Research Article  Open Access
Ting Bai, YuanYuan Guo, BaoChun Li, "Dihadron Azimuthal Correlations in pp Collisions at TeV and pPb Collisions at TeV", Advances in High Energy Physics, vol. 2015, Article ID 190714, 9 pages, 2015. https://doi.org/10.1155/2015/190714
Dihadron Azimuthal Correlations in pp Collisions at TeV and pPb Collisions at TeV
Abstract
The dihadron azimuthal correlations in pp collisions at TeV and pPb collisions at TeV are investigated in the framework of a multisource thermal model. The model can approximately describe the experimental results measured in the Large Hadron Collider. We find the amplitude of the source is magnified and the source translates along the direction.
1. Introduction
The theory of Quantum Chromodynamics (QCD) predicts that a nearly perfect quarkgluon plasma (QGP) is formed in the initial stage of highenergy nuclear collisions. The colordeconfined and thermalized state of strongly coupled quarks and gluons exists for only a short time [1, 2]. Effort to investigate the properties of the QGP is an essential subject of high energy physics. We cannot observe the matter directly in the existing laboratory conditions because it is only created for the briefest of instants. However, we can extract potential information about the QGP by measuring and analyzing the properties of finalstate particles produced after thermal freezeout in high energy collisions.
For these years, dihadron correlations in and have been observed in nucleusnucleus collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [3–10]. Surprisingly, a ridge structure of hadron correlations was also observed in protonproton and protonnucleus collisions. It greatly motivated physicists to further study those small collision systems, which are used as baseline measurements for nucleusnucleus collisions [11]. A variety of physical models have been proposed to explain the peak structure and discuss the dynamics origin of jet characteristics. These mechanisms include gluon saturation [12], multiparton interactions [13], and collective expansion of the final state [14]. The fact that the dihadron correlation distribution is different from the one expected in normal nucleonnucleon collisions may be considered as a consequence of QGP formation [15]. Therefore, the measurement of dihadron correlations opens a new window into the study of the QGP. In this paper, we would like to use a multisource thermal model to investigate the dihadron azimuthal correlations in pp collisions at TeV and pPb collisions at TeV, measured recently by the ALICE Collaboration and the CMS Collaboration at the LHC [16–20]. Significance of the work is to verify whether the model can describe the azimuthal correlations of the dihadron for different colliding systems and different particle correlations.
The paper is organized as follows: in Section 2, the multisource thermal model is introduced; in Section 3, we compare the modeling results with the experimental data; at the end, we provide a summary in Section 4.
2. Dihadron Azimuthal Correlation in the Model
According to the multisource thermal model [21–25], identified particles are emitted isotropically from different emission sources formed in the reaction process. Many emission points compose a space of emission sources, which are at local equilibrium states.
The oz axis is defined as the beam direction and the yoz plane is defined as the reaction plane. The schematic sketch is given in Figure 1. Many thermal sources of finalstate particles are assumed to be formed in high energy collisions. In the rest frame of the source, the particles are emitted isotropically. Due to the interactions between the emissions, the sources will expand and translate. For a dihadron observed in final state, the two particles may be considered to be from two emission coordinates in one source or two sources. In the laboratory reference frame, in momentum space , , and , the particle distributions are given by where and indicate the amplitude change of the momenta and , respectively; and indicate the translational amplitude along and , respectively. In the Monte Carlo calculation, the particle momenta arewhere , and are random numbers in (0, 1) and is the standard deviation. The formulation of the azimuthal angle can be written asIn the calculation, and are regarded as free parameters; the other parameters are taken to be the defaults.
3. Comparison and Discussion
Figure 2(a) presents dihadron azimuthal correlations in rapidity interval for in pp collisions at TeV [16]. and ranges are GeV/c and GeV/c, respectively. The symbols in Figure 2(aA) denote the experimental data of the ALICE Collaboration at the LHC [16], and the symbols in Figures 2(aB), 2(aC), 2(aD), and 2(aE) correspond to results calculated by the Monte Carlo generators PHOJET [26], PYTHIA6 Perugia2011 [27], PYTHIA8 4C [28], and PYTHIA6 Perugia0 [27], respectively. The lines in the figure are our results calculated by the multisource thermal model. The values of parameters and with the per degree of freedom () are shown in Table 1. The amplitude of the source is magnified, and the source translates along the positive direction. The peak at is visible in the figure.

Figure 3 shows dependence of the associated yield per trigger particle for correlations for GeV/c for the centrality (0–20%)–(60–100%) in pPb collisions at TeV. The range is averaged over on the near side and on the away side. The symbols denote the data of the ALICE Collaboration at the LHC [17], and the solid line is the modeling result. It is seen that the model can approximately describe the experimental data. The values of parameters and extracted from the fits with the are shown in Table 1. The amplitude of the source is magnified, and the source translates along a negative direction of . In the figure, there is a doubleridge structure.
Figure 4 presents the baselinesubtracted D mesoncharged hadron correlations as a function of for in pp collisions at TeV (a, b) and pPb collisions at TeV (c, d), for D mesons with GeV/c and associated hadrons with GeV/c (a, c), and for GeV/c and GeV/c (b, d). The symbols denote the data of the ALICE Collaboration [18], and the lines are the modeling results. The modeling results are in approximate agreement with the experimental data. The values of , , and are listed in Table 1. The amplitude of the source is magnified, and the source translates along the positive direction. In both pp and pPb collisions, the values of and for GeV/c and GeV/c are smaller than those for GeV/c and GeV/c. For both collision systems, a doublepeak shape can be observed in the figure.
(a)
(b)
(c)
(d)
Figure 5 shows dihadron azimuthal correlations for the shortrange region () minus longrange region () in pPb collisions at TeV in the multiplicity ranges (a, c, e) and (b, d, f). Both and intervals are 1–3 GeV. (a, b), (c, d), and (e, f) of Figure 5 correspond to , , and correlations, respectively. The symbols denote the data of the CMS Collaboration at the LHC [19], and the lines denote the modeling results. The values of , , and are given in Table 1. The results are in good agreement with the experimental data. The amplitude of the source is magnified, and the source translates along the positive direction. For the three species of particle correlations, the values of in the multiplicity range are greater than those in . From the figure, it is found that the magnitude of the peak is larger for correlations than for correlations.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 7 presents the baselinesubtracted twoparticle correlations as a function of for and correlations in pp collisions at TeV. The trigger particle is with in 6–12 GeV/c. (a) and (b) of the figure correspond to associated particles and with in 1–6 GeV/c, respectively. The symbols denote the experimental data of the ALICE Collaboration at the LHC [20], and the lines are the modeling results. 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. The values of and for are greater than those for . The peak at is visible in the figure.
(a)
(b)
4. Discussions and Summary
The dihadron azimuthal correlations of different particles for different and intervals in pp collisions at TeV and pPb collisions at TeV have been investigated in the framework of the multisource thermal model. From the above discussions, it is seen that the model can approximately describe the experimental data of LHC. In the model, the parameters and indicate the deformation and displacement of the source along the direction, respectively. In the calculation, different and are taken to fit the experimental data. The results show that the amplitude of the source is magnified and the source translates along the positive direction. In addition, there is a peak structure in all the figures. In momentum space, the thermalsource changes in the and directions can be described by and or and , respectively. The parameters , , and present the source expansion, the source isotropy, and the source compression in the direction, respectively. The parameters and present the source translation along the positive direction and the negative direction, respectively.
In the multisource thermal model, a particle pair at final state is assumed to be emitted from the two points in a single source or two sources formed in the reaction process. One point projects the “trigger” particle and the other point projects the “associated” particle. There are interactions between the two emission points, which lead to the twoparticle azimuthal correlation. The model can be used to describe the dihadron azimuthal correlation. The modeling results reveal a multisource production phenomenon in the colliding process. In fact, the model has also been employed to describe the (pseudo)rapidity, elliptic flow, and multiplicity distributions of the finalstate particles [29, 30]. The analysis of dihadron azimuthal correlations in the high energy collisions is expected to provide important input for the underlying mechanism of the particle production. It is of great significance to discuss the dihadron azimuthal correlations of different types of colliding systems and different types of particle pair.
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 Grants nos. 11247250 and 10975095, the National Fundamental Fund of Personnel Training under Grant no. J1103210, and the Shanxi Provincial Natural Science Foundation under Grant no. 2013021006.
References
 J. Adams, C. Adler, M. M. Aggarwal et al., “Azimuthal anisotropy at the relativistic heavy ion collider: the first and fourth harmonics,” Physical Review Letters, vol. 92, no. 6, Article ID 062301, 6 pages, 2004. View at: Publisher Site  Google Scholar
 E. T. Tomboulis and A. Velytsky, “Deconfinement transition dynamics and early thermalization in quarkgluon plasma,” Physical Review D, vol. 72, no. 7, Article ID 074509, 2005. View at: Publisher Site  Google Scholar
 A. Adare, S. Afanasiev, C. Aidala et al., “Dihadron azimuthal correlations in Au+Au collisions at $\sqrt{{s}_{\text{N}\text{N}}}=200$ GeV,” Physical Review C, vol. 78, Article ID 014901, 2008. View at: Publisher Site  Google Scholar
 T. Renk and K. J. Eskola, “Expectations for dihadron correlation measurements extrapolated to 5.5A TeV,” Physical Review C, vol. 77, Article ID 044905, 2008. View at: Publisher Site  Google Scholar
 A. Adare, S. Afanasiev, C. Aidala et al., “Transverse momentum and centrality dependence of dihadron correlations in $\text{Au+Au}$ collisions at $\sqrt{{s}_{\text{N}\text{N}}}=200$ GeV: jet quenching and the response of partonic matter,” Physical Review C, vol. 77, Article ID 011901, 2008. View at: Publisher Site  Google Scholar
 B. I. Abelev, M. M. Aggarwal, Z. Ahammed et al., “Long range rapidity correlations and jet production in high energy nuclear collisions,” Physical Review C, vol. 80, Article ID 064912, 2009. View at: Publisher Site  Google Scholar
 S. Chatrchyan, A. Hektor, M. Kadastik et al., “Longrange and shortrange dihadron angular correlations in central PbPb collisions at root $\sqrt{{s}_{\text{N}\text{N}}}=2.76$ Tev,” Journal of High Energy Physics, vol. 2011, no. 7, article 76, 2011. View at: Publisher Site  Google Scholar
 T. Renk and K. J. Eskola, “Hard dihadron correlations in heavyion collisions at RHIC and LHC,” Physical Review C, vol. 84, Article ID 054913, 2011. View at: Google Scholar
 G. Agakishiev, M. M. Aggarwal, Z. Ahammed et al., “System size and energy dependence of nearside dihadron correlations,” Physical Review C, vol. 85, no. 1, Article ID 014903, 16 pages, 2012. View at: Publisher Site  Google Scholar
 S. Chatrchyan, V. Khachatryan,, A. M. Sirunyan et al., “Studies of azimuthal dihadron correlations in ultracentral PbPb collisions at $\sqrt{{s}_{NN}}=2.76$ TeV,” Journal of High Energy Physics, vol. 2014, no. 2, article 088, 2014 (Arabic). View at: Publisher Site  Google Scholar
 F. Q. Wang, X. N. Wang, J. Harris et al., “Dihadron correlations in d+Au collisions from STAR,” Nuclear Physics A, vol. 926, pp. 250–257, 2014. View at: Publisher Site  Google Scholar
 K. Dusling and R. Venugopalan, “Evidence for BFKL and saturation dynamics from dihadron spectra at the LHC,” Physical Review D, vol. 87, no. 5, Article ID 051502, 7 pages, 2013. View at: Publisher Site  Google Scholar
 M. G. Ryskin, A. D. Martin, and V. A. Khoze, “Probes of multiparticle production at the LHC,” Journal of Physics G: Nuclear and Particle Physics, vol. 38, no. 8, Article ID 085006, 2011. View at: Publisher Site  Google Scholar
 E. Avsar, C. Flensburg, Y. Hatta, J.Y. Ollitrault, and T. Ueda, “Eccentricity and elliptic flow in protonproton collisions from parton evolution,” Physics Letters, Section B: Nuclear, Elementary Particle and HighEnergy Physics, vol. 702, no. 5, pp. 394–397, 2011. 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
 B. Abelev, J. Adam, D. Adamová et al., “Multiplicity dependence of twoparticle azimuthal correlations in pp collisions at the LHC,” Journal of High Energy Physics, vol. 2013, no. 9, article 049, 2013. View at: Publisher Site  Google Scholar
 L. Milano, “Longrange angular correlations at the LHC with ALICE,” Nuclear Physics A, vol. 931, pp. 1017–1021, 2014. View at: Publisher Site  Google Scholar
 F. Colamaria, “Measurement of azimuthal correlations between D mesons and charged hadrons with ALICE at the LHC,” EPJ Web of Conferences, vol. 80, Article ID 00034, 6 pages, 2014. View at: Publisher Site  Google Scholar
 V. Khachatryan, A. Apresyan, A. Bornheim et al., “Longrange twoparticle correlations of strange hadrons with charged particles in pPb and PbPb collisions at LHC energies,” Physics Letters B, vol. 742, pp. 200–224, 2015. View at: Publisher Site  Google Scholar
 S. Jayarathna, “Strangeness production in twoparticle azimuthal correlations on the near and away side measured with ALICE in pp collisions at 7 TeV,” http://arxiv.org/abs/1409.3498. View at: Google Scholar
 B. C. Li, Y. Y. Fu, L. L. Wang, E. Q. Wang, and F. H. Liu, “Transverse momentum distributions of strange hadrons produced in nucleusnucleus collisions at $\sqrt{{s}_{\text{N}\text{N}}}=62.4$ and 200 GeV,” Journal of Physics G, vol. 39, Article ID 025009, 2012. View at: Publisher Site  Google Scholar
 B.C. Li, Y.Z. Wang, and F.H. Liu, “Formulation of transverse mass distributions in AuAu collisions at $\sqrt{{s}_{\text{N}\text{N}}}=200$ GeV/nucleon,” Physics Letters B, vol. 725, no. 45, pp. 352–356, 2013. View at: Publisher Site  Google Scholar
 Y.Q. Gao, T. Tian, S. Fakhraddin, M. A. Rahim, and F.H. Liu, “Doubledifferential production cross sections of charged pions in charged pion induced nuclear reactions at high momentums,” Advances in High Energy Physics, vol. 2014, Article ID 892582, 20 pages, 2014. View at: Publisher Site  Google Scholar
 F.H. Liu, “Unified description of multiplicity distributions of finalstate particles produced in collisions at high energies,” Nuclear Physics A, vol. 810, no. 1–4, pp. 159–172, 2008. View at: Publisher Site  Google Scholar
 F.H. Liu, X.Y. Yin, J.L. Tian, and N. N. Abd Allah, “Chargedparticle (pseudo)rapidity distributions in e^{+}e^{−}, $P\stackrel{}{P}$, and AA collisions at high energies,” Physical Review C, vol. 69, no. 3, Article ID 034905, 2004. View at: Publisher Site  Google Scholar
 R. Engel, J. Ranft, and S. Roesler, “Hard diffraction in hadronhadron interactions and in photoproduction,” Physical Review D, vol. 52, no. 3, pp. 1459–1468, 1995. View at: Publisher Site  Google Scholar
 P. Z. Skands, “Tuning Monte Carlo generators: the Perugia tunes,” Physical Review D, vol. 82, no. 7, Article ID 074018, 25 pages, 2010. View at: Publisher Site  Google Scholar
 T. Sjöstrand, S. Mrenna, and P. Z. Skands, “A brief introduction to PYTHIA 8.1,” Computer Physics Communications, vol. 178, no. 11, pp. 852–867, 2008. View at: Publisher Site  Google Scholar
 B.C. Li, Y.Z. Wang, F.H. Liu, X.J. Wen, and Y.E. Dong, “Particle production in relativistic $pp(\stackrel{}{p})$ and $AA$ collisions at RHIC and LHC energies with Tsallis statistics using the twocylindrical multisource thermal model,” Physical Review D, vol. 89, Article ID 054014, 2014. 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, vol. 40, no. 2, Article ID 025104, 2013. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2015 Ting Bai 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}.