Global Properties in High Energy CollisionsView this Special Issue
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 GeV and over a centrality range from 10–15% to 70–80% in Pb-Pb 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 Pb-Pb collisions at TeV.
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 . 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) . 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, proton-nucleus, and nucleus-nucleus collisions. Some theoretical investigations [5–10] 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 intervals in 20–40% and 50–80%, which are measured in Au-Au collisions at GeV . 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 TeV .
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 high-energy 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 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 , 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 . 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 single-peak structure.
Figure 3 shows the azimuthal correlations of the per-trigger-particle associated hadrons produced in Pb-Pb collisions at TeV. The symbols indicate the data measured by the CMS collaboration at the LHC , 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 in Figures 4 and 5. The symbols indicate the data  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.
In a multisource thermal model, we investigate the dihadron azimuthal correlations for 20–40% and 50–80% in Au-Au 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 Pb-Pb 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 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 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 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.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
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).
L. Adamczyk, J. K. Adkins, G. Agakishiev et al., “Energy dependence of moments of net-proton 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 cross-section 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 , and production in Pb-Pb collisions at 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 production in collisions at 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 high-energy proton-nucleus collisions,” Physical Review C, vol. 88, Article ID 014903, 2013.View at: Google Scholar
K. Werner, I. Karpenko, and T. Pierog, “‘Ridge’ in proton-proton 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 GeV and at 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 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 high-energy 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 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, “Two-component model of 2D trigger-associated hadron correlations on rapidity space derived from 1D spectra for p–p collisions at 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 two-particle rapidity correlations in A + A collisions from high energy QCD evolution,” Nuclear Physics A, vol. 836, no. 1-2, 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 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 centrality-dependent direct photon pt spectra in collisions at 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., “System-size dependence of transverse momentum correlations at 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