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On two-ridge structure in two-particle azimuthal correlations in proton-lead collisions at Large Hadron Collider energy.

1. Introduction

Two-particle correlations are important experimental phenomenons in high energy collisions. These correlations contain azimuthal correlations, (pseudo)rapidity correlations, momentum correlations, and so on. As a type of long-range correlation, two-particle azimuthal correlations were studied in recent years. Particularly, at the eras of the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), particle and nuclear physicists have been obtaining some interesting results on the azimuthal correlations in proton-proton (pp), proton-nucleus, and nucleus-nucleus collisions. Some features are observed in the three types of collisions.

For example, the first studies of two-particle azimuthal correlation function in highest-multiplicity pp collision at the LHC present an enhancement of particle pair production at relative azimuth [DELTA][phi] [approximately equal to] 0, which results in a "ridge" structure at the "near-side" [1]. However, in peripheral proton-lead (p-Pb) collisions in which there are only a few nucleons to take part in the collisions and which are similar to pp collision, a ridge structure is observed at the "away-side" ([DELTA][phi] [approximately equal to] [pi]) [2]. The different results between pp and peripheral p-Pb collisions are possibly caused by the infection of nuclear effects (spectator nucleons). In central p-Pb collisions, a double ridge structure is observed, which is consistent with Pb-Pb collisions [3].

To explain the near-side and away-side ridges, many physics mechanisms are proposed in literature, such as the parton saturation [4, 5], gluon saturation and color connections [6-11], parton-induced interactions [12-14], multiparton interactions [15], collective expansion of the final state [16], and collective effects arising in a high-density system [17-23]. If we regard a parton as an emission point and multiple emission points are assumed to form a source, the high energy collisions can be treated by a multisource interacting system. Thus, a multisource thermal model [24-26] can be considered in the studies of near-side and away-side ridges in the two-particle azimuthal correlations. The effects listed here are not completely included in this study, but the collective effect is included.

In this paper, in the framework of the multisource thermal model [24-26], we consider two emission points (subsources) in a single or two sources. The two emission points are assumed to emit respectively the "trigger" particle and the "associated" particle in a particle pair. After considering oscillations and other interactions between the two emission points, the azimuthal correlations are studied.

2. The Model and Method

In the multisource thermal model [24-26], we assume that many emission points (subsources) are formed in high energy collisions. These subsources can form a few sources which stay in local equilibrium sates. The Maxwell, Boltzmann, and other distributions can be used to describe spectrums of final-state particles in which productions of particle pairs are included. For a particle pair measured in final state, both the two emission points take part in the production process. The two emission points may be in a single or two sources. The first emission point corresponds to the production of "trigger" particle and the second one corresponds to the production of "associated" particle. There are oscillations between the two emission points, which results in the momentum of produced particle to depart from the original one. In the meantime, the multiple partons interactions [15], collective expansion of the final state [16], and other collective effects [17-23] can affect the momentum spectrums of final-state particles. Because the total physical extent of the interacting system is about 2 times the nuclear size, the average extent of a source is only a few fm in the case of considering two or three sources (temperatures).

Let the beam direction be the oz axis, and let the transverse momentum direction of the "associated" particle be the positive direction of the ox axis. A right-hand reference frame is established. In the rest frame of the second emission point, let [p.sub.x] and [p.sub.y] denote, respectively, the x- and y-components of the "trigger" particle momentum with oscillations and other interactions, and let [p'.sub.x] and [p'.sub.y] denote those without oscillations and other interactions. The simplest relations between [p.sub.x] and [p'.sub.x,] as well as [p.sub.y] and [p'.sub.y] are linear:

[P.sub.x] = ([a.sub.x][P'.sub.x]) + [b.sub.x][sigma], [P.sub.y] = ([a.sub.y][P'.sub.y]) + [b.sub.y][sigma], (1)

where [a.sub.x,y] and [b.sub.x,y] are parameters to characterize the strength of oscillations, and [sigma] is a parameter to characterize the distribution width of original momentum components. The default values of [a.sub.x,y] and [b.sub.x,y] are 1 and 0, respectively.

From the original [p'.sub.x,y] to the final-state [p.sub.x,y], a detailed consideration on the relativistic effect needs Lorentz transformation. Although there is no particular consideration on the relativistic effect in the above equations for the purpose of convenience, the present expression reflects approximately the mean result of the relativistic effect [24]. Meanwhile, the conservation laws are applicable in the interacting system. We would like to point out that in the above consideration both the "trigger" and "associated" particles are firstly assumed to emit isotropically from two subsources which have no oscillations and other interactions at this assumption state. Then, the momentum components are transformed from original [p'.sub.x,y] to final-state [p.sub.x,y] due to the oscillations and other interactions between the two subsources.

As the first approximation, the original momentum components [p'.sub.x,y] are assumed to obey Gaussian distribution with the width a, which results in the transverse momentum, momentum, and nonrelativistic kinetic energy spectrums to be Rayleigh, Maxwell, and Boltzmann distributions, respectively. In the Monte Carlo calculation, let [r.sub.1,2,3,4] be random numbers distributed evenly in (0, 1]. We have

[p'.sub.x] = [sigma][square root of -2 ln [r.sub.1]] cos (2[pi][r.sub.2]), [p'.sub.y] = [sigma][square root of -2 ln [r.sub.3]] cos (2[pi][r.sub.4]), (2)

which distributes the azimuth of the particle randomly. The relative azimuth between the "trigger" and "associated" particles is

[DELTA][phi] = arctan[[[square root of -2 ln [r.sub.3]] cos (2[pi][r.sub.4])]/[a.sub.x] [square root of -2 ln [r.sub.1]] cos (2[pi][r.sub.2]) + [b.sub.x]], (3)

due to [a.sub.y] = 1 and [b.sub.y] = 0 for the near-side and away-side ridge structures in general. A statistical calculation can give the normalization distribution f([DELTA][phi]) of [DELTA][phi].

We would like to point out that (3) simply calculates the [phi] of the "trigger" particle using [phi] = arctan([p.sub.y]/[p.sub.x]). Although implied in the description of the coordinate system, it might be specified reiterated that [DELTA][phi] = ([[phi].sub.trig]) - ([[phi].sub.assoc]) = ([[phi].sub.trig]) due to ([[phi].sub.assoc]) = 0 (the transverse momentum direction of the "associated" particle being the positive direction of the ox axis) can be represented using (3), where [[phi].sub.trig] and [[phi].sub.assoc] denote the azimuths of "trigger" and "associated" particles, respectively. Then, (3) uses (1) to obtain [DELTA][phi]. In addition, because we focus our attention on the relative magnitudes of [a.sub.x] and [a.sub.y] ([b.sub.x] and [b.sub.y]), we may choose [a.sub.x] = 1 ([a.sub.x] = 0) or [a.sub.y] = 1 ([b.sub.y] = 0). Conventionally, we have [a.sub.y] = 1 and [b.sub.y] = 0.

The physics condition gives that [a.sub.x] [greater than or equal to] 1. Generally, [a.sub.x] = 1 and [b.sub.x] = 0 describe the state without oscillations and other interactions. [a.sub.x] > 1 reflects an expansion of the subsource along ox axis in the momentum space. [b.sub.x] > 0 and [b.sub.x] < 0 present respectively a near-displacement and an away displacement of the first subsource to the second one along the ox axis. The near-side and away-side phenomenons are partly determined by [b.sub.x] > 0 and [b.sub.x] < 0, respectively, and partly determined by [a.sub.x] > 1.

Before giving comparisons with experimental data, we need to introduce two representations which are used in the literature [2, 3, 27]. The first representation uses unidentified charged tracks as "trigger" particles and combines them with [pi] and p as "associated" particles (denoted by h - [pi] and h - p, resp.) [2, 3, 27]. The correlation C([DELTA][eta], [DELTA][phi]) is expressed in terms of the "associated" yield per "trigger" particle where both particles are from a given transverse momentum ([p.sub.T]) interval and pseudorapidity ([eta]) region:

C([DELTA][eta], [DELTA][phi]) = [1/[[N.sub.trig]]][[d.sup.2][N.sub.assoc]/[d[DELTA][eta]d[delta][phi]]] = [S([DELTA][eta], [DELTA][phi])/[B([DELTA][eta], [DELTA][phi])]], (4)

where [N.sub.trig] and [N.sub.assoc] are the numbers of "trigger" and "associated" particles, respectively, and S([DELTA][eta], [DELTA][phi]) and B([DELTA][eta], [DELTA][phi]) are the signal and background distributions [3, 27] and constructed from the same event and "mixed events," respectively [2, 28]. If we integrate over [DELTA][eta] in the above equation or if [DELTA][eta] is a small value in general, we have

C([DELTA][phi]) = [1/[[N.sub.trig]]][[dN.sub.assoc]/d[DELTA][phi]] = [[S([DELTA][phi])]/B([DELTA][phi])]. (5)

Because the background B([DELTA][phi]) constructed from the isotropic "mixed events" in our model is a constant, we have

C([DELTA][phi]) = [c.sub.1]S([DELTA][phi]) = [c.sub.1]f([DELTA][phi]), (6)

where [c.sub.1] is the normalization constant and the signal S([DELTA][phi]) [equivalent to] f([DELTA][phi]).

The second representation uses the "per-trigger yield" Y([DELTA][phi]) to measure the average number of particles correlated with each "trigger" particle, folded into [0, [pi]] [1, 29-31] and integrated over [DELTA][eta] in C([DELTA][eta], [DELTA][phi]), S([DELTA][eta], [DELTA][phi]), and B([DELTA][eta], [DELTA][phi]):

Y([DELTA][phi])= [[[integral]B([DELTA][phi])d[DELTA][phi]]/[pi][N.sub.a]] x C([DELTA][phi]) - [b.sub.ZYAM], (7)

where [N.sub.a] denotes the number of efficiency-weighted "trigger" particles and [b.sub.ZYAM] represents the pedestal arising from uncorrelated pairs [3, 27]. By using a zero-yield-at-minimum (ZYAM) method [29, 32], the parameter [b.sub.ZYAM] can be determined in experiments [3, 27, 29, 32]. Because C([DELTA][phi]) = [c.sub.1]f([DELTA][phi]), we have

Y([DELTA][phi]) = [c.sub.2]f([DELTA][phi]) + [b.sub.0], (8)

where [b.sub.0] is a shift parameter which can be obtained by fitting experimental data and [c.sub.2] is the normalization constant.

To perform the calculation, we probe a set of [a.sub.x] and [b.sub.x] and use (3) to give a lots of [DELTA][phi] by using many random numbers. Then, the normalized distribution f([DELTA][phi]) which is normalized to 1 can be obtained. Introducing f([DELTA][phi]) into (6) (or (8)) which is normalized to the experimental cross section or yield, the parameter [c.sub.1] (or the parameters [c.sub.2] and [b.sub.0]) can be sounded out. By changing the parameters step by step, many repeating calculations can determine the best parameters and their uncertainties. In the real calculation, we can use the idea of the least-square fitting method. The minimum [chi square] corresponds to the best parameter values, and the acceptable [chi square] determines the uncertainties of the parameters.

3. Comparison with Experimental Data and Discussions

Figure 1 presents the correlations versus A0 in transverse momentum interval 1.5 < [p.sub.T] < 2.0 GeV/c in p-Pb collisions at [square root of [s.sub.NN]] = 5.02 TeV, one of the LHC energies. The circles represent the experimental data of the ALICE Collaboration [3, 27] and the curves are our results calculated by the multisource thermal model. Figures 1(a), 1(b), and 1(c) correspond to h - [pi] in centrality 0-20%, h - [pi] in centrality (0-20%)-(60-100%), and h - p in centrality (0-20%)-(60-100%), respectively. The values of free parameters [a.sub.x] and [b.sub.x], normalization constant [c.sub.1], and [chi square] per degree of freedom ([chi square]/dof) obtained by fitting the experimental data are listed in Table 1. In the Monte Carlo calculation, we have used the idea of least-square fitting method. Many tries on the calculation have been applied to get the minimum and acceptable [chi square]. Then, the best parameter values and their uncertainties can be determined. From the table, one can see that the model describes well the experimental data of the ALICE Collaboration. The subsource has an expansion and an away-displacement along the ox axis.

Figure 2 shows Y([DELTA][phi]) x [absolute value of [DELTA][phi]] relations in p-Pb collisions at [square root of [s.sub.NN]] = 5.02 TeV. The closed and open circles represent, respectively, the central (denoted "C" in the panel) and peripheral collisions (denoted "P" in the panel) measured by the ATLAS Collaboration [2], and the curves are our results calculated by the model. From Figures 2(a) to 2(f), different transverse momentum intervals for the "trigger" particle ([p.sup.a.sub.T]) and for the "associated" particle ([p.sup.b.sub.T]) are shown in the panels. The values of related parameters [a.sub.x], [b.sub.x], [c.sub.2], and [b.sub.0] as well as [chi square]/dof are listed in Table 1. Once more, the model describes well the experimental data of the ATLAS Collaboration. In most cases, the subsource in central collisions has a larger expansion and a smaller away-displacement along the ox axis, while the subsource in peripheral collisions is opposite. These differences between the central and peripheral collisions are rendered by the number of participant nucleons.

The difference (C - P) on Y([DELTA][phi])-[absolute value of [DELTA][phi]] relations between the central and peripheral p-Pb collisions at [square root of [s.sub.NN]] = 5.02 TeV is shown in Figure 3. The circles represent the experimental data of the ATLAS Collaboration [2] and the curves are our results calculated by the model. The values of related parameters and [chi square]/dof are given in Table 1. We see that the model describes the the difference between the central and peripheral collisions. The values of [a.sub.x] (=1.04) and [b.sub.x] ([approximately equal to] 0) obtained from Figure 3 are consistent with those obtained from Figures 1(b) and 1(c). Because there is no direct proportional relation between the parameter values and the correlation magnitude, we cannot obtain simply the parameter values for Figure 3 by the method of central minus peripheral collisions.

From the above comparisons we see that we have used the same method to describe the central, peripheral, and central-peripheral collisions. Different participant nucleon numbers (different spectator nucleon numbers) in central and peripheral collisions reflect different parameter values. As an integrative result, the oscillation and other interactions existing between the two subsources cause [a.sub.x] to be greater than 1 and [b.sub.x] to be less than 0. Generally, [a.sub.x] in central collisions is greater than that in peripheral collisions, and [absolute value of [b.sub.x]] in central collisions is less than that in peripheral collisions, due to the effect of participant nucleon number. By comparison with Figures 1(a) and 2, as the difference between the central and peripheral collisions, Figures 1(b), 1(c), and 3 do not contain new content but the effect of participant nucleon number.

In the comparisons, because our calculation is performed on a purely signal sample, and experimental data are usually presented by a admixture of signal and background samples, we need the normalized constants [c.sub.1] and [c.sub.2]. Our results show that [c.sub.1] > 1 and [c.sub.2] > 1 for both the central and peripheral collisions, which render that the magnitude of signal is greater than that of background. There are strong correlations between two particles in the production in p-Pb collisions at LHC energy.

Looking at the results in Table 1, the source with oscillations becomes less displaced in peripheral collisions compared to central collisions. The standard deviation of the momentum components also becomes larger in peripheral collisions. These phenomenons may be caused by different numbers of participant nucleons in peripheral and central collisions.

In heavy ion collisions, the current consensus is that a primary component of the ridge effect is caused by fluctuations in the initial state geometry with a major contribution from "triangular flow," which generates a significant third Fourier coefficient contribution to the azimuthal correlations.

These may be the reasons which cause oscillations and other interactions between the two subsources. In fact, other reasons can cause similar results.

High energy collisions contain abundant contents such as multiplicity, transverse energy, entropy [33], phase transition [34], and flow effects [35]. There are strong relations between flow effects and azimuthal distributions and correlations. Particularly, the azimuthal distribution and correlations of produced particles, target fragments, and projectile fragments have important worth of studies. The present work can be referenced in further.

4. Conclusions

From the above discussions, we obtain following conclusions.

(a) The near-side and away-side ridge structures in two-particle azimuthal correlation produced in high energy collisions can be explained by the multisource thermal model. The modelling results are in agreement with the experimental data of p-Pb collisions at [square root of [s.sub.NN]] = 5.02 GeV measured by the ALICE and ATLAS Collaborations. This renders that our modelling assumption is correct. The two correlated particles are initially assumed to produce isotropically in two rest subsources. Then, the momentum components are transformed from original one to final-state one due to the oscillations and other interactions between the two subsources.

(b) Two emission points (subsources) are assumed and used to perform the calculation. One subsource corresponds to the production of "trigger" particle, and the other subsource corresponds to the production of "associated" particle. There are oscillations and other interactions between the two subsources, which results in the momentum of "trigger" particle, in the rest frame of "associated" particle's source, to depart from the original one.

(c) There are two main parameters, [a.sub.x] and [b.sub.x], in the modelling calculation on correlations. [a.sub.x] = 1 and [b.sub.x] = 0 describe the state without oscillations and other interactions. [a.sub.x] > 1 reflects an expansion of the subsource along the ox axis in the momentum space. [b.sub.x] > 0 and [b.sub.x] < 0 present, respectively, a near-displacement and an away-displacement of the "trigger" particle's subsource to the "associated" particle's subsource along the ox axis. The magnitude of near-side and away-side ridges is partly determined by [b.sub.x] > 0 and [b.sub.x] < 0, respectively, and partly determined by [a.sub.x] > 1.

(d) In central and peripheral p-Pb collisions at the LHC energy, our modelling results show that [a.sub.x] > 1 and [b.sub.x] < 0. In most cases, the subsource in central collisions has a larger expansion and a smaller away-displacement along the ox axis, while the subsource in peripheral collisions is opposite. The difference between the central and peripheral collisions shows a very small [b.sub.x] ([approximately equal to] 0) which means a nearly zero displacement of the subsource. The values of [a.sub.x] and [b.sub.x] extracted from the central and difference (C - P) data of the ALICE and ATLAS Collaborations are consistent with each other.

(e) The present model describes the central and peripheral p-Pb collisions by using a uniform method. Although there are different participant nucleon numbers (or spectator nucleon numbers) between the central and peripheral collisions, the interacting mechanisms which include the oscillations and other interactions between the two subsources are the same except the intensity. The treatment on the difference C - P does not introduce new content but the effect of participant nucleon number.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

http://dx.doi.org/10.1155/2014/296145

Acknowledgments

This work was partly finished at the State University of New York at Stony Brook, USA. One of the authors (Fu-Hu Liu) thanks Professor Dr. Roy A. Lacey and the members of the Nuclear Chemistry Group of Stony Brook University for their hospitality. The authors acknowledge the support of the National Natural Science Foundation of China (under Grants no. 10975095, no. 11247250, and no. 11005071), China National Fundamental Fund of Personnel Training (under Grant no. J1103210), the Open Research Subject of the Chinese Academy of Sciences Large-Scale Scientific Facility (under Grant no. 2060205), Shanxi Scholarship Council of China, and the Overseas Training Project for Teachers at Shanxi University.

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Fu-Hu Liu, Tian Tian, and Ya-Qin Gao

Institute of Theoretical Physics, Shanxi University, Taiyuan, Shanxi 030006, China

Correspondence should be addressed to Fu-Hu Liu; fuhuliu@163.com

Received 21 February 2014; Revised 23 April 2014; Accepted 29 April 2014; Published 20 May 2014

Academic Editor: Bao-Chun Li

Table 1: Values of parameters and [chi square]/dof corresponding
to the curves in Figures 1-3.

Figures                         Type

Figure 1(a)                0-20%, h--[pi]
Figure 1(b)          (0-20%)-(60-100%), h--[pi]
Figure 1(c)           (0-20%)-(60-100%), h--p
Figure 2(a)     0.3 < [p.sup.a.sub.T] < 0.5 GeV/c, C
Figure 2(b)      0.5 < [p.sup.a.sub.T] < 1 GeV/c, C
Figure 2(c)       1 < [p.sup.a.sub.T] < 2 GeV/c, C
Figure 2(d)       2 < [p.sup.a.sub.T] < 3 GeV/c, C
Figure 2(e)       3 < [p.sup.a.sub.T] < 4 GeV/c, C
Figure 2(f)       4 < [p.sup.a.sub.T] < 5 GeV/c, C
Figure 2(a)     0.3 < [p.sup.a.sub.T] < 0.5 GeV/c, P
Figure 2(b)      0.5 < [p.sup.a.sub.T] <1 GeV/c, P
Figure 2(c)       1 < [p.sup.a.sub.T] <2 GeV/c, P
Figure 2(d)       2 < [p.sup.a.sub.T] <3 GeV/c, P
Figure 2(e)       3 < [p.sup.a.sub.T] <4 GeV/c, P
Figure 2(f)       4 < [p.sup.a.sub.T] <5 GeV/c, P
Figure 3(a)   0.3 < [p.sup.a.sub.T] < 0.5 GeV/c, C--P
Figure 3(b)    0.5 < [p.sup.a.sub.T] < 1 GeV/c, C--P
Figure 3(c)     1 < [p.sup.a.sub.T] < 2 GeV/c, C--P
Figure 3(d)     2 < [p.sup.a.sub.T] < 3 GeV/c, C--P
Figure 3(e)     3 < [p.sup.a.sub.T] < 4 GeV/c, C--P
Figure 3(f)     4 < [p.sup.a.sub.T] < 5 GeV/c, C--P

Figures            [a.sub.x]              [b.sub.x]

Figure 1(a)   1.045 [+ or -] 0.002  -0.020 [+ or -] 0.002
Figure 1(b)   1.040 [+ or -] 0.002  -0.005 [+ or -] 0.001
Figure 1(c)   1.030 [+ or -] 0.002  -0.003 [+ or -] 0.001
Figure 2(a)   1.040 [+ or -] 0.002  -0.024 [+ or -] 0.002
Figure 2(b)   1.040 [+ or -] 0.002  -0.020 [+ or -] 0.002
Figure 2(c)   1.040 [+ or -] 0.002  -0.019 [+ or -] 0.002
Figure 2(d)   1.040 [+ or -] 0.002  -0.020 [+ or -] 0.002
Figure 2(e)   1.040 [+ or -] 0.002  -0.025 [+ or -] 0.003
Figure 2(f)   1.040 [+ or -] 0.002  -0.029 [+ or -] 0.003
Figure 2(a)   1.010 [+ or -] 0.001  -0.045 [+ or -] 0.005
Figure 2(b)   1.010 [+ or -] 0.001  -0.035 [+ or -] 0.004
Figure 2(c)   1.012 [+ or -] 0.001  -0.030 [+ or -] 0.003
Figure 2(d)   1.013 [+ or -] 0.001  -0.030 [+ or -] 0.003
Figure 2(e)   1.013 [+ or -] 0.001  -0.030 [+ or -] 0.003
Figure 2(f)   1.013 [+ or -] 0.001  -0.025 [+ or -] 0.003
Figure 3(a)   1.040 [+ or -] 0.002  -0.006 [+ or -] 0.001
Figure 3(b)   1.040 [+ or -] 0.002  0.000 [+ or -] 0.000
Figure 3(c)   1.040 [+ or -] 0.002  0.000 [+ or -] 0.000
Figure 3(d)   1.040 [+ or -] 0.002  0.002 [+ or -] 0.001
Figure 3(e)   1.040 [+ or -] 0.002  0.004 [+ or -] 0.001
Figure 3(f)   1.040 [+ or -] 0.002  0.002 [+ or -] 0.001

Figures       [c.sub.1] ([c.sub.2])        [b.sub.o]           [chi
                                                             square]/
                                                               dof

Figure 1(a)   1.197 [+ or -] 0.012             --             0.872
Figure 1(b)   0.915 [+ or -] 0.010             --             1.129
Figure 1(c)   0.208 [+ or -] 0.002             --             1.105
Figure 2(a)   16.498 [+ or -] 0.172  -2.528 [+ or -] 0.026    1.051
Figure 2(b)   25.146 [+ or -] 0.310  -3.840 [+ or -] 0.040    0.595
Figure 2(c)   40.516 [+ or -] 0.422  -6.200 [+ or -] 0.065    0.470
Figure 2(d)   60.233 [+ or -] 0.650  -9.230 [+ or -] 0.096    0.282
Figure 2(e)   66.202 [+ or -] 0.680  -10.100 [+ or -] 0.105   0.356
Figure 2(f)   69.403 [+ or -] 0.710  -10.600 [+ or -] 0.110   0.819
Figure 2(a)   7.540 [+ or -] 0.080   -1.145 [+ or -] 0.012    0.755
Figure 2(b)   14.363 [+ or -] 0.145  -2.215 [+ or -] 0.024    1.322
Figure 2(c)   27.830 [+ or -] 0.303  -4.315 [+ or -] 0.045    1.101
Figure 2(d)   45.741 [+ or -] 0.470  -7.100 [+ or -] 0.072    0.575
Figure 2(e)   60.354 [+ or -] 0.630  -9.360 [+ or -] 0.095    1.634
Figure 2(f)   86.098 [+ or -] 0.900  -13.390 [+ or -] 0.135   1.903
Figure 3(a)   12.533 [+ or -] 0.122  -1.950 [+ or -] 0.020    1.808
Figure 3(b)   21.923 [+ or -] 0.220  -3.400 [+ or -] 0.037    0.938
Figure 3(c)   32.036 [+ or -] 0.332  -4.950 [+ or -] 0.051    0.912
Figure 3(d)   42.163 [+ or -] 0.405  -6.520 [+ or -] 0.066    0.353
Figure 3(e)   50.203 [+ or -] 0.527  -7.790 [+ or -] 0.080    1.074
Figure 3(f)   40.485 [+ or -] 0.500  -6.280 [+ or -] 0.065    1.278
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Title Annotation:Research Article
Author:Liu, Fu-Hu; Tian, Tian; Gao, Ya-Qin
Publication:Advances in High Energy Physics
Date:Jan 1, 2014
Words:5602
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