#### Abstract

The dihadron azimuthal correlations in *p*-*p* collisions at TeV and *p*-Pb 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 quark-gluon plasma (QGP) is formed in the initial stage of high-energy nuclear collisions. The color-deconfined 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 final-state particles produced after thermal freeze-out in high energy collisions.

For these years, dihadron correlations in and have been observed in nucleus-nucleus 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 proton-proton and proton-nucleus collisions. It greatly motivated physicists to further study those small collision systems, which are used as baseline measurements for nucleus-nucleus 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 nucleon-nucleon 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* p*-*p* collisions at TeV and* p*-Pb 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 final-state 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* p*-*p* collisions at TeV [16]. and ranges are GeV/*c* and GeV/*c*, respectively. The symbols in Figure 2(a-A) denote the experimental data of the ALICE Collaboration at the LHC [16], and the symbols in Figures 2(a-B), 2(a-C), 2(a-D), and 2(a-E) correspond to results calculated by the Monte Carlo generators PHOJET [26], PYTHIA6 Perugia-2011 [27], PYTHIA8 4C [28], and PYTHIA6 Perugia-0 [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* p*-Pb 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 double-ridge structure.

Figure 4 presents the baseline-subtracted D meson-charged hadron correlations as a function of for in* p*-*p* collisions at TeV (a, b) and* p*-Pb 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* p*-*p* and* p*-Pb 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 double-peak shape can be observed in the figure.

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Figure 5 shows dihadron azimuthal correlations for the short-range region () minus long-range region () in* p*-Pb 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.

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Figure 7 presents the baseline-subtracted two-particle correlations as a function of for and correlations in* p*-*p* 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.

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#### 4. Discussions and Summary

The dihadron azimuthal correlations of different particles for different and intervals in* p*-*p* collisions at TeV and* p*-Pb 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 thermal-source 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 two-particle 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 final-state 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.