# Transverse Momentum and Pseudorapidity Spectrum of the Top Quark, Lepton, andb Jet in Proton-Proton Collisions at LHC

Authors: Li-Na Gao; Er-Qin Wang
Journal: Advances in High Energy Physics
 (2021)

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## Abstract

We study the transverse momentum and pseudorapidity spectrum of the top quark and their decay products, thett¯ system, and the total number of jets in proton-proton (pp) collisions at 13 TeV by using the Tsallis-Pareto-type function and the three-source Landau hydrodynamic model, respectively. The related parameters, such as the effective temperature of the interacting system (T), the nonextensivity of the process (n), and the width (σ) of pseudorapidity distribution, are extracted.


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## Body

## 1. Introduction

The top quark is an interesting particle. It was first found by the Tevatron detector of Fermi National Accelerator Laboratory in 1995 [1–3]. As the heaviest particle in the Standard Model, the top quark is very different from the other quark. Its biggest mass is one of the hotspots for physicists. And it is the only one quark which will decay before it becomes hadron. These unique properties make top quark occupy a very important position in particle physics.The Large Hadron Collider (LHC) has created a lot of top quark events since 2010. Physicists could study the top quark in detail with the help of the LHC. By studying the final state particles produced in high-energy collisions, physicists could obtain some information about the evolution of the collision system. The spectra of transverse momenta (pT) and (pseudo)rapidity (η/y) are important quantities measured in experiments. Many models and functions are used to describe the transverse momentum and pseudorapidity spectra.In this paper, we use the Tsallis-Pareto-type function [4, 5] and the three-source Landau hydrodynamic model [6] to describe the transverse momentum and pseudorapidity spectra of the top quark, lepton, and bottom quark produced in proton-proton (pp) collisions at the center of mass energy s=13 TeV measured at the parton level and particle level, in the full phase space and in the fiducial phase by CMS Collaboration at the LHC [7]. The values of related parameters are extracted and analyzed.The present paper is organized as follows. We briefly introduce the Tsallis-Pareto-type function and the three-source Landau hydrodynamic model in Section2. The result of comparisons with experimental data is given in Section 3. Moreover, we outlined the conclusions in Section 4.


## 2. The Model and Formalism

### 2.1. The Tsallis-Pareto-Type Function

There are some models and functions that could be used to analyze the transverse momentum distribution, such as the Erlang distribution [8–10], the inverse power law [11–14], the Schwinger mechanism [9, 10, 15, 16], Lévy distribution [16], and the Tsallis statistics [17–22]. In a lot of models and formulas, the Tsallis-Pareto-type function is a good choice for transverse momentum spectra. Whether in the relative high pT region or the relative low pT region, people could use the Tsallis-Pareto-type function to fit the experimental data well [5]. So, in this work, we chose the Tsallis-Pareto-type function to describe the transverse momentum spectra. The Tsallis-Pareto-type function can be written as [5]
(1)d2NdydpT=dNdyCpT1+mT−m0nT−n,where m0 is the rest mass of each particle; C and mT are given by
(2)C=n−1n−2nTnT+n−2m0,mT=m02+pT2.T and n are free parameters. T means the mean effective temperature of the interacting system, and it is connected with the average particle energy. n reveals the nonextensivity of the process, and it denotes the departure of the spectra from the Boltzmann distribution [5]. We could obtain values of the two free parameters (T and n) by using the Tsallis-Pareto-type function to fit the pT spectra.


### 2.2. The Three-Source Landau Hydrodynamic Model

The three-source Landau hydrodynamic model has become a mature theoretical model in research for the pseudorapidity distributions at nuclear collisions. In our previous work, this model has described the experimental data successfully [6]. In the present work, we will use it to fit the pseudorapidity distributions of particles (top quark, lepton, and bottom quark) produced in pp collisions at s=13 TeV again. The following is a brief description of the three-source Landau hydrodynamic model.The source means particle emission source. We think the rapidity distribution of particles produced in high-energy collisions is contributed by the three emission sources. The three emission sources are a central source (C), a target source (T), and a projectile (P). The central source is located at the central of rapidity distribution and covers the whole rapidity range. The target source and projectile source are located at the left and right side of the central source, respectively. And the target source and projectile source are revisions for the central source. For the rapidity distribution of particles produced in each emission source, we can use a Gaussian form of the Landau solution to describe it [23–25]:
(3)dNchdy=N02πσXexp−y−yX22σX2,where N0 is the normalization constant, y is rapidity, σ denote the width of rapidity distribution, and X represents the type of emission source.Actually, the three-source Landau hydrodynamic model can be written as a form of a superposition of three-Gaussian forms of the Landau solution:(4)dNchdy=N02πkTσTexp−y−yT22σT2+kCσCexp−y−yC22σC2+kPσPexp−y−yP22σP2.A given parameterk is the contribution of each emission source, kT+kC+kP=1. For the symmetric collision, we think kT=kP. Because of y≈η at very high energy, we could describe the pseudorapidity distributions of lepton by the following formula:
(5)dNchdη=N02πkTσTexp−η−ηT22σT2+kCσCexp−η−ηC22σC2+kPσPexp−η−ηP22σP2.Significantly, as a revision of the central source, the contributions of the target source and projectile source are small.


## 2.1. The Tsallis-Pareto-Type Function

There are some models and functions that could be used to analyze the transverse momentum distribution, such as the Erlang distribution [8–10], the inverse power law [11–14], the Schwinger mechanism [9, 10, 15, 16], Lévy distribution [16], and the Tsallis statistics [17–22]. In a lot of models and formulas, the Tsallis-Pareto-type function is a good choice for transverse momentum spectra. Whether in the relative high pT region or the relative low pT region, people could use the Tsallis-Pareto-type function to fit the experimental data well [5]. So, in this work, we chose the Tsallis-Pareto-type function to describe the transverse momentum spectra. The Tsallis-Pareto-type function can be written as [5]
(1)d2NdydpT=dNdyCpT1+mT−m0nT−n,where m0 is the rest mass of each particle; C and mT are given by
(2)C=n−1n−2nTnT+n−2m0,mT=m02+pT2.T and n are free parameters. T means the mean effective temperature of the interacting system, and it is connected with the average particle energy. n reveals the nonextensivity of the process, and it denotes the departure of the spectra from the Boltzmann distribution [5]. We could obtain values of the two free parameters (T and n) by using the Tsallis-Pareto-type function to fit the pT spectra.


## 2.2. The Three-Source Landau Hydrodynamic Model

The three-source Landau hydrodynamic model has become a mature theoretical model in research for the pseudorapidity distributions at nuclear collisions. In our previous work, this model has described the experimental data successfully [6]. In the present work, we will use it to fit the pseudorapidity distributions of particles (top quark, lepton, and bottom quark) produced in pp collisions at s=13 TeV again. The following is a brief description of the three-source Landau hydrodynamic model.The source means particle emission source. We think the rapidity distribution of particles produced in high-energy collisions is contributed by the three emission sources. The three emission sources are a central source (C), a target source (T), and a projectile (P). The central source is located at the central of rapidity distribution and covers the whole rapidity range. The target source and projectile source are located at the left and right side of the central source, respectively. And the target source and projectile source are revisions for the central source. For the rapidity distribution of particles produced in each emission source, we can use a Gaussian form of the Landau solution to describe it [23–25]:
(3)dNchdy=N02πσXexp−y−yX22σX2,where N0 is the normalization constant, y is rapidity, σ denote the width of rapidity distribution, and X represents the type of emission source.Actually, the three-source Landau hydrodynamic model can be written as a form of a superposition of three-Gaussian forms of the Landau solution:(4)dNchdy=N02πkTσTexp−y−yT22σT2+kCσCexp−y−yC22σC2+kPσPexp−y−yP22σP2.A given parameterk is the contribution of each emission source, kT+kC+kP=1. For the symmetric collision, we think kT=kP. Because of y≈η at very high energy, we could describe the pseudorapidity distributions of lepton by the following formula:
(5)dNchdη=N02πkTσTexp−η−ηT22σT2+kCσCexp−η−ηC22σC2+kPσPexp−η−ηP22σP2.Significantly, as a revision of the central source, the contributions of the target source and projectile source are small.


## 3. Comparisons with Experimental Data

From the experimental point of view, the particle-level definition is expected to result in decreased uncertainties with respect to a definition at the parton level [26]. So, in this work, we use the same approach to analyze the experimental data.In this section, we study the transverse momentum and pseudorapidity spectrum of the top quark, lepton, andb jet in proton-proton collisions at LHC. Based on the Tsallis-Pareto-type function, we describe the transverse momentum spectra of the related product. And we use the three-source Landau hydrodynamic model to analyze the pseudorapidity and rapidity distribution.Figures1 and 2 show the transverse momentum and rapidity cross sections of (a) the top quark (t), (b) the top antiquark (t¯), (c) the top quark or top antiquark with the largest pT (t (leading)), (d) the top quark or top antiquark with the second-largestpT (t (trailing)), and (e) the top quark in the rest frame of the tt¯system (tt¯ RF) at the parton level in the full phase space produced in pp collisions at s=13 TeV. The same as Figures 1 and 2, but Figures 3 and 4 show the results at the particle level in the fiducial phase space. In these four figures, the solid circles represent the experimental data recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 35.9 fb-1 in 2016 [7]. In Figures 1 and 3, the curves are our results calculated by the Tsallis-Pareto-type function. In Figures 2 and 4, the curves show the calculate results of the three-Gaussian functions. Obviously, our results fit well with the experimental data. One can see that the Tsallis-Pareto-type function and the three-Gaussian functions are very helpful approaches to describe the transverse momentum and rapidity cross sections of particles, respectively. The related parameter values (n, T, k, yP, σ) extracted from the transverse momentum and rapidity cross sections and χ2/dof are given in Tables 1 and 2. We could find that the values ofnandToft(leading) are the biggest in the five-type particles at the parton and particle level in the full and fiducial phase space. The values of yP are the same in the scope of consideration. The values of k, σC, and σP are basically the same within the margin of error in the t, t¯, t (leading), and t (trailing), but these three parameter values decreased significantly in the rest frame of the tt¯ system.Figure 1
Transverse momentum distribution of (a) the top quark (pTt), (b) the top antiquark (pTt¯), (c) the top quark or top antiquark with the largest pT (pTt(leading)), (d) the top quark or top antiquark with the second-largest pT (pTt(trailing)), and (e) the top quark in the rest frame of the tt¯ system (pTt (tt¯RF)) at the parton level in the full phase space produced in pp collisions at s=13 TeV. The solid circles represent the experimental data of the CMS Collaboration in literature [7]; the curves are our results calculated by the Tsallis-Pareto-type function.
(a)(b)(c)(d)(e)Figure 2
Rapidity distributions of (a) the top quark (yt), (b) the top antiquark (yt¯), (c) the top quark or top antiquark with the largest pT (yt (leading)), (d) the top quark or top antiquark with the second-largest pT (yt (trailing)), and (e) the tt¯ system (ytt¯) at the parton level in the full phase space produced in pp collisions at s=13 TeV. The solid circles represent the experimental data of the CMS Collaboration in literature [7]; the curves are our results calculated by the three-Gaussian functions.
(a)(b)(c)(d)(e)Figure 3
The same as Figure1 but showing the results of transverse-momentum distribution of (a) pTt, (b) pTt¯, (c) pTt (leading), (d) pTt (trailing), and (e) pTt (tt¯RF) at the particle level in the fiducial phase space.
(a)(b)(c)(d)(e)Figure 4
The same as Figure2 but showing the results of (a) yt, (b) yt¯, (c) yt (leading), (d) yt (trailing), and (e) ytt¯ at the particle level in the fiducial phase space.
(a)(b)(c)(d)(e)Table 1
Values of parameters andχ2/dof corresponding to the curves in Figures 1, 3, 5, 7, 11, 12, 13, 15, and 16.
FigureTypenT (GeV)χ2/dof13 TeV1(a)t9.23±0.6529.26±2.980.0211(b)t¯9.32±0.6829.02±2.580.0121(c)t (leading)22.00±0.9341.56±3.540.4111(d)t (trailing)8.05±0.5322.25±2.130.0371(e)t (tt¯ RF)9.22±0.6226.25±2.250.0223(a)t8.80±0.5731.00±2.850.0183(b)t¯9.20±0.6531.50±3.000.0833(c)t (leading)10.20±0.7036.00±2.950.7323(d)t (trailing)8.20±0.5224.00±2.200.1503(e)t (tt¯ RF)9.50±0.6729.20±2.500.0305(a)l4.72±1.008.50±1.300.0565(b)l¯4.80±1.108.55±1.300.0365(c)l (leading)5.80±1.2513.00±2.603.5175(d)l (trailing)4.15±0.853.90±0.700.3245(e)ll¯7.88±1.5514.50±3.000.6117(a)b (leading)15.00±2.0028.00±3.006.5507(b)b (trailing)10.00±1.3015.20±2.301.1017(c)bb¯23.00±2.8030.00±3.0013.9037 TeV11(a)t9.52±0.6825.00±2.500.02411(c)t¯1.40±0.150.27±0.070.07812(a)b21.40±1.8028.80±2.800.40612(c)l3.95±0.407.30±0.900.1048 TeV13(a)t8.96±0.8626.82±2.520.06413(b)tt¯2.32±0.303.10±0.401.20613(c)t (leading)13.54±1.1633.68±2.801.14413(d)t (trailing)7.12±0.8220.23±2.100.06113(e)t (tt¯ RF)9.35±0.9024.45±2.500.11615(a)l4.97±0.578.50±0.5059.83915(b)ll¯6.80±0.8012.60±1.101.14416(a)b16.95±1.2525.58±2.530.98816(b)bb¯16.32±1.0829.06±2.8619.317Table 2
Values of parameters andχ2/dof corresponding to the curves in Figures 2, 4, 6, 8, 11, 12, 14, 15, and 16.
FigureTypekCyP/ηPσCσPχ2/dof13 TeV2(a)t0.887±0.0171.354±0.0741.230±0.0250.718±0.0150.0132(b)t¯0.892±0.0201.354±0.0741.230±0.0250.718±0.0180.0262(c)t (leading)0.908±0.0221.354±0.0741.245±0.0300.725±0.0180.0192(d)t (trailing)0.892±0.0181.354±0.0741.265±0.0330.720±0.0150.0122(e)tt¯0.935±0.0251.354±0.0741.040±0.0250.518±0.0080.0204(a)t0.840±0.0201.100±0.0601.000±0.0200.470±0.0060.0374(b)t¯0.875±0.0221.100±0.0601.020±0.0200.425±0.0080.1024(c)t (leading)0.875±0.0221.100±0.0601.020±0.0220.425±0.0070.0534(d)t (trailing)0.875±0.0251.100±0.0601.020±0.0200.425±0.0080.0324(e)tt¯0.905±0.0271.100±0.0600.780±0.0180.355±0.0050.2326(a)l0.915±0.1031.225±0.3001.235±0.0400.650±0.0350.0276(b)l¯0.912±0.1001.225±0.3001.235±0.0400.672±0.0400.0146(c)l (leading)0.950±0.1100.990±0.2851.235±0.0300.560±0.0300.0336(d)l (trailing)0.918±0.1051.265±0.3101.268±0.0350.670±0.0400.0408(a)b (leading)0.930±0.1101.225±0.2801.210±0.0500.650±0.0450.0128(b)b (trailing)0.915±0.1051.550±0.3001.270±0.0500.680±0.0600.0127 TeV11(b)t0.880±0.1101.290±0.3280.970±0.0150.430±0.0100.08811(d)tt¯0.950±0.1301.290±0.3150.840±0.0100.450±0.0130.05612(b)b0.920±0.1251.290±0.3251.190±0.0300.700±0.0200.04012(c)l0.904±0.1101.290±0.3201.120±0.0300.700±0.0220.0098 TeV14(a)t0.900±0.0801.290±0.2901.110±0.0200.680±0.0150.02814(b)tt¯0.900±0.1001.290±0.3000.875±0.0150.540±0.0100.07015(c)l0.905±0.1001.280±0.2601.140±0.0250.570±0.0180.23216(c)b0.923±0.1121.280±0.2551.240±0.0300.550±0.0150.027Figures5 and 6 show the transverse momentum and rapidity cross sections of (a) the lepton (l), (b) the antilepton (l¯), (c) the lepton or antilepton with the largest pT (l (leading)), and (d) the lepton or antilepton with the second-largest pT (l (trailing)), and Figure 5(e) shows the transverse momentum cross sections of the dilepton system (ll¯) at the particle level in the fiducial phase space produced in pp collisions at s=13 TeV. The solid circles and curves represent the experimental data and our calculated results, respectively. One can see that the results calculated by using the theoretical functions are in agreement with the experimental data. The related parameters are extracted and listed in Tables 1 (5(a)–(e)) and 2 (6(a)–(d)). The values of n and T of the ll¯ system are bigger than the other particles. The values of k, yP, σC, and σP of the considered particles are not different obviously.Figure 5
The same as Figure1 but showing the results of transverse momentum distribution of (a) the lepton (pTl), (b) the antilepton (pTl¯), (c) the lepton or antilepton with the largest pT (pTl (leading)), (d) the lepton or antilepton with the second-largest pT (pTl (trailing)), and (e) the dilepton system (pTll¯) at the particle level in the fiducial phase space.
(a)(b)(c)(d)(e)Figure 6
The same as Figure2 but showing the results of pseudorapidity distribution of (a) the lepton (ηl), (b) the antilepton (ηl¯), (c) the lepton or antilepton with the largest pT (ηl (leading)), and (d) the lepton or antilepton with the second-largest pT (ηl (trailing)).
(a)(b)(c)(d)The results of transverse momentum and rapidity cross sections of (a) theb jet with the largest pT (b (leading)) and (b) the b jet with the second-largest pT (b (trailing)) are showed in Figures 7 and 8, and Figure 7(c) shows the transverse momentum cross sections of the bb¯ system at the particle level in the fiducial phase space produced in pp collisions at s=13 TeV. We have extracted the related parameters by describing the transverse momentum and rapidity cross section distributions and listed them in Tables 1 (7(a)–(c)) and 2 (8(a)–(b)). The values of parameters are not in an obvious relationship.Figure 7
The same as Figure1 but showing the results of transverse momentum distribution of (a) the b jet with the largest pT (pTb (leading)), (b) the b jet with the second-largest pT (pTb (trailing)), and (c) the bb¯ system (pTbb¯) at the particle level in the fiducial phase space.
(a)(b)(c)Figure 8
The same as Figure2 but showing the results of pseudorapidity distribution of (a) the b jet with the largest pT (ηb (leading)) and (b) the b jet with the second-largest pT (ηb (trailing)).
(a)(b)Generally, the initial temperature (Ti) and mean transverse momentum (pT) are important physical quantities to understand the excitation degree of the interacting system. The two physical quantities are not dependent on the selected models and functions; they are only dependent on the experimental data. According to the literatures [27–29], Ti can be described by the ratio of root-mean-square pT to2 (pT2/2) approximately. So, we calculated the values of pT andpT2/2 by the curves in Figures 1, 3, 5, and 7 and listed them in Table 3. Figures 9 and 10 show the pT and pT2/2 of each particle. From Figures 9 and 10, we could observe that thepTandpT2/2of each particle are big. This phenomenon means that the excitation degree of the interacting system is violent.Table 3
The values ofpT andpT2/2 are calculated by the curves in Figures 1, 3, 5, and 7.
FigureTypepT (GeV/c)pT2/2 (GeV/c)At parton level in the full phase space9(a)/10(a)t120.691±0.014102.471±6.971t¯119.785±0.012101.604±6.247t (leading)137.210±0.015114.073±7.430t (trailing)103.660±0.00688.028±3.131tt¯112.256±0.00894.944±4.114At particle level in the fiducial phase space9(b)/10(b)t126.834±0.017108.302±8.416t¯127.002±0.018108.153±8.762t (leading)136.458±0.022115.996±10.800t (trailing)108.473±0.00892.235±3.834tt¯119.830±0.012101.536±5.9589(c)/10(c)l53.617±0.00449.657±1.768l¯53.322±0.00349.075±1.703l (leading)64.970±0.00558.171±2.743l (trailing)34.914±0.00132.255±0.450ll¯81.272±0.00368.092±1.4289(d)/10(d)b (leading)69.613±0.00462.890±1.861b (trailing)42.804±0.00139.883±0.348bb¯69.127±0.00261.179±0.867Figure 9
The values ofpT for different particles.Figure 10
The same as Figure9 but showing the values of pT2/2.In order to find the relationship between the free parameter and collision energy, we have extracted the related parameters from the transverse momentum and rapidity cross sections at 7 TeV and 8 TeV (Figures11–16), together. In Figures 11 and 12, the solid circles represent the experimental data recorded by the CMS experiment at 7 TeV and correspond to an integrated luminosity of 5.0 fb-1 in 2011 [30]. In Figures 13–16, the solid circles represent the experimental data recorded by the CMS experiment at 8 TeV and correspond to an integrated luminosity of 19.7 fb-1 in 2012 [31]. From the transverse momentum and rapidity cross sections of final state particles, we extracted the values of free parameters and listed them in Tables 1 and 2. And we plot the T, n, and σ values listed in Tables 1 and 2 in Figure 17. In the panel, the symbols represent the values of T, n, and σ, and the lines are linear fitting functions. The intercepts, slopes, and χ2/dof corresponding to the lines are listed in Table 4. From Figure 17 and Table 4, we found that the values of T show a slight increase with the collision energy increased; this phenomenon may be affected by QGP. It can be explained by the influence of jet quenching effect (quickly energy loss) in the case of high-energy quark and gluon jets penetrating through the dense deconfined matter [32]. σC shows to be increased with the collision energy increased. The values of n about t and l do not show obvious change, and the values of n about b decreased when the collision energy increased. Besides, we found that there is no linear relationship σP/T and s, so the values of χ2/dof for this relationship are large which are listed in Table 4.Figure 11
The same as Figures1 and 2, but showing the results of t and tt¯ produced in pp collisions at the parton level in the full phase space at s=7 TeV.
(a)(b)(c)(d)Figure 12
The same as Figures1 and 5, but showing the results of b and l produced in pp collisions at the particle level in the visible phase space at s=7 TeV.
(a)(b)(c)(d)Figure 13
The same as Figure1 but showing the results of transverse momentum distribution of (a) pTt, (b) pTtt¯, (c) pTt (leading), (d) pTt (trailing), and (e) pTt (tt¯RF) at the parton level in the full phase space at s=8 TeV.
(a)(b)(c)(d)(e)Figure 14
The same as Figure2 but showing the results of rapidity distribution of t and tt¯ at the parton level in the full phase space at s=8 TeV.
(a)(b)Figure 15
The same as Figures1 and 5, but showing the results of l and ll¯ produced in pp collisions at the particle level in the fiducial phase space at s=8 TeV.
(a)(b)(c)Figure 16
The same as Figures1 and 5, but showing the results of b and bb¯ produced in pp collisions at the particle level in the fiducial phase space at s=8 TeV.
(a)(b)(c)Figure 17
The relationship of the free parameter and collision energy.
(a)(b)(c)(d)Table 4
Values of intercepts, slopes, andχ2/dofcorresponding to the lines in Figure 17.
ParticleInterceptSlopeχ2/dofT−st21.068±1.2760.638±0.1320.113b26.846±3.5470.066±0.3660.796l6.835±1.1490.135±0.1181.643n−st9.380±0.588−0.015±0.0610.258b25.702±3.888−0.848±0.4013.324l3.886±1.0250.071±0.1061.996σC−st0.757±0.1110.037±0.0119.802b1.210±0.0540.000±0.0061.405l0.987±0.0010.019±0.0000.001σP/T−st0.283±0.2320.035±0.024158.376b0.626±0.1630.001±0.01741.913l0.644±0.1400.001±0.01422.677


## 4. Conclusion

We summarize here our main observations and conclusions.(a)
We use the Tsallis-Pareto-type function to describe the transverse momentum cross-section spectrum oftt¯ different cross sections in pp collisions at 7, 8, and 13 TeV. The values of the effective temperature of the interacting system (T) and the nonextensivity of the process (n) parameters are extracted and listed in Table 1(b)
The rapidity cross sections of the spectrum oftt¯ different cross sections in pp collisions at 7, 8, and 13 TeV are analyzed by the three-source Landau hydrodynamic model. We have obtained the values of the contribution of central emission source (kC) and the width of rapidity distribution (σC, σP) and calculated the values of χ2/dof. The values of related parameters and χ2/dof are given in Table 2. In fact, because of the relationship kT+kC+kP=1, kT=kP, and σT=σP (for the symmetric collision), we can calculate the contributions of the target and projectile source and the width of rapidity distribution of the target source(c)
We have plotted the relationship of free parameters and collision energy in Figure17. For the particles of t, l, and b, σC shows an increasing trend with the collision energy increased. And T shows a slight increase with the collision energy increased; this phenomenon may be affected by QGP(d)
As has been mentioned in Section3, the initial temperature (Ti) can be described by pT2/2 approximately. In order to understand the excitation degree of the interacting system, we calculated the values of pT andpT2/2 by the curves in Figures 1, 3, 5, and 7. We found that the values of pT and pT2/2 are large; this could mean the high excitation degree of the interacting system



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