam, D. Adamová (ALICE Collaboration) et al., “Centrality dependence of $\mathit{\pi},\mathit{K}$, and $\mathit{p}$ production in PbPb collisions at $\sqrt{{S}_{NN}}=2.76$ TeV,” Physical Review C, vol. 88, Article ID 044910, 2013. View at: Publisher Site  Google Scholar
 A. Adare, S. Afanasiev, C. Aidala et al., “Cross section and double helicity asymmetry for η mesons and their comparison to ${\pi}^{0}$ production in $p+p$ collisions at $\sqrt{s}=200$ GeV,” Physical Review D, vol. 83, p. 032001, 2011. View at: Publisher Site  Google Scholar
 N. Armesto, C. A. Salgado, and U. A. Wiedemann, “Measuring the collective flow with jets,” Physical Review Letters, vol. 93, no. 24, Article ID 242301, 2004. View at: Publisher Site  Google Scholar
 P. Bożek and W. Broniowski, “Collective dynamics in highenergy protonnucleus collisions,” Physical Review C, vol. 88, Article ID 014903, 2013. View at: Google Scholar
 K. Werner, I. Karpenko, and T. Pierog, “‘Ridge’ in protonproton scattering at 7 TeV,” Physical Review Letters, vol. 106, Article ID 122004, 2011. View at: Publisher Site  Google Scholar
 M. Petran and J. Rafelski, “Universal hadronization condition in heavy ion collisions at $\sqrt{{s}_{NN}}=62$ GeV and at $\sqrt{{s}_{NN}}=2.76$ TeV,” Physical Review C, vol. 88, Article ID 021901(R), 2013. View at: Publisher Site  Google Scholar
 B.C. Li, Y.Y. Fu, L.L. Wang, and F.H. Liu, “Dependence of elliptic flows on transverse momentum and number of participants in Au+Au collisions at $\sqrt{{S}_{NN}}=200$ GeV,” Journal of Physics G: Nuclear and Particle PhysicsEmail alert RSS feed, vol. 40, no. 2, Article ID 025104, 2013. View at: Publisher Site  Google Scholar
 F.H. Liu, T. Tian, H. Zhao, and B.C. Li, “Extracting chemical potentials of quarks from ratios of negatively/positively charged particles in highenergy collisions,” The European Physical Journal A, vol. 50, p. 62, 2014. View at: Publisher Site  Google Scholar
 Y. H. Zhu, Y. G. Ma, J. H. Chen, G. L. Ma, S. Zhang, and C. Zhong, “Nonflow contribution to dihadron azimuthal correlations in 200 GeV/c Au + Au collisions,” http://arxiv.org/abs/1212.0192. View at: Google Scholar
 S. Chatrchyan, V. Khachatryan, A. M. Sirunyan et al., “Centrality dependence of dihadron correlations and azimuthal anisotropy harmonics in PbPb collisions at $\sqrt{{s}_{NN}}=2.76$ TeV,” The European Physical Journal C, vol. 72, article 2012, 2012. View at: Publisher Site  Google Scholar
 F.H. Liu, T. Tian, J.X. Sun, and B.C. Li, “What can we learn from (Pseudo) rapidity distribution in high energy collisions?” Advances in High Energy Physics, vol. 2014, Article ID 863863, 10 pages, 2014. View at: Publisher Site  Google Scholar
 B.C. Li, Y.Z. Wang, and E.Q. Wang, “Meson production in high energy p+p collisions at the RHIC energies,” Advances in High Energy Physics, vol. 2013, Article ID 486476, 7 pages, 2013. View at: Publisher Site  Google Scholar
 T. A. Trainor and D. J. Prindle, “Twocomponent model of 2D triggerassociated hadron correlations on rapidity space ${y}_{ta}\times {y}_{tt}$ derived from 1D ${p}_{t}$ spectra for p–p collisions at $\sqrt{s}=200$ GeV,” Physical Review D, vol. 88, Article ID 094018, 2013. View at: Publisher Site  Google Scholar
 K. Dusling, F. Gelis, T. Lappi, and R. Venugopalan, “Long range twoparticle rapidity correlations in A + A collisions from high energy QCD evolution,” Nuclear Physics A, vol. 836, no. 12, pp. 159–182, 2010. View at: Publisher Site  Google Scholar
 A. Adare, S. Afanasiev, C. Aidala et al., “Spectra and ratios of identified particles in Au+Au and d+Au collisions at $\sqrt{{s}_{NN}}=200$ GeV,” Physical Review C, vol. 88, Article ID 024906, 2013. View at: Publisher Site  Google Scholar
 B. G. Zakharov, “Nuclear suppression of light hadrons and single electrons at the RHIC and LHC,” Journal of Physics G, vol. 40, Article ID 085003, 2013. View at: Publisher Site  Google Scholar
 F.M. Liu, “A theoretical review of centralitydependent direct photon pt spectra in $\text{Au+Au}$ collisions at $\sqrt{SNN}=200$ GeV,” Nuclear Physics A, vol. 855, no. 1, pp. 355–358, 2011. View at: Publisher Site  Google Scholar
 L. Adamczyk, J. K. Adkins, G. Agakishiev et al., “Systemsize dependence of transverse momentum correlations at $\sqrt{{s}_{NN}}=62.4$ and 200 GeV at the BNL Relativistic Heavy Ion Collider,” Physical Review C, vol. 87, Article ID 064902, 2013. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2014 G. X. Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.