Kinetic Freeze-Out Temperature and Transverse Flow Velocity in Au-Au Collisions at RHIC-BES Energies

Abstract

By using the method of data-driven reanalysis, the midrapidity transverse momentum $\left(p_{\text{T}}\right)$ spectra of charged hadrons (${\pi }^{+}$, $K^{+}$, and $p$) produced in central and peripheral gold-gold (Au-Au) collisions from the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) are fitted by using the blast-wave model with the Boltzmann-Gibbs statistics. The model results are in agreement with the experimental data measured by the STAR Collaboration at the RHIC-BES energies. We observe that the kinetic freeze-out temperature $\left(T_0\right)$, transverse flow velocity $\left({\beta }_{\text{T}}\right)$, mean transverse momentum $\left(〈p_{\text{T}}〉\right)$, and initial temperature $\left(T_{\text{i}}\right)$ increase with collision energy as well as with event centrality.

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 .

1. Introduction

One of the most fundamental questions in high energy and nuclear physics is to determine the phase structure of the strongly interacting quantum chromodynamics (QCD) matter [1–3]. The yield ratios, transverse momentum $\left(p_{\text{T}}\right)$ spectra, and other data for various identified particles produced in proton-proton $\left(pp\right)$, proton-nucleus ($pA$), and nucleus-nucleus ($AA$) collisions at high energies are important observable quantities for determining the phase structure. The experimental facilities such as the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) provide excellent tools to study the properties of Quark-Gluon Plasma (QGP) [4–6], which are expected to create collision events with high multiplicities.

The phase diagram of the QCD matter is usually expressed in terms of the chemical freeze-out temperature ($T_{\text{ch}}$) and the baryon chemical potential (${\mu }_{\text{B}}$) [7, 8]. Besides, other quantities such as the kinetic freeze-out temperature ($T_{\text{kin}}$ or $T_0$) and transverse flow velocity (${\beta }_{\text{T}}$) are useful to understand the phase diagram [9]. To search for the possible critical energy in the phase transition from hadronic matter to QGP in high-energy collisions, the STAR Collaboration has been performing the Beam Energy Scan (BES) program [10–13] at the RHIC. Besides, other experiments at similar or lower energies at other accelerators are scheduled [14, 15].

Generally, the processes of high-energy collisions result possibly in three main stages [16–18]:

(i)

The initial stage: at this stage, the collisions are in the beginning. The temperature at this stage is called the initial temperature which is one of the main factors to affect the particle spectra, which is less studied in the community comparatively. After the initial state, the “fireball” leads to a decrease in the temperature and finally to the hadronization

(ii)

The chemical freeze-out stage: at this stage, the inner collisions among various particles are elastic and the yield ratios of differential types of particles remain invariant. The chemical freeze-out temperature $T_{\text{ch}}$ can be obtained from the particle ratios, which is much studied in the community comparatively

(iii)

The kinetic freeze-out stage: at this stage, the scattering processes stop, the hadrons decouple from the rest of the system, and the hadron’s energy/momentum spectra freeze in time. The temperature at this stage is known as the kinetic freeze-out temperature $T_0$ which can be obtained from the $p_{\text{T}}$ spectra

When one studies $T_0$ from the $p_{\text{T}}$ spectra, the effect of ${\beta }_{\text{T}}$ should be eliminated. If the effect of ${\beta }_{\text{T}}$ is not eliminated in the temperature, this temperature is called the effective temperature ($T_{\text{eff}}$ or $T$). At the stage of kinetic freeze-out, $T_0$ and ${\beta }_{\text{T}}$ are two important parameters which describe the thermal motion of the produced particles and the collective expansion of the emission source, respectively. The spectra in a low-$p_{\text{T}}$ region ($p_{\text{T}}=2–3\text{GeV}/c$) which is mainly contributed by the soft excitation process essentially separate the contribution of the thermal motion and the collective expansion, if one only extracts $T_0$ and ${\beta }_{\text{T}}$. The spectra in a high-$p_{\text{T}}$ region are contributed by the hard scattering process which is not needed in extracting $T_0$ and ${\beta }_{\text{T}}$.

We are very interested in the extraction of $T_0$ and ${\beta }_{\text{T}}$ in collisions at the RHIC-BES energies which are very suitable to study the spectra in a low-$p_{\text{T}}$ region, where the spectra in a high-$p_{\text{T}}$ region are not produced due to not too high energies. In this work, the double-differential $p_{\text{T}}$ spectra of charged particle dependences on collision energy and event centrality in gold-gold (Au-Au) collisions are analyzed with the blast-wave model with the Boltzmann-Gibbs statistics by means of data-driven analysis. The model results are compared with the data measured by the STAR Collaboration at the RHIC-BES energies [19, 20].

The remainder of this work consists of The Method and Formalism, Results and Discussion, and Conclusions. We shall describe the remanent parts orderly.

2. The Method and Formalism

Various methods can be used for the extraction of $T_0$ and ${\beta }_{\text{T}}$, e.g., the blast-wave model with the Boltzmann-Gibbs statistics [21–23], the blast-wave model with the Tsallis statistics [24–26], an alternative method by using the Boltzmann-Gibbs statistics [22, 27–33], and the alternative method by using the Tsallis distribution [33–39]. In this work, we choose the blast-wave model with the Boltzmann-Gibbs statistics due to its similarity with the ideal gas model in thermodynamics and few parameters. However, these methods only describe the spectra in the low-$p_{\text{T}}$ region. For the spectra in the high-$p_{\text{T}}$ region if available, the Hagedorn function which is known as the inverse power law [40, 41] can be used. We shall discuss these issues in detail as follows.

In general, there are two main processes responsible for the contribution of $p_{\text{T}}$ spectra. They are (i) the soft excitation process which contributes the soft component in the low-$p_{\text{T}}$ region and (ii) the hard scattering process which contributes the hard component in the whole $p_{\text{T}}$ region if one uses the general superposition function or in the high-$p_{\text{T}}$ region if one uses the usual step function.

For the soft component, according to Refs. [21–23], the probability density function of the $p_{\text{T}}$ spectra in the blast-wave model with the Boltzmann-Gibbs statistics results in $$\begin{array}{}\text{(1)}& f_1\left(p_{\text{T}}\right)=\frac{1}{N}\frac{dN}{{dp}_{\text{T}}}=C_{p_{\text{T}}{m}_{\text{T}}}{\int }_0^{R}rdr\times I_0\left[\frac{p_{\text{T}}\sinh \left(\rho \right)}{T_0}\right]K_1\left[\frac{m_{\text{T}}\cosh \left(\rho \right)}{T_0}\right],\end{array}$$where $N$ is the number of particles, $C$ is the normalization constant, $m_{\text{T}}=\sqrt{p_{\text{T}}^2+m_0^2}$ is the transverse mass, $m_0$ is the rest mass of the considered particle, $r$ and $R$ are the radial position and the maximum radial position, respectively, $I_0$ and $K_1$ are the modified Bessel functions of the first and second kinds, respectively, $\rho ={\tanh }^{-1}\left[\beta \left(r\right)\right]$ is the boost angle, $\beta \left(r\right)={\beta }_{\text{S}}{\left(r/R\right)}^{n_0}$ is a self-similar flow profile, ${\beta }_{\text{S}}$ is the flow velocity on the surface, and $n_0=2$ is used in the original form [21]. Particularly, ${\beta }_{\text{T}}=\left(2/R^2\right){\int }_0^{R}r\beta \left(r\right)dr=2{\beta }_{\text{S}}/\left(n_0+2\right)=0.5{\beta }_{\text{S}}$. The parameter $n_0$ is used in different works, e.g., $n_0=1$ or noninteger in Refs. [22, 24, 42], which corresponds to the centrality from the center to the periphery.

Equation (1) and similar or related functions are not enough to describe the whole $p_{\text{T}}$ spectra. In particular, the maximum $p_{\text{T}}$ reaches up to $100\text{GeV}/c$ in collisions at the LHC [43]. Then, one needs other functions such as the Tsallis–Lévy- [44, 45] or Tsallis–Pareto-type function [44, 46] and the Hagedorn function [40, 41] or inverse power law [47–49] to the spectra in high- and very high-$p_{\text{T}}$ regions. In this work, the hard component is simply represented by the inverse power law. That is, $$\begin{array}{}\text{(2)}& f_2\left(p_T\right)=\frac{1}{N}\frac{dN}{{dp}_{\text{T}}}={Ap}_{\text{T}}{\left(1+\frac{p_{\text{T}}}{p_0}\right)}^{-n},\end{array}$$where $p_0$ and $n$ are free parameters and $A$ is the normalization constant which is related to the free parameters.

However, the structure of $p_{\text{T}}$ spectra is very complex. In fact, several regions have been observed and analyzed in Ref. [50]. These regions include the first one with $p_{\text{T}}<4–6\text{GeV}/c$, the second one with $4–6\text{GeV}/c<p_{\text{T}}<17–20\text{GeV}/c$, and the third one with $p_{\text{T}}>17–20\text{GeV}/c$. Different regions may correspond to different mechanisms. The first $p_{\text{T}}$ region in our discussion is regarded as the region of the soft excitation process, while the second and third $p_{\text{T}}$ regions are regarded as the regions of the hard and the very hard excitation process, respectively. In particular, a special region with $p_{\text{T}}<0.2–0.3\text{GeV}/c$ is considered due to the resonant production in some cases, and it is regarded as the region of the very soft excitation process.

Generally, the whole $p_{\text{T}}$ region discussed above can be uniformly superposed by two methods: (i) the general superposition in which the contribution regions of different components overlap each other and (ii) the Hagedorn model (the usual step function) [40] in which there is no overlapping of different regions of different components.

Considering $f_1\left(p_{\text{T}}\right)$, $f_2\left(p_{\text{T}}\right)$, $f_{\text{VS}}\left(p_{\text{T}}\right)$, and $f_{\text{VH}}\left(p_{\text{T}}\right)$ which denote the probability density functions by the soft, hard, very soft, and very hard components, respectively, where $f_{\text{VS}}\left(p_{\text{T}}\right)$ and $f_{\text{VH}}\left(p_{\text{T}}\right)$ are assumed to be in the form of $f_1\left(p_{\text{T}}\right)$ and $f_2\left(p_{\text{T}}\right)$, respectively, the unified superposition according to the first method is $$\begin{array}{}\text{(3)}& f_0\left(p_{\text{T}}\right)=\frac{1}{N}\frac{dN}{{dp}_{\text{T}}}=k_{\text{VS}}{f}_{\text{VS}}\left(p_{\text{T}}\right)+{kf}_1\left(p_{\text{T}}\right)+\left(1-k-k_{\text{VS}}-k_{\text{VH}}\right)f_2\left(p_{\text{T}}\right)+k_{\text{VH}}{f}_{\text{VH}}\left(p_{\text{T}}\right),\end{array}$$where $k_{\text{VS}}$ is the contribution fraction of the very soft component, while $k$ and $k_{\text{VH}}$ denote the contributions of the soft and very hard components, respectively.

The step function can be used to structure the superposition according to the Hagedorn model [40]; i.e., $$\begin{array}{}\text{(4)}& f_0\left(p_{\text{T}}\right)=\frac{1}{N}\frac{dN}{{dp}_{\text{T}}}=A_{\text{VS}}\theta \left(p_{\text{VS}}-p_{\text{T}}\right)f_{\text{VS}}\left(p_{\text{T}}\right)+A_1\theta \left(p_{\text{T}}-p_{\text{VS}}\right)\theta \left(p_1-p_{\text{T}}\right)f_1\left(p_{\text{T}}\right)+A_2\theta \left(p_{\text{T}}-p_1\right)\theta \left(p_{\text{VH}}-p_{\text{T}}\right)f_2\left(p_{\text{T}}\right)+A_{\text{VH}}\theta \left(p_{\text{T}}-p_{\text{VH}}\right)f_{\text{VH}}\left(p_{\text{T}}\right),\end{array}$$where $A_{\text{VS}}$, $A_1$, $A_2$, and $A_{\text{VH}}$ are the constants which make the interfacing components link to each other perfectly.

Particularly, if the contributions of the very soft and very hard components can be neglected, Equations (3) and (4) are, respectively, simplified to be $$\begin{array}{}\text{(5)}& f_0\left(p_{\text{T}}\right)=\frac{1}{N}\frac{dN}{{dp}_{\text{T}}}={kf}_1\left(p_{\text{T}}\right)+\left(1-k\right)f_2\left(p_{\text{T}}\right),\text{(6)}& f_0\left(p_{\text{T}}\right)=\frac{1}{N}\frac{dN}{{dp}_{\text{T}}}=A_1\theta \left(p_1-p_{\text{T}}\right)f_1\left(p_{\text{T}}\right)+A_2\theta \left(p_{\text{T}}-p_1\right)f_2\left(p_{\text{T}}\right).\end{array}$$Further, if the contribution of the hard component at the RHIC-BES energies can be neglected, Equations (5) and (6) are simplified to be the same form: $$\begin{array}{}\text{(7)}& f_0\left(p_{\text{T}}\right)=\frac{1}{N}\frac{dN}{{dp}_{\text{T}}}=f_1\left(p_{\text{T}}\right).\end{array}$$

This work deals with Au-Au collisions at the RHIC-BES energies, for which Equation (7), i.e., Equation (1), is suitable. In the following section, we shall use Equation (1) to fit the experimental data measured by the STAR Collaboration at the RHIC-BES energies [19, 20].

In particular, the mean $p_{\text{T}}\left(⟨p_{\text{T}}⟩\right)$ and the root-mean-square $p_{\text{T}}\left(\sqrt{⟨p_{\text{T}}^2⟩}\right)$ can be expressed, respectively, as $$\begin{array}{}\text{(8)}& ⟨p_{\text{T}}⟩={\int }_0^{p_{\text{T}\max }}{p}_{\text{T}}{f}_0\left(p_{\text{T}}\right){dp}_{\text{T}},\text{(9)}& \sqrt{⟨p_{\text{T}}^2⟩}=\sqrt{{\int }_0^{p_{\text{T}\max }}{p}_{\text{T}}^2{f}_0\left(p_{\text{T}}\right){dp}_{\text{T}}},\end{array}$$due to $$\begin{array}{}\text{(10)}& {\int }_0^{p_{\text{Tmax}}}{f}_0\left(p_{\text{T}}\right){dp}_{\text{T}}=1,\end{array}$$where $p_{\text{Tmax}}$ denotes the maximum $p_{\text{T}}$ considered by us. In this work, we take $p_{\text{Tmax}}=2.5\text{GeV}/c$.

It should be noted that although only Equation (1) is used in the analysis, we would like to continue to have the statement and formalism for other functions or distributions such as the inverse power law and its superposition with thermal distribution and the discussions on the very soft, hard, and very hard components. In fact, due to the existence of other functions or distributions, the mentioned method of data-driven reanalysis can be used in the spectra in wide $p_{\text{T}}$ coverage, which is not the case in this work. In addition, it is possible to use simultaneously the (very) soft and (very) hard components in other cases which are more universal.

3. Results and Discussion

Figure 1 presents the event centrality-dependent double-differential $p_{\text{T}}$ spectra, $\left(1/2\pi p_{\text{T}}\right)d^{2}N/{dp}_{\text{T}}dy$, of ${\pi }^{+}$, $K^{+}$, and $p$ produced in the midrapidity interval $\mid y\mid <0.1$ in Au-Au collisions at the center-of-mass energy per nucleon pair $\sqrt{{}^{s}NN}=7.7\text{GeV}$ at the RHIC-BES, where $y$ denotes the rapidity. The symbols represent the experimental data measured by the STAR Collaboration [19], and the curves are our fitting results by using the blast-wave model with the Boltzmann-Gibbs statistics, Equation (1) [21–23]. The spectra in centrality classes 0–5%, 5–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%, 60–70%, and 70–80% are scaled by 1, 1/2, 1/4, 1/6, 1/8, 1/10, 1/12, 1/14, and 1/16, respectively. In the fit, the least-square method is used to determine the best values of parameters. The related parameters along with ${\chi }^2$ and degree of freedom (dof) are listed in Table 1, where the centrality classes are listed together. One can see that Equation (1) fits well the data in Au-Au collisions at 7.7 GeV at the RHIC.

[figures omitted; refer to PDF]

Table 1

Values of free parameters ($T_0$ and ${\beta }_{\text{T}}$), normalization constant ($N_0$), ${\chi }^2$, and dof corresponding to the curves in Figures 1–6.

Figure	Particle	Centrality	$T_0$	${\beta }_{\text{T}}$	$N_0$	${\chi }^2$	dof
Figure 1Au-Au7.7 GeV	$${\pi }^{+}$$	0–5%	$$0.130\pm 0.004$$	$$0.306\pm 0.006$$	$$15.00\pm 1.00$$	17	26
		5–10%	$$0.129\pm 0.005$$	$$0.305\pm 0.005$$	$$6.02\pm 0.9$$	14	26
		10–20%	$$0.128\pm 0.004$$	$$0.303\pm 0.007$$	$$2.35\pm 1.05$$	20	26
		20–30%	$$0.126\pm 0.005$$	$$0.302\pm 0.006$$	$$1.09\pm 0.60$$	18	26
		30–40%	$$0.124\pm 0.004$$	$$0.300\pm 0.006$$	$$0.54\pm 0.43$$	19	23
		40–50%	$$0.122\pm 0.003$$	$$0.297\pm 0.007$$	$$0.28\pm 0.02$$	13	23
		50–60%	$$0.120\pm 0.004$$	$$0.292\pm 0.004$$	$$0.14\pm 0.02$$	20	22
		60–70%	$$0.118\pm 0.004$$	$$0.280\pm 0.005$$	$$0.067\pm 0.001$$	16	21
		70–80%	$$0.115\pm 0.005$$	$$0.269\pm 0.007$$	$$0.030\pm 0.008$$	11	18
	$$K^{+}$$	0–5%	$$0.133\pm 0.005$$	$$0.305\pm 0.005$$	$$3.65\pm 0.20$$	99	20
		5–10%	$$0.131\pm 0.004$$	$$0.304\pm 0.005$$	$$1.50\pm 0.15$$	76	22
		10–20%	$$0.130\pm 0.004$$	$$0.302\pm 0.007$$	$$0.53\pm 0.05$$	55	22
		20–30%	$$0.128\pm 0.005$$	$$0.301\pm 0.007$$	$$0.24\pm 0.17$$	27	22
		30–40%	$$0.127\pm 0.004$$	$$0.299\pm 0.009$$	$$0.11\pm 0.01$$	27	21
		40–50%	$$0.125\pm 0.006$$	$$0.296\pm 0.008$$	$$0.050\pm 0.002$$	16	20
		50–60%	$$0.123\pm 0.005$$	$$0.278\pm 0.007$$	$$0.23\pm 0.02$$	34	19
		60–70%	$$0.118\pm 0.004$$	$$0.265\pm 0.008$$	$$0.0093\pm 0.0007$$	34	18
		70–80%	$$0.116\pm 0.004$$	$$0.250\pm 0.008$$	$$0.0034\pm 0.0003$$	29	15
	$$p$$	0–5%	$$0.134\pm 0.004$$	$$0.340\pm 0.005$$	$$9.31\pm 0.60$$	54	29
		5–10%	$$0.133\pm 0.005$$	$$0.328\pm 0.006$$	$$3.90\pm 0.15$$	47	29
		10–20%	$$0.132\pm 0.006$$	$$0.318\pm 0.008$$	$$1.50\pm 0.20$$	46	29
		20–30%	$$0.130\pm 0.005$$	$$0.310\pm 0.008$$	$$0.65\pm 0.05$$	28	29
		30–40%	$$0.128\pm 0.004$$	$$0.301\pm 0.006$$	$$0.32\pm 0.04$$	14	25
		40–50%	$$0.126\pm 0.005$$	$$0.280\pm 0.007$$	$$0.15\pm 0.03$$	13	25
		50–60%	$$0.124\pm 0.004$$	$$0.271\pm 0.006$$	$$0.070\pm 0.008$$	7	24
		60–70%	$$0.122\pm 0.003$$	$$0.250\pm 0.005$$	$$0.030\pm 0.004$$	8	25
		70–80%	$$0.120\pm 0.006$$	$$0.204\pm 0.009$$	$$0.013\pm 0.001$$	14	18
Figure 2Au-Au11.5 GeV	$${\pi }^{+}$$	0–5%	$$0.132\pm 0.004$$	$$0.315\pm 0.005$$	$$19.11\pm 1.60$$	5	26
		5–10%	$$0.130\pm 0.005$$	$$0.313\pm 0.005$$	$$7.60\pm 1.40$$	16	26
		10–20%	$$0.129\pm 0.004$$	$$0.312\pm 0.006$$	$$2.90\pm 0.50$$	14	26
		20–30%	$$0.128\pm 0.003$$	$$0.311\pm 0.007$$	$$1.36\pm 0.10$$	34	26
		30–40%	$$0.127\pm 0.003$$	$$0.310\pm 0.008$$	$$0.38\pm 0.05$$	15	26
		40–50%	$$0.126\pm 0.006$$	$$0.307\pm 0.007$$	$$0.34\pm 0.03$$	16	26
		50–60%	$$0.124\pm 0.004$$	$$0.305\pm 0.005$$	$$0.16\pm 0.01$$	7	23
		60–70%	$$0.121\pm 0.004$$	$$0.296\pm 0.006$$	$$0.080\pm 0.007$$	6	21
		70–80%	$$0.119\pm 0.005$$	$$0.288\pm 0.008$$	$$0.040\pm 0.005$$	10	21
	$$K^{+}$$	0–5%	$$0.135\pm 0.005$$	$$0.314\pm 0.009$$	$$4.23\pm 0.30$$	64	22
		5–10%	$$0.133\pm 0.004$$	$$0.312\pm 0.008$$	$$1.72\pm 0.10$$	62	23
		10–20%	$$0.132\pm 0.006$$	$$0.310\pm 0.010$$	$$0.60\pm 0.05$$	46	23
		20–30%	$$0.130\pm 0.003$$	$$0.308\pm 0.004$$	$$0.27\pm 0.02$$	45	23
		30–40%	$$0.129\pm 0.004$$	$$0.307\pm 0.006$$	$$0.13\pm 0.01$$	59	23
		40–50%	$$0.128\pm 0.005$$	$$0.306\pm 0.007$$	$$0.060\pm 0.006$$	11	23
		50–60%	$$0.126\pm 0.004$$	$$0.300\pm 0.006$$	$$0.026\pm 0.002$$	15	22
		60–70%	$$0.124\pm 0.003$$	$$0.288\pm 0.005$$	$$0.011\pm 0.001$$	6	20
		70–80%	$$0.122\pm 0.004$$	$$0.264\pm 0.011$$	$$0.0050\pm 0.0003$$	26	19
	$$p$$	0–5%	$$0.136\pm 0.005$$	$$0.323\pm 0.007$$	$$7.74\pm 1.00$$	55	25
		5–10%	$$0.135\pm 0.005$$	$$0.321\pm 0.007$$	$$2.90\pm 0.25$$	56	26
		10–20%	$$0.134\pm 0.005$$	$$0.318\pm 0.006$$	$$1.12\pm 0.15$$	40	26
		20–30%	$$0.132\pm 0.004$$	$$0.311\pm 0.007$$	$$0.50\pm 0.03$$	24	26
		30–40%	$$0.130\pm 0.005$$	$$0.308\pm 0.007$$	$$0.24\pm 0.01$$	13	26
		40–50%	$$0.128\pm 0.003$$	$$0.285\pm 0.006$$	$$0.12\pm 0.01$$	10	25
		50–60%	$$0.125\pm 0.004$$	$$0.274\pm 0.008$$	$$0.55\pm 0.01$$	13	25
		60–70%	$$0.123\pm 0.00414$$	$$0.251\pm 0.006$$	$$0.024\pm 0.004$$	7	25
		70–80%	$$0.121\pm 0.004$$	$$0.231\pm 0.007$$	$$0.010\pm 0.003$$	23	26
Figure 3Au-Au14.5 GeV	$${\pi }^{+}$$	0–5%	$$0.135\pm 0.003$$	$$0.320\pm 0.005$$	$$22.14\pm 2.00$$	4	25
		5–10%	$$0.133\pm 0.003$$	$$0.318\pm 0.006$$	$$8.50\pm 2.00$$	10	25
		10–20%	$$0.132\pm 0.004$$	$$0.317\pm 0.006$$	$$3.50\pm 0.25$$	12	25
		20–30%	$$0.131\pm 0.004$$	$$0.315\pm 0.005$$	$$1.60\pm 0.13$$	15	25
		30–40%	$$0.130\pm 0.004$$	$$0.314\pm 0.007$$	$$0.80\pm 0.06$$	10	25
		40–50%	$$0.128\pm 0.004$$	$$0.311\pm 0.006$$	$$0.40\pm 0.03$$	16	25
		50–60%	$$0.126\pm 0.004$$	$$0.307\pm 0.007$$	$$0.19\pm 0.02$$	7	25
		60–70%	$$0.124\pm 0.004$$	$$0.299\pm 0.007$$	$$0.093\pm 0.014$$	8	25
		70–80%	$$0.120\pm 0.005$$	$$0.291\pm 0.005$$	$$0.040\pm 0.006$$	14	25
	$$K^{+}$$	0–5%	$$0.137\pm 0.005$$	$$0.318\pm 0.007$$	$$4.36\pm 0.40$$	16	23
		5–10%	$$0.136\pm 0.004$$	$$0.314\pm 0.008$$	$$1.86\pm 0.20$$	8	23
		10–20%	$$0.135\pm 0.005$$	$$0.313\pm 0.008$$	$$0.70\pm 0.08$$	21	23
		20–30%	$$0.134\pm 0.004$$	$$0.312\pm 0.006$$	$$0.31\pm 0.03$$	15	23
		30–40%	$$0.132\pm 0.004$$	$$0.310\pm 0.009$$	$$0.14\pm 0.01$$	9	23
		40–50%	$$0.130\pm 0.003$$	$$0.308\pm 0.008$$	$$0.067\pm 0.006$$	7	21
		50–60%	$$0.128\pm 0.006$$	$$0.305\pm 0.010$$	$$0.025\pm 0.003$$	9	21
		60–70%	$$0.127\pm 0.004$$	$$0.294\pm 0.007$$	$$0.012\pm 0.001$$	3	19
		70–80%	$$0.125\pm 0.005$$	$$0.267\pm 0.008$$	$$0.0060\pm 0.0006$$	4	17
	$$p$$	0–5%	$$0.139\pm 0.005$$	$$0.335\pm 0.009$$	$$6.47\pm 0.70$$	22	23
		5–10%	$$0.137\pm 0.004$$	$$0.328\pm 0.008$$	$$2.90\pm 0.30$$	20	23
		10–20%	$$0.135\pm 0.003$$	$$0.326\pm 0.008$$	$$1.03\pm 0.12$$	18	23
		20–30%	$$0.134\pm 0.004$$	$$0.323\pm 0.007$$	$$0.46\pm 0.07$$	15	23
		30–40%	$$0.132\pm 0.004$$	$$0.315\pm 0.008$$	$$0.21\pm 0.03$$	12	23
		40–50%	$$0.130\pm 0.005$$	$$0.311\pm 0.007$$	$$0.096\pm 0.012$$	11	23
		50–60%	$$0.128\pm 0.005$$	$$0.294\pm 0.005$$	$$0.042\pm 0.007$$	13	23
		60–70%	$$0.126\pm 0.005$$	$$0.270\pm 0.008$$	$$0.018\pm 0.004$$	18	23
		70–80%	$$0.123\pm 0.004$$	$$0.236\pm 0.007$$	$$0.0080\pm 0.0019$$	26	23
Figure 4Au-Au19.6 GeV	$${\pi }^{+}$$	0–5%	$$0.138\pm 0.004$$	$$0.322\pm 0.004$$	$$24.14\pm 2.00$$	9	23
		5–10%	$$0.137\pm 0.004$$	$$0.321\pm 0.005$$	$$9.50\pm 0.80$$	6	23
		10–20%	$$0.135\pm 0.005$$	$$0.319\pm 0.008$$	$$3.75\pm 0.25$$	7	23
		20–30%	$$0.134\pm 0.004$$	$$0.317\pm 0.005$$	$$1.97\pm 0.16$$	12	23
		30–40%	$$0.132\pm 0.003$$	$$0.315\pm 0.005$$	$$0.87\pm 0.06$$	18	23
		40–50%	$$0.130\pm 0.004$$	$$0.312\pm 0.006$$	$$0.43\pm 0.04$$	20	23
		50–60%	$$0.129\pm 0.005$$	$$0.311\pm 0.008$$	$$0.22\pm 0.02$$	16	23
		60–70%	$$0.128\pm 0.004$$	$$0.308\pm 0.008$$	$$0.10\pm 0.01$$	16	23
		70–80%	$$0.125\pm 0.005$$	$$0.303\pm 0.009$$	$$0.048\pm 0.004$$	14	23
	$$K^{+}$$	0–5%	$$0.140\pm 0.003$$	$$0.320\pm 0.007$$	$$4.98\pm 0.30$$	24	23
		5–10%	$$0.138\pm 0.005$$	$$0.319\pm 0.009$$	$$2.00\pm 0.20$$	33	23
		10–20%	$$0.136\pm 0.005$$	$$0.318\pm 0.007$$	$$0.75\pm 0.05$$	33	23
		20–30%	$$0.135\pm 0.005$$	$$0.314\pm 0.007$$	$$0.34\pm 0.02$$	21	23
		30–40%	$$0.133\pm 0.004$$	$$0.311\pm 0.007$$	$$0.16\pm 0.03$$	12	23
		40–50%	$$0.130\pm 0.005$$	$$0.309\pm 0.009$$	$$0.075\pm 0.005$$	15	22
		50–60%	$$0.129\pm 0.004$$	$$0.307\pm 0.008$$	$$0.036\pm 0.005$$	8	22
		60–70%	$$0.128\pm 0.006$$	$$0.300\pm 0.010$$	$$0.016\pm 0.001$$	23	20
		70–80%	$$0.126\pm 0.004$$	$$0.294\pm 0.009$$	$$0.0070\pm 0.0003$$	25	19
	$$p$$	0–5%	$$0.142\pm 0.005$$	$$0.338\pm 0.006$$	$$5.84\pm 0.70$$	41	26
		5–10%	$$0.140\pm 0.006$$	$$0.336\pm 0.008$$	$$2.40\pm 0.30$$	28	22
		10–20%	$$0.138\pm 0.005$$	$$0.334\pm 0.005$$	$$0.91\pm 0.12$$	19	20
		20–30%	$$0.136\pm 0.005$$	$$0.324\pm 0.007$$	$$0.37\pm 0.06$$	41	20
		30–40%	$$0.133\pm 0.004$$	$$0.316\pm 0.005$$	$$0.18\pm 0.03$$	20	20
		40–50%	$$0.131\pm 0.006$$	$$0.312\pm 0.008$$	$$0.090\pm 0.016$$	8	20
		50–60%	$$0.129\pm 0.005$$	$$0.295\pm 0.009$$	$$0.042\pm 0.007$$	14	20
		60–70%	$$0.128\pm 0.004$$	$$0.275\pm 0.008$$	$$0.019\pm 0.003$$	2	20
		70–80%	$$0.125\pm 0.004$$	$$0.237\pm 0.007$$	$$0.0080\pm 0.0013$$	11	20
Figure 5Au-Au27 GeV	$${\pi }^{+}$$	0–5%	$$0.139\pm 0.004$$	$$0.326\pm 0.006$$	$$26.14\pm 1.80$$	5	23
		5–10%	$$0.138\pm 0.004$$	$$0.324\pm 0.008$$	$$11.07\pm 2.00$$	8	23
		10–20%	$$0.136\pm 0.005$$	$$0.323\pm 0.004$$	$$4.25\pm 0.25$$	10	23
		20–30%	$$0.135\pm 0.004$$	$$0.322\pm 0.004$$	$$1.90\pm 0.15$$	14	23
		30–40%	$$0.133\pm 0.003$$	$$0.321\pm 0.004$$	$$0.98\pm 0.10$$	23	23
		40–50%	$$0.131\pm 0.004$$	$$0.320\pm 0.006$$	$$0.50\pm 0.03$$	26	23
		50–60%	$$0.130\pm 0.005$$	$$0.318\pm 0.005$$	$$0.23\pm 0.03$$	19	23
		60–70%	$$0.129\pm 0.005$$	$$0.317\pm 0.009$$	$$0.11\pm 0.01$$	21	23
		70–80%	$$0.128\pm 0.004$$	$$0.315\pm 0.005$$	$$0.048\pm 0.005$$	19	23
	$$K^{+}$$	0–5%	$$0.142\pm 0.005$$	$$0.324\pm 0.008$$	$$5.11\pm 0.60$$	53	23
		5–10%	$$0.140\pm 0.005$$	$$0.322\pm 0.007$$	$$2.15\pm 0.20$$	52	23
		10–20%	$$0.139\pm 0.003$$	$$0.321\pm 0.008$$	$$0.82\pm 0.10$$	55	23
		20–30%	$$0.137\pm 0.006$$	$$0.321\pm 0.005$$	$$0.37\pm 0.03$$	43	23
		30–40%	$$0.136\pm 0.004$$	$$0.320\pm 0.007$$	$$0.18\pm 0.01$$	25	23
		40–50%	$$0.134\pm 0.004$$	$$0.318\pm 0.008$$	$$0.86\pm 0.01$$	9	23
		50–60%	$$0.132\pm 0.005$$	$$0.316\pm 0.005$$	$$0.040\pm 0.005$$	8	23
		60–70%	$$0.130\pm 0.004$$	$$0.311\pm 0.006$$	$$0.014\pm 0.003$$	12	23
		70–80%	$$0.128\pm 0.004$$	$$0.304\pm 0.007$$	$$0.0070\pm 0.0004$$	27	23
	$$p$$	0–5%	$$0.144\pm 0.004$$	$$0.343\pm 0.007$$	$$5.31\pm 0.40$$	34	20
		5–10%	$$0.143\pm 0.004$$	$$0.341\pm 0.007$$	$$2.20\pm 0.22$$	27	20
		10–20%	$$0.141\pm 0.005$$	$$0.336\pm 0.007$$	$$0.84\pm 0.09$$	21	20
		20–30%	$$0.139\pm 0.005$$	$$0.330\pm 0.006$$	$$0.37\pm 0.05$$	15	20
		30–40%	$$0.137\pm 0.005$$	$$0.326\pm 0.008$$	$$0.18\pm 0.03$$	9	20
		40–50%	$$0.134\pm 0.005$$	$$0.318\pm 0.005$$	$$0.090\pm 0.016$$	8	20
		50–60%	$$0.131\pm 0.004$$	$$0.300\pm 0.008$$	$$0.042\pm 0.005$$	3	20
		60–70%	$$0.129\pm 0.004$$	$$0.280\pm 0.005$$	$$0.019\pm 0.002$$	6	20
		70–80%	$$0.126\pm 0.004$$	$$0.257\pm 0.007$$	$$0.0070\pm 0.0003$$	9	20
Figure 6Au-Au39 GeV	$${\pi }^{+}$$	0–5%	$$0.141\pm 0.004$$	$$0.330\pm 0.007$$	$$27.84\pm 2.30$$	7	23
		5–10%	$$0.139\pm 0.005$$	$$0.328\pm 0.007$$	$$11.60\pm 0.70$$	14	23
		10–20%	$$0.138\pm 0.004$$	$$0.326\pm 0.006$$	$$4.50\pm 0.30$$	23	23
		20–30%	$$0.136\pm 0.004$$	$$0.325\pm 0.005$$	$$2.12\pm 0.10$$	38	23
		30–40%	$$0.135\pm 0.003$$	$$0.324\pm 0.008$$	$$1.05\pm 0.08$$	42	23
		40–50%	$$0.135\pm 0.005$$	$$0.322\pm 0.005$$	$$0.52\pm 0.02$$	36	23
		50–60%	$$0.134\pm 0.004$$	$$0.321\pm 0.008$$	$$0.27\pm 0.02$$	39	23
		60–70%	$$0.132\pm 0.004$$	$$0.320\pm 0.007$$	$$0.12\pm 0.01$$	36	23
		70–80%	$$0.130\pm 0.005$$	$$0.319\pm 0.008$$	$$0.062\pm 0.005$$	51	23
	$$K^{+}$$	0–5%	$$0.148\pm 0.004$$	$$0.328\pm 0.005$$	$$5.29\pm 0.40$$	35	23
		5–10%	$$0.147\pm 0.004$$	$$0.327\pm 0.006$$	$$2.30\pm 0.15$$	15	23
		10–20%	$$0.146\pm 0.005$$	$$0.328\pm 0.005$$	$$0.90\pm 0.08$$	29	23
		20–30%	$$0.145\pm 0.006$$	$$0.324\pm 0.009$$	$$0.40\pm 0.03$$	19	23
		30–40%	$$0.144\pm 0.005$$	$$0.323\pm 0.008$$	$$0.19\pm 0.01$$	12	23
		40–50%	$$0.143\pm 0.005$$	$$0.321\pm 0.006$$	$$0.090\pm 0.010$$	10	23
		50–60%	$$0.142\pm 0.003$$	$$0.317\pm 0.006$$	$$0.0040\pm 0.0004$$	12	23
		60–70%	$$0.140\pm 0.004$$	$$0.316\pm 0.005$$	$$0.019\pm 0.001$$	15	23
		70–80%	$$0.138\pm 0.005$$	$$0.313\pm 0.008$$	$$0.0083\pm 0.0003$$	18	23
	$$p$$	0–5%	$$0.149\pm 0.005$$	$$0.359\pm 0.008$$	$$4.38\pm 0.50$$	34	19
		5–10%	$$0.148\pm 0.004$$	$$0.348\pm 0.006$$	$$1.94\pm 0.30$$	36	19
		10–20%	$$0.146\pm 0.005$$	$$0.346\pm 0.006$$	$$0.80\pm 0.12$$	22	19
		20–30%	$$0.145\pm 0.004$$	$$0.340\pm 0.007$$	$$0.33\pm 0.05$$	16	19
		30–40%	$$0.144\pm 0.004$$	$$0.335\pm 0.005$$	$$0.16\pm 0.03$$	8	19
		40–50%	$$0.144\pm 0.004$$	$$0.330\pm 0.006$$	$$0.078\pm 0.014$$	13	19
		50–60%	$$0.143\pm 0.004$$	$$0.300\pm 0.006$$	$$0.040\pm 0.005$$	1	19
		60–70%	$$0.139\pm 0.004$$	$$0.281\pm 0.005$$	$$0.017\pm 0.002$$	4	19
		70–80%	$$0.127\pm 0.004$$	$$0.274\pm 0.007$$	$$0.0080\pm 0.0006$$	10	19

Figure 2 is the same as Figure 1, but it shows the $p_{\text{T}}$ spectra at $\sqrt{{}^{s}NN}=11.5\text{GeV}$. One can see that Equation (1) fits well the data in Au-Au collisions at 11.5 GeV at the RHIC-BES.

[figures omitted; refer to PDF]

Figure 3 is also the same as Figure 1, but it shows the $p_{\text{T}}$ spectra at $\sqrt{{}^{s}NN}=14.5\text{GeV}$, where the data are cited from Ref. [20]. Once again, Equation (1) fits well the data in Au-Au collisions at 14.5 GeV at the RHIC-BES.

[figures omitted; refer to PDF]

Figures 4–6 are also the same as Figure 1, but they show the $p_{\text{T}}$ spectra at $\sqrt{{}^{s}NN=19.6}$, 27, and 39 GeV, respectively. Once more, Equation (1) fits well the data in Au-Au collisions at other RHIC-BES energies.

[figures omitted; refer to PDF]

[figures omitted; refer to PDF]

[figures omitted; refer to PDF]

It is noteworthy to point out that Equation (1) for the blast-wave model in the system is assumed to be in local thermodynamic equilibrium, and therefore, a single $T_0$ and ${\beta }_{\text{T}}$ should be obtained by the weight average of different particle species. To see clearly the trends of weight average parameters, Figures 7(a) and 7(b) show the dependences of weight averages $T_0$ and ${\beta }_{\text{T}}$ on $\sqrt{{}^{s}NN}$ for different event centralities. The symbols represent the parameter values averaged by weighting the yields of different particles which are listed in Table 1. One can see that $T_0$ and ${\beta }_{\text{T}}$ increase with the increase in $\sqrt{{}^{s}NN}$ from 7.7 to 39 GeV. Meanwhile, $T_0$ and ${\beta }_{\text{T}}$ increase with the increase in the event centrality from the periphery to the center.

[figures omitted; refer to PDF]

In addition, the variation of weight averages $T_0$ on ${\beta }_{\text{T}}$ for different collision energies and event centralities is displayed in Figure 7(c), where the symbols represent the parameter values averaged by weighting the yields of different particles. One can see that $T_0$ increases with the increase in ${\beta }_{\text{T}}$. At higher energy and in central collisions, one sees larger $T_0$ and ${\beta }_{\text{T}}$. There is a positive correlation between $T_0$ and ${\beta }_{\text{T}}$.

The dependences of mean transverse momentum $\left(⟨p_{\text{T}}⟩\right)$ and initial temperature ($T_{\text{i}}$) on $\sqrt{{}^{s}NN}$ for different event centralities obtained by weighting the yields of different particles are shown in Figures 8(a) and 8(b), respectively, where $T_{\text{i}}=\sqrt{⟨p_{\text{T}}^2⟩/2}$ according to the color string percolation model [51–53]. One can see that $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$ increase with the increase in $\sqrt{{}^{s}NN}$ from 7.7 to 39 GeV. Meanwhile, $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$ increase with the increase in event centrality from the periphery to the center.

[figures omitted; refer to PDF]

We notice that $T_{\text{i}}=0.28–0.38\text{GeV}$ which is quite high for the considered collision energies. Because we obtain $T_{\text{i}}$ from the spectra of particles with nonzero masses, it is possible to have a high value. If we obtain $T_{\text{i}}$ from the spectra of photons, the value will be small. High $T_{\text{i}}$ renders that the excitation degree of the emission source at the stage of the initial state is high. Meanwhile, one of the key issues is whether the transverse flow should be also considered at the initial stage. Naturally, after considering the transverse flow at the initial stage, $T_{\text{i}}$ will be small. It is regretful that we have no clear idea on the extraction of transverse flow at the initial stage. As an alternative method, if we redefine $T_{\text{i}}=k_0\sqrt{⟨p_T^2⟩/2}$ as the initial temperature and ${\beta }_{\text{Ti}}=\left(1-k_0\right)\sqrt{⟨p_T^2⟩/2}$ as the initial transverse flow velocity, where $0<k_0<1$ is to be determined, we may obtain a small $T_{\text{i}}$ and a nonzero ${\beta }_{\text{Ti}}$.

The reason for the increase in $T_0$ and ${\beta }_{\text{T}}$ with the increase in collision energy is due to the fact that more energies are deposited in collisions at higher energy in the considered RHIC-BES energy range. Meanwhile, the system size at higher energy decreases due to a relativistic constriction effect, which results in a smaller volume and then a larger energy density and larger $T_0$. Meanwhile, at higher energy, the squeeze is more violent, which results in a rapider expansion and larger ${\beta }_{\text{T}}$.

The reason for the increase in $T_0$ and ${\beta }_{\text{T}}$ with the increase in event centrality is due to the fact that the central collisions contain more nucleons than the peripheral collisions; then, more energies are deposited in central collisions. Meanwhile, a rapider expansion appears due to more violent squeeze in central collisions, compared to peripheral collisions. As a result, both $T_0$ and ${\beta }_{\text{T}}$ in central collisions are larger than those in peripheral collisions.

Because of $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$ being positive correlation with $T_0$ and ${\beta }_{\text{T}}$, with increasing collision energy and event centrality, the increasing trend of $T_0$ and ${\beta }_{\text{T}}$ results naturally in the increasing trend of $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$. This work shows that the two free parameters $T_0$ and ${\beta }_{\text{T}}$ and the two derived parameters $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$ appear to be similar law on the dependences of collision energy and event centrality. In particular, $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$ are model-independent, though we obtain them from model-dependent free parameters $T_0$ and ${\beta }_{\text{T}}$ in this work. In fact, $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$ can be obtained by the $p_{\text{T}}$ data themselves if the data are across the possible $p_{\text{T}}$ range.

It seems that there are nonmonotonous changes at 11.5 GeV in the excitation functions of ${\beta }_{\text{T}}$, $⟨p_{\text{T}}⟩$, and $T_{\text{i}}$ in the most central Au-Au collisions. These nonmonotonous changes reflect the minimum or maximum point of equation of state (EoS) of the matter formed in collisions. At a few GeV to about 10 GeV, the matter formed in collisions is baryon-dominant. At above 10 GeV, the matter formed in collisions is meson-dominant. At around 10 GeV, the baryon number density is the largest [54] due to the competition between projectile/target penetrating/stopping and longitudinal contraction.

It is hard to say whether the minimum or maximum point of EoS of the matter formed in the most central Au-Au collisions at 11.5 GeV is related to the search for the QCD critical end point (CEP) which is the main objective of the BES program performed by the STAR Collaboration. Generally, large nonmonotonous changes or saturations or a slight increase should appear in the excitation functions of some quantities at the critical energy which is the energy corresponding to the CEP. The excitation functions considered in this paper change slightly. Although there is no value in the energy range of less than 7.7 GeV, it is expected that the excitation function increases quickly in the energy range of a few GeV while the onset stage of a slight increase appears at around 10 GeV in the excitation functions of $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$.

It should be noted that there is entanglement in the extraction of $T_0$ and ${\beta }_{\text{T}}$. In fact, if one uses smaller $T_0$ and larger ${\beta }_{\text{T}}$ for central collisions, a decreasing trend for $T_0$ from peripheral to central collisions can be obtained. Meanwhile, a negative correlation between $T_0$ and ${\beta }_{\text{T}}$ can also be obtained. Thus, this situation is in agreement with some current references [19, 55, 56]. If one even uses almost invariant or slightly larger $T_0$ and properly larger ${\beta }_{\text{T}}$ for central collisions, an almost invariant or slightly increased trend for $T_0$ from peripheral to central collisions can be obtained [57]. To show the flexibility in the extraction of $T_0$ and ${\beta }_{\text{T}}$, this work has reported an increasing trend for $T_0$ from peripheral to central collisions and a positive correlation between $T_0$ and ${\beta }_{\text{T}}$.

In addition, we have taken $n_0=2$ in this work, which closely resembles the hydrodynamic profile as mentioned in Ref. [21]. Although Ref. [58] shows that $n_0=1$ is the closest approximation to hydrodynamics at freeze-out, Ref. [36] shows that $n_0=2$ or 1 does not affect obviously the fit curve and free parameters $T_0$ and ${\beta }_{\text{T}}$. If we consider that $\beta \left(r\right)$ decays quickly from the surface to the center of the emission source, we are inclined to use $n_0=2$. Anyhow, we are not inclined to regard $n_0$ as a free parameter which is too mutable and debatable in our opinion. In current analysis with the blast-wave model [22], not only is $n_0$ mutable (from $0.0\pm 10.1$ to $4.3\pm 1.7$) but also the $p_{\text{T}}$ coverage is narrow and particle-dependent ($p_{\text{T}}\approx 0.20–0.70\text{GeV}/c$ for ${\pi }^{+}$, $0.25–0.75\text{GeV}/c$ for $K^{+}$, and $0.35–1.15\text{GeV}/c$ for $p$), which uses a single kinetic freeze-out scenario and results in different trends of $T_0$ versus ${\beta }_{\text{T}}$ from this work. If we also regard $n_0$ as a free parameter and use narrow and particle-dependent $p_{\text{T}}$ coverage, consistent result with current analysis [22] can be naturally obtained by us.

Indeed, there are too much uncertainties arising from the choice of fit function and flow profile and from the well-known ambiguity in the fit results—in a single $p_{\text{T}}$ spectrum, it is always possible to trade ${\beta }_{\text{T}}$ against $T_0$. That is, $T_0$ and ${\beta }_{\text{T}}$ is negatively correlative for a given $p_{\text{T}}$ spectrum. It is possible that we may use suitable $T_0$ and ${\beta }_{\text{T}}$ for a set of $p_{\text{T}}$ spectra and obtain a positive or negative correlation. In a positive correlation, decreasing $T_0$ and increasing ${\beta }_{\text{T}}$ will result in a negative correlation. Contrarily, in a negative correlation, increasing $T_0$ and decreasing ${\beta }_{\text{T}}$ will result in a positive correlation. Indeed, there is an influence if we use a changeable $p_{\text{T}}$ coverage and/or $n_0$ choice on the extraction of the two free parameters. In our opinion, to reduce the uncertainties, one should use a fixed flow profile ($n_0$) and wide and fixed $p_{\text{T}}$ coverage for different particles. In fact, we have used $n_0=2$ and $p_{\text{T}}<2.5\text{GeV}/c$ for different particles in this work and used a multiple freeze-out scenario such as that used in Ref. [59].

Our result (Table 1) shows that the heavier the particle is, the higher $T_0$ and the smaller ${\beta }_{\text{T}}$ correspond. This result is in agreement with the hydrodynamic-type behavior [4]. The final $T_0$ and ${\beta }_{\text{T}}$ are averaged by weighting different particle yields, which shows a positive correlation between $T_0$ and ${\beta }_{\text{T}}$ (Figure 7). Our result is in agreement with the alternative method [36, 37] in which $T_0$ is regarded as the intercept in the linear relation of $T$ versus $m_0$ and ${\beta }_{\text{T}}$ is regarded as the slope in the linear relation of $⟨p_{\text{T}}⟩$ versus $m_0\overline{\gamma }$, where $\overline{\gamma }$ is the mean Lorentz factor in the source rest frame. Our result is also in agreement with a very recent work [60] which uses the same method as ours. If the negative correlation can be explained as the result of a longer lifetime (lower excitation degree) which corresponds to lower $T_0$ and a quicker expansion (stronger squeeze) which corresponds to larger ${\beta }_{\text{T}}$, the positive correlation can be explained as the result of a high excitation degree which corresponds to high $T_0$ and quick expansion (strong squeeze) which corresponds to large ${\beta }_{\text{T}}$.

This whole phenomenal analysis results in degrees of thermal motion and collective expansion that are reflected by $T_0$ and ${\beta }_{\text{T}}$, respectively. With the increasing collision energy, the system may undergo different evolution processes. In the considered RHIC-BES energy range, the violent degree of collisions increases with increasing collision energy. The trends of $T_0$ and ${\beta }_{\text{T}}$ show approximately monotonous increase in which large fluctuation does not appear, though there are nonmonotonous changes at 11.5 GeV in some cases. The evolution processes at the considered six energies show similar behaviors to each other.

4. Conclusions

The main observations and conclusions are summarized as follows.

(a)

By using the method of data-driven reanalysis, the blast-wave model with the Boltzmann-Gibbs statistics is used to analyze the collision energy-dependent and event centrality-dependent double-differential transverse momentum spectra of charged particles (${\pi }^{+}$, $K^{+}$, and $p$) produced in the midrapidity interval in Au-Au collisions at the RHIC-BES energies. The contribution of soft excitation is considered in this work, but the contribution of the hard process is not excluded if available

(b)

As the free parameters, the kinetic freeze-out temperature $T_0$ and transverse flow velocity ${\beta }_{\text{T}}$ are extracted with the blast-wave model. Both $T_0$ and ${\beta }_{\text{T}}$ increase with the increase in collision energy due to more violent collisions at higher energy. The two parameters also increase with the increase in event centrality, as the central collisions contain more nucleons which means more energy deposited and more violent collisions and squeeze, compared with peripheral collisions

(c)

As the derived parameters, the mean transverse momentum $⟨p_{\text{T}}⟩$ and initial temperature $T_{\text{i}}$ appear to be similar law to the free parameters $T_0$ and ${\beta }_{\text{T}}$ when we study the dependences of parameters on collision energy and event centrality. Although $T_0$ and ${\beta }_{\text{T}}$ are model-dependent, $⟨p_{\text{T}}⟩$ and $T_{\text{i}}$ are generally model-independent. There is no large fluctuation in the excitation function of the considered parameters at the RHIC-BES, which means a similar collision mechanism

Ethical Approval

The authors declare that they are in compliance with ethical standards regarding the content of this paper.

Disclosure

The funding agencies have no role in the design of the study; in the collection, analysis, or interpretation of the data; in the writing of the manuscript; or in the decision to publish the results.

Acknowledgments

We thank Dr. Muhammad Usman Ashraf for his kind help. This work was supported by the National Natural Science Foundation of China under Grant No. 11575103, the Chinese Government Scholarship (China Scholarship Council), the Scientific and Technological Innovation Programs (STIP) of Higher Education Institutions in Shanxi under Grant No. 201802017, the Shanxi Provincial Natural Science Foundation under Grant No. 201701D121005, and the Fund for Shanxi “1331 Project” Key Subjects Construction.

References

[1] S. Mukherjee, V. Skokov, "Universality driven analytic structure of QCD crossover: radius of convergence in baryon chemical potential," . https://arxiv.org/abs/1909.04639

[2] W.-J. Fu, J. M. Pawlowski, F. Rennecke, "The QCD phase structure at finite temperature and density," . https://arxiv.org/abs/1909.02991

[3] G.-Y. Shao, W.-B. He, X.-Y. Gao, "Deformed QCD phase structure and entropy oscillation in the presence of a magnetic background," Physical Review D, vol. 100 no. 1, article 014020,DOI: 10.1103/PhysRevD.100.014020, 2019.

[4] R. Sahoo, "Possible formation of QGP-droplets in proton-proton collisions at the CERN Large Hadron Collider," AAPPS Bulletin, vol. 29 no. 4,DOI: 10.22661/AAPPSBL.2019.29.4.16, 2019.

[5] M. Gyulassy, L. McLerran, "New forms of QCD matter discovered at RHIC," Nuclear Physics A, vol. 750 no. 1, pp. 30-63, DOI: 10.1016/j.nuclphysa.2004.10.034, 2005.

[6] M. T. AlFiky, O. T. ElSherif, A. M. Hamed, "Quark gluon plasma formation in proton-proton collisions using PYTHIA," . https://arxiv.org/abs/1902.05114

[7] F. Rennecke, W.-J. Fu, J. M. Pawlowski, "Strangeness neutrality and the QCD phase diagram," . https://arxiv.org/abs/1907.08179

[8] A. Andronic, P. Braun-Munzinger, J. Stachel, "Hadron production in central nucleus–nucleus collisions at chemical freeze-out," Nuclear Physics A, vol. 772 no. 3-4, pp. 167-199, DOI: 10.1016/j.nuclphysa.2006.03.012, 2006.

[9] G. Inghirami, P. Hillmann, B. Tomášik, M. Bleicher, "Temperatures and chemical potentials at kinetic freeze-out in relativistic heavy ion collisions from coarse grained transport simulations," . https://arxiv.org/abs/1909.00643

[10] C. Yang, "The STAR detector upgrades and physics in beam energy scan phase II," EPJ Web of Conferences, vol. 182, article 02130,DOI: 10.1051/epjconf/201818202130, 2018.

[11] K. C. Meehan, "Fixed target collisions at STAR," Nuclear Physics A, vol. 956, pp. 878-881, DOI: 10.1016/j.nuclphysa.2016.04.016, 2016.

[12] X. Sun, the STAR Collaboration, "Flow in the RHIC Beam Energy Scan from STAR," Journal of Physics: Conference Series, vol. 535, article 012005,DOI: 10.1088/17426596/535/1/012005, 2014.

[13] K. C. Meehan, "The fixed-target experiment at STAR," Journal of Physics: Conference Series, vol. 742, article 012022,DOI: 10.1088/1742-6596/742/1/012022, 2016.

[14] T. Ablyazimov, A. Abuhoza, R. P. Adak, M. Adamczyk, K. Agarwal, M. M. Aggarwal, Z. Ahammed, F. Ahmad, N. Ahmad, S. Ahmad, A. Akindinov, "Challenges in QCD matter physics – the scientific programme of the Compressed Baryonic Matter experiment at FAIR," The European Physical Journal A, vol. 53, 2017.

[15] J. Chen, D. Keane, Y. G. Ma, A. Tang, Z. Xu, "Antinuclei in heavy-ion collisions," Physics Reports, vol. 760,DOI: 10.1016/j.physrep.2018.07.002, 2018.

[16] N. Xu, "An overview of STAR experimental results," Nuclear Physics A, vol. 931,DOI: 10.1016/j.nuclphysa.2014.10.022, 2014.

[17] S. Chatterjee, S. Das, L. Kumar, D. Mishra, B. Mohanty, R. Sahoo, N. Sharma, "Freeze-out parameters in heavy-ion collisions at AGS, SPS, RHIC, and LHC energies," Advances in High Energy Physics, vol. 2015,DOI: 10.1155/2015/349013, 2015.

[18] S. Uddin, I. Bashir, R. A. Bhat, "Transverse momentum distributions of hadrons produced in Pb-Pb collisions at LHC energy s NN = 2.76 TeV," Advances in High Energy Physics, vol. 2015,DOI: 10.1155/2015/154853, 2015.

[19] L. Adamczyk, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, N. N. Ajitanand, I. Alekseev, D. M. Anderson, R. Aoyama, A. Aparin, D. Arkhipkin, E. C. Aschenauer, M. U. Ashraf, A. Attri, G. S. Averichev, X. Bai, V. Bairathi, A. Behera, R. Bellwied, A. Bhasin, A. K. Bhati, P. Bhattarai, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. Bouchet, J. D. Brandenburg, A. V. Brandin, D. Brown, I. Bunzarov, J. Butterworth, H. Caines, M. Calderón de la Barca Sánchez, J. M. Campbell, D. Cebra, I. Chakaberia, P. Chaloupka, Z. Chang, N. Chankova-Bunzarova, A. Chatterjee, S. Chattopadhyay, X. Chen, J. H. Chen, X. Chen, J. Cheng, M. Cherney, W. Christie, G. Contin, H. J. Crawford, S. Das, L. C. de Silva, R. R. Debbe, T. G. Dedovich, J. Deng, A. A. Derevschikov, L. Didenko, C. Dilks, X. Dong, J. L. Drachenberg, J. E. Draper, L. E. Dunkelberger, J. C. Dunlop, L. G. Efimov, N. Elsey, J. Engelage, G. Eppley, R. Esha, S. Esumi, O. Evdokimov, J. Ewigleben, O. Eyser, R. Fatemi, S. Fazio, P. Federic, P. Federicova, J. Fedorisin, Z. Feng, P. Filip, E. Finch, Y. Fisyak, C. E. Flores, L. Fulek, C. A. Gagliardi, D. Garand, F. Geurts, A. Gibson, M. Girard, D. Grosnick, D. S. Gunarathne, Y. Guo, A. Gupta, S. Gupta, W. Guryn, A. I. Hamad, A. Hamed, A. Harlenderova, J. W. Harris, L. He, S. Heppelmann, S. Heppelmann, A. Hirsch, G. W. Hoffmann, S. Horvat, T. Huang, B. Huang, X. Huang, H. Z. Huang, T. J. Humanic, P. Huo, G. Igo, W. W. Jacobs, A. Jentsch, J. Jia, K. Jiang, S. Jowzaee, E. G. Judd, S. Kabana, D. Kalinkin, K. Kang, K. Kauder, H. W. Ke, D. Keane, A. Kechechyan, Z. Khan, D. P. Kikoła, I. Kisel, A. Kisiel, L. Kochenda, M. Kocmanek, T. Kollegger, L. K. Kosarzewski, A. F. Kraishan, P. Kravtsov, K. Krueger, N. Kulathunga, L. Kumar, J. Kvapil, J. H. Kwasizur, R. Lacey, J. M. Landgraf, K. D. Landry, J. Lauret, A. Lebedev, R. Lednicky, J. H. Lee, X. Li, C. Li, W. Li, Y. Li, J. Lidrych, T. Lin, M. A. Lisa, H. Liu, P. Liu, Y. Liu, F. Liu, T. Ljubicic, W. J. Llope, M. Lomnitz, R. S. Longacre, S. Luo, X. Luo, G. L. Ma, L. Ma, Y. G. Ma, R. Ma, N. Magdy, R. Majka, D. Mallick, S. Margetis, C. Markert, H. S. Matis, K. Meehan, J. C. Mei, Z. W. Miller, N. G. Minaev, S. Mioduszewski, D. Mishra, S. Mizuno, B. Mohanty, M. M. Mondal, D. A. Morozov, M. K. Mustafa, M. Nasim, T. K. Nayak, J. M. Nelson, M. Nie, G. Nigmatkulov, T. Niida, L. V. Nogach, T. Nonaka, S. B. Nurushev, G. Odyniec, A. Ogawa, K. Oh, V. A. Okorokov, D. Olvitt, B. S. Page, R. Pak, Y. Pandit, Y. Panebratsev, B. Pawlik, H. Pei, C. Perkins, P. Pile, J. Pluta, K. Poniatowska, J. Porter, M. Posik, A. M. Poskanzer, N. K. Pruthi, M. Przybycien, J. Putschke, H. Qiu, A. Quintero, S. Ramachandran, R. L. Ray, R. Reed, M. J. Rehbein, H. G. Ritter, J. B. Roberts, O. V. Rogachevskiy, J. L. Romero, J. D. Roth, L. Ruan, J. Rusnak, O. Rusnakova, N. R. Sahoo, P. K. Sahu, S. Salur, J. Sandweiss, M. Saur, J. Schambach, A. M. Schmah, W. B. Schmidke, N. Schmitz, B. R. Schweid, J. Seger, M. Sergeeva, P. Seyboth, N. Shah, E. Shahaliev, P. V. Shanmuganathan, M. Shao, A. Sharma, M. K. Sharma, W. Q. Shen, Z. Shi, S. S. Shi, Q. Y. Shou, E. P. Sichtermann, R. Sikora, M. Simko, S. Singha, M. J. Skoby, N. Smirnov, D. Smirnov, W. Solyst, L. Song, P. Sorensen, H. M. Spinka, B. Srivastava, T. D. S. Stanislaus, M. Strikhanov, B. Stringfellow, T. Sugiura, M. Sumbera, B. Summa, Y. Sun, X. M. Sun, X. Sun, B. Surrow, D. N. Svirida, A. H. Tang, Z. Tang, A. Taranenko, T. Tarnowsky, A. Tawfik, J. Thäder, J. H. Thomas, A. R. Timmins, D. Tlusty, T. Todoroki, M. Tokarev, S. Trentalange, R. E. Tribble, P. Tribedy, S. K. Tripathy, B. A. Trzeciak, O. D. Tsai, T. Ullrich, D. G. Underwood, I. Upsal, G. van Buren, G. van Nieuwenhuizen, A. N. Vasiliev, F. Videbæk, S. Vokal, S. A. Voloshin, A. Vossen, G. Wang, Y. Wang, F. Wang, Y. Wang, J. C. Webb, G. Webb, L. Wen, G. D. Westfall, H. Wieman, S. W. Wissink, R. Witt, Y. Wu, Z. G. Xiao, W. Xie, G. Xie, J. Xu, N. Xu, Q. H. Xu, Y. F. Xu, Z. Xu, Y. Yang, Q. Yang, C. Yang, S. Yang, Z. Ye, Z. Ye, L. Yi, K. Yip, I. K. Yoo, N. Yu, H. Zbroszczyk, W. Zha, Z. Zhang, X. P. Zhang, J. B. Zhang, S. Zhang, J. Zhang, Y. Zhang, J. Zhang, S. Zhang, J. Zhao, C. Zhong, L. Zhou, C. Zhou, X. Zhu, Z. Zhu, M. Zyzak, STAR Collaboration, "Bulk properties of the medium produced in relativistic heavy-ion collisions from the Beam Energy Scan program," Physical Review C, vol. 96 no. 4, article 044904,DOI: 10.1103/PhysRevC.96.044904, 2017.

[20] V. Bairathi, "Study of the bulk properties of the system formed in Au + Au collisions at s N N = 14.5 GeV using the STAR detector at RHIC," Nuclear Physics A, vol. 956, pp. 292-295, DOI: 10.1016/j.nuclphysa.2016.02.066, 2016.

[21] E. Schnedermann, J. Sollfrank, U. Heinz, "Thermal phenomenology of hadrons from 200 A GeV S+S collisions," Physical Review C, vol. 48 no. 5, pp. 2462-2475, DOI: 10.1103/PhysRevC.48.2462, 1993.

[22] B. I. Abelev, M. M. Aggarwal, Z. Ahammed, B. D. Anderson, D. Arkhipkin, G. S. Averichev, Y. Bai, J. Balewski, O. Barannikova, L. S. Barnby, J. Baudot, S. Baumgart, D. R. Beavis, R. Bellwied, F. Benedosso, R. R. Betts, S. Bhardwaj, A. Bhasin, A. K. Bhati, H. Bichsel, J. Bielcik, J. Bielcikova, B. Biritz, L. C. Bland, M. Bombara, B. E. Bonner, M. Botje, J. Bouchet, E. Braidot, A. V. Brandin, E. Bruna, S. Bueltmann, T. P. Burton, M. Bystersky, X. Z. Cai, H. Caines, M. C. B. Sánchez, J. Callner, O. Catu, D. Cebra, R. Cendejas, M. C. Cervantes, Z. Chajecki, P. Chaloupka, S. Chattopadhyay, H. F. Chen, J. H. Chen, J. Y. Chen, J. Cheng, M. Cherney, A. Chikanian, K. E. Choi, W. Christie, S. U. Chung, R. F. Clarke, M. J. M. Codrington, J. P. Coffin, T. M. Cormier, M. R. Cosentino, J. G. Cramer, H. J. Crawford, D. Das, S. Dash, M. Daugherity, C. D. Silva, T. G. Dedovich, M. DePhillips, A. A. Derevschikov, R. D. de Souza, L. Didenko, P. Djawotho, S. M. Dogra, X. Dong, J. L. Drachenberg, J. E. Draper, F. du, J. C. Dunlop, M. R. D. Mazumdar, "Systematic measurements of identified particle spectra in pp , d + Au, and Au+Au collisions at the STAR detector," Physical Review C, vol. 79 no. 3, article 034909,DOI: 10.1103/PhysRevC.79.034909, 2009.

[23] B. I. Abelev, M. M. Aggarwal, Z. Ahammed, A. V. Alakhverdyants, B. D. Anderson, D. Arkhipkin, G. S. Averichev, J. Balewski, O. Barannikova, L. S. Barnby, S. Baumgart, D. R. Beavis, R. Bellwied, F. Benedosso, M. J. Betancourt, R. R. Betts, A. Bhasin, A. K. Bhati, H. Bichsel, J. Bielcik, J. Bielcikova, B. Biritz, L. C. Bland, I. Bnzarov, B. E. Bonner, J. Bouchet, E. Braidot, A. V. Brandin, A. Bridgeman, E. Bruna, S. Bueltmann, T. P. Burton, X. Z. Cai, H. Caines, M. C. B. Sánchez, O. Catu, D. Cebra, R. Cendejas, M. C. Cervantes, Z. Chajecki, P. Chaloupka, S. Chattopadhyay, H. F. Chen, J. H. Chen, J. Y. Chen, J. Cheng, M. Cherney, A. Chikanian, K. E. Choi, W. Christie, P. Chung, R. F. Clarke, M. J. M. Codrington, R. Corliss, J. G. Cramer, H. J. Crawford, D. Das, S. Dash, L. C. de Silva, R. R. Debbe, T. G. Dedovich, M. DePhillips, A. A. Derevschikov, R. D. de Souza, L. Didenko, P. Djawotho, S. M. Dogra, X. Dong, J. L. Drachenberg, J. E. Draper, J. C. Dunlop, M. R. D. Mazumdar, L. G. Efimov, E. Elhalhuli, M. Elnimr, J. Engelage, G. Eppley, B. Erazmus, M. Estienne, L. Eun, P. Fachini, R. Fatemi, J. Fedorisin, R. G. Fersch, P. Filip, E. Finch, V. Fine, Y. Fisyak, C. A. Gagliardi, D. R. Gangadharan, M. S. Ganti, E. J. Garcia-Solis, A. Geromitsos, F. Geurts, V. Ghazikhanian, P. Ghosh, Y. N. Gorbunov, A. Gordon, O. Grebenyuk, D. Grosnick, B. Grube, S. M. Guertin, A. Gupta, N. Gupta, W. Guryn, B. Haag, T. J. Hallman, A. Hamed, L. . X. Han, J. W. Harris, J. P. Hays-Wehle, M. Heinz, S. Heppelmann, A. Hirsch, E. Hjort, A. M. Hoffman, G. W. Hoffmann, D. J. Hofman, R. S. Hollis, H. Z. Huang, T. J. Humanic, L. Huo, G. Igo, A. Iordanova, P. Jacobs, W. W. Jacobs, P. Jakl, C. Jena, F. Jin, C. L. Jones, P. G. Jones, J. Joseph, E. G. Judd, S. Kabana, K. Kajimoto, K. Kang, J. Kapitan, K. Kauder, D. Keane, A. Kechechyan, D. Kettler, V. Y. Khodyrev, D. P. Kikola, J. Kiryluk, A. Kisiel, S. R. Klein, A. G. Knospe, A. Kocoloski, D. D. Koetke, T. Kollegger, J. Konzer, M. Kopytine, I. Koralt, W. Korsch, L. Kotchenda, V. Kouchpil, P. Kravtsov, V. I. Kravtsov, K. Krueger, M. Krus, L. Kumar, P. Kurnadi, M. A. C. Lamont, J. M. Landgraf, S. LaPointe, J. Lauret, A. Lebedev, R. Lednicky, C. . H. Lee, J. H. Lee, W. Leight, M. J. LeVine, C. Li, N. Li, Y. Li, Z. Li, G. Lin, X. Lin, S. J. Lindenbaum, M. A. Lisa, F. Liu, H. Liu, J. Liu, T. Ljubicic, W. J. Llope, R. S. Longacre, W. A. Love, Y. Lu, T. Ludlam, G. L. Ma, Y. G. Ma, D. P. Mahapatra, R. Majka, O. I. Mall, L. K. Mangotra, R. Manweiler, S. Margetis, C. Markert, H. Masui, H. S. Matis, Y. A. Matulenko, D. McDonald, T. S. McShane, A. Meschanin, R. Milner, N. G. Minaev, S. Mioduszewski, A. Mischke, M. K. Mitrovski, B. Mohanty, D. A. Morozov, M. G. Munhoz, B. K. Nandi, C. Nattrass, T. K. Nayak, J. M. Nelson, P. K. Netrakanti, M. J. Ng, L. V. Nogach, S. B. Nurushev, G. Odyniec, A. Ogawa, H. Okada, V. Okorokov, D. Olson, M. Pachr, B. S. Page, S. K. Pal, Y. Pandit, Y. Panebratsev, T. Pawlak, T. Peitzmann, V. Perevoztchikov, C. Perkins, W. Peryt, S. C. Phatak, P. Pile, M. Planinic, M. A. Ploskon, J. Pluta, D. Plyku, N. Poljak, A. M. Poskanzer, B. V. K. S. Potukuchi, D. Prindle, C. Pruneau, N. K. Pruthi, P. R. Pujahari, J. Putschke, R. Raniwala, S. Raniwala, R. L. Ray, R. Redwine, R. Reed, J. M. Rehberg, A. Ridiger, H. G. Ritter, J. B. Roberts, O. V. Rogachevskiy, J. L. Romero, A. Rose, C. Roy, L. Ruan, M. J. Russcher, R. Sahoo, S. Sakai, I. Sakrejda, T. Sakuma, S. Salur, J. Sandweiss, J. Schambach, R. P. Scharenberg, N. Schmitz, T. R. Schuster, J. Seele, J. Seger, I. Selyuzhenkov, P. Seyboth, E. Shahaliev, M. Shao, M. Sharma, S. S. Shi, E. P. Sichtermann, F. Simon, R. N. Singaraju, M. J. Skoby, N. Smirnov, P. Sorensen, J. Sowinski, H. M. Spinka, B. Srivastava, T. D. S. Stanislaus, D. Staszak, G. S. F. Stephans, R. Stock, M. Strikhanov, B. Stringfellow, A. A. P. Suaide, M. C. Suarez, N. L. Subba, M. Sumbera, X. M. Sun, Y. Sun, Z. Sun, B. Surrow, T. J. M. Symons, A. S. de Toledo, J. Takahashi, A. H. Tang, Z. Tang, L. H. Tarini, T. Tarnowsky, D. Thein, J. H. Thomas, J. Tian, A. R. Timmins, S. Timoshenko, D. Tlusty, M. Tokarev, T. A. Trainor, V. N. Tram, S. Trentalange, R. E. Tribble, O. D. Tsai, J. Ulery, T. Ullrich, D. G. Underwood, G. V. Buren, G. van Nieuwenhuizen, J. A. Vanfossen, R. Varma, G. M. S. Vasconcelos, A. N. Vasiliev, F. Videbaek, Y. P. Viyogi, S. Vokal, S. A. Voloshin, M. Wada, M. Walker, F. Wang, G. Wang, H. Wang, J. S. Wang, Q. Wang, X. Wang, X. L. Wang, Y. Wang, G. Webb, J. C. Webb, G. D. Westfall, C. Whitten, H. Wieman, S. W. Wissink, R. Witt, Y. Wu, W. Xie, N. Xu, Q. H. Xu, W. Xu, Y. Xu, Z. Xu, L. Xue, Y. Yang, P. Yepes, K. Yip, I. . K. Yoo, Q. Yue, M. Zawisza, H. Zbroszczyk, W. Zhan, S. Zhang, W. M. Zhang, X. P. Zhang, Y. Zhang, Z. P. Zhang, Y. Zhao, C. Zhong, J. Zhou, W. Zhou, X. Zhu, Y. . H. Zhu, R. Zoulkarneev, Y. Zoulkarneeva, "Identified particle production, azimuthal anisotropy, and interferometry measurements in Au + Au collisions at s N N = 9.2 GeV," Physical Review C, vol. 81 no. 2, article 024911,DOI: 10.1103/PhysRevC.81.024911, 2010.

[24] Z. Tang, Y. Xu, L. Ruan, G. van Buren, F. Wang, Z. Xu, "Spectra and radial flow in relativistic heavy ion collisions with Tsallis statistics in a blast-wave description," Physical Review C, vol. 79 no. 5, article 051901,DOI: 10.1103/PhysRevC.79.051901, 2009.

[25] Z.-B. Tang, L. Yi, L. J. Ruan, M. Shao, C. Li, H. F. Chen, B. Mohanty, Z. B. Xu, "The statistical origin of constituent-quark scaling in QGP hadronization," Chinese Physics Letters, vol. 30 no. 3, article 031201,DOI: 10.1088/0256-307X/30/3/031201, 2013.

[26] K. Jiang, Y. Zhu, W. Liu, H. Chen, C. Li, L. Ruan, Z. Tang, Z. Xu, "Onset of radial flow in p + p collisions," Physical Review C, vol. 91 no. 2, article 024910,DOI: 10.1103/PhysRevC.91.024910, 2015.

[27] S. Takeuchi, K. Murase, T. Hirano, P. Huovinen, Y. Nara, "Effects of hadronic rescattering on multistrange hadrons in high-energy nuclear collisions," Physical Review C, vol. 92 no. 4, article 044907,DOI: 10.1103/PhysRevC.92.044907, 2015.

[28] H. Heiselberg, A.-M. Levy, "Elliptic flow and Hanbury-Brown–Twiss correlations in noncentral nuclear collisions," Physical Review C, vol. 59 no. 5, pp. 2716-2727, DOI: 10.1103/PhysRevC.59.2716, 1999.

[29] U. W. Heinz, "Hydrodynamics at RHIC: how well does it work, where and how does it break down?," Journal of Physics G: Nuclear and Particle Physics, vol. 31 no. 6, article S717,DOI: 10.1088/0954-3899/31/6/012, 2005.

[30] R. Russo, "Measurement of D+ meson production in pPb collisions with the ALICE detector," . 2015, https://arxiv.org/abs/1511.04380

[31] S. Sadhu, P. Ghosh, "Anomalous features of particle production in high-multiplicity events of pp collisions at the LHC energies," Physical Review D, vol. 99 no. 3, article 034020,DOI: 10.1103/PhysRevD.99.034020, 2019.

[32] G. Bíró, G. Barnaföldi, T. Biró, K. Ürmössy, Á. Takács, "Systematic analysis of the non-extensive statistical approach in high energy particle collisions - experiment vs. theory," Entropy, vol. 19 no. 3, article e19030088,DOI: 10.3390/e19030088, 2017.

[33] H.-R. Wei, F.-H. Liu, R. A. Lacey, "Disentangling random thermal motion of particles and collective expansion of source from transverse momentum spectra in high energy collisions," Journal of Physics G: Nuclear and Particle Physics, vol. 43 no. 12, article 125102,DOI: 10.1088/0954-3899/43/12/125102, 2016.

[34] H.-R. Wei, F.-H. Liu, R. A. Lacey, "Kinetic freeze-out temperature and flow velocity extracted from transverse momentum spectra of final-state light flavor particles produced in collisions at RHIC and LHC," The European Physical Journal A, vol. 52 no. 4,DOI: 10.1140/epja/i2016-16102-6, 2016.

[35] H.-L. Lao, H.-R. Wei, F.-H. Liu, R. A. Lacey, "An evidence of mass-dependent differential kinetic freeze-out scenario observed in Pb-Pb collisions at 2.76 TeV," The European Physical Journal A, vol. 52 no. 7,DOI: 10.1140/epja/i2016-16203-2, 2016.

[36] H.-L. Lao, F.-H. Liu, B.-C. Li, M.-Y. Duan, "Kinetic freeze-out temperatures in central and peripheral collisions: which one is larger?," Nuclear Science and Techniques, vol. 29 no. 6,DOI: 10.1007/s41365-018-0425-x, 2018.

[37] H.-L. Lao, F.-H. Liu, B.-C. Li, M.-Y. Duan, R. A. Lacey, "Examining the model dependence of the determination of kinetic freeze-out temperature and transverse flow velocity in small collision system," Nuclear Science and Techniques, vol. 29 no. 11,DOI: 10.1007/s41365-018-0504-z, 2018.

[38] J. Cleymans, D. Worku, "Relativistic thermodynamics: transverse momentum distributions in high-energy physics," The European Physical Journal A, vol. 48 no. 11,DOI: 10.1140/epja/i2012-12160-0, 2012.

[39] H. Zheng, L. Zhu, "Comparing the Tsallis distribution with and without thermodynamical description in p + p collisions," Advances in High Energy Physics, vol. 2016,DOI: 10.1155/2016/9632126, 2016.

[40] R. Hagedorn, "Multiplicities, p T distributions and the expected hadron → quark-gluon phase transition," La Rivista del Nuovo Cimento, vol. 6 no. 10,DOI: 10.1007/BF02740917, 1983.

[41] ALICE Collaboration, B. Abelev, J. Adam, D. Adamová, M. M. Aggarwal, G. A. Rinella, M. Agnello, A. Agostinelli, N. Agrawal, Z. Ahammed, N. Ahmad, I. Ahmed, S. U. Ahn, S. A. Ahn, I. Aimo, S. Aiola, M. Ajaz, A. Akindinov, S. N. Alam, D. Aleksandrov, B. Alessandro, D. Alexandre, A. Alici, A. Alkin, J. Alme, T. Alt, S. Altinpinar, I. Altsybeev, C. A. G. Prado, C. Andrei, A. Andronic, V. Anguelov, J. Anielski, T. Antičić, F. Antinori, P. Antonioli, L. Aphecetche, H. Appelshäuser, S. Arcelli, N. Armesto, R. Arnaldi, T. Aronsson, I. C. Arsene, M. Arslandok, A. Augustinus, R. Averbeck, T. C. Awes, M. D. Azmi, M. Bach, A. Badalà, Y. W. Baek, S. Bagnasco, R. Bailhache, R. Bala, A. Baldisseri, F. B. D. S. Pedrosa, R. C. Baral, R. Barbera, F. Barile, G. G. Barnaföldi, L. S. Barnby, V. Barret, J. Bartke, M. Basile, N. Bastid, S. Basu, B. Bathen, G. Batigne, A. B. Camejo, B. Batyunya, P. C. Batzing, C. Baumann, I. G. Bearden, H. Beck, C. Bedda, N. K. Behera, I. Belikov, F. Bellini, R. Bellwied, E. Belmont-Moreno, R. Belmont, V. Belyaev, G. Bencedi, S. Beole, I. Berceanu, A. Bercuci, Y. Berdnikov, D. Berenyi, M. E. Berger, R. A. Bertens, D. Berzano, L. Betev, A. Bhasin, I. R. Bhat, A. K. Bhati, B. Bhattacharjee, J. Bhom, L. Bianchi, N. Bianchi, C. Bianchin, J. Bielčík, J. Bielčíková, A. Bilandzic, S. Bjelogrlic, F. Blanco, D. Blau, C. Blume, F. Bock, A. Bogdanov, H. Bøggild, M. Bogolyubsky, F. V. Böhmer, L. Boldizsár, M. Bombara, J. Book, H. Borel, A. Borissov, F. Bossú, M. Botje, E. Botta, S. Böttger, P. Braun-Munzinger, M. Bregant, T. Breitner, T. A. Broker, T. A. Browning, M. Broz, E. Bruna, G. E. Bruno, D. Budnikov, H. Buesching, S. Bufalino, P. Buncic, O. Busch, Z. Buthelezi, D. Caffarri, X. Cai, H. Caines, L. C. Diaz, A. Caliva, E. C. Villar, P. Camerini, F. Carena, W. Carena, J. C. Castellanos, E. A. R. Casula, V. Catanescu, C. Cavicchioli, C. C. Sanchez, J. Cepila, P. Cerello, B. Chang, S. Chapeland, J. L. Charvet, S. Chattopadhyay, S. Chattopadhyay, V. Chelnokov, M. Cherney, C. Cheshkov, B. Cheynis, V. C. Barroso, D. D. Chinellato, P. Chochula, M. Chojnacki, S. Choudhury, P. Christakoglou, C. H. Christensen, P. Christiansen, T. Chujo, S. U. Chung, C. Cicalo, L. Cifarelli, F. Cindolo, J. Cleymans, F. Colamaria, D. Colella, A. Collu, M. Colocci, G. C. Balbastre, Z. C. del Valle, M. E. Connors, J. G. Contreras, T. M. Cormier, Y. C. Morales, P. Cortese, I. C. Maldonado, M. R. Cosentino, F. Costa, P. Crochet, R. C. Albino, E. Cuautle, L. Cunqueiro, A. Dainese, R. Dang, A. Danu, D. Das, I. Das, K. Das, S. Das, A. Dash, S. De Dash, H. Delagrange, A. Deloff, E. Dénes, G. D’Erasmo, A. De Caro, G. de Cataldo, J. de Cuveland, A. De Falco, D. De Gruttola, N. De Marco, S. De Pasquale, R. de Rooij, M. A. D. Corchero, T. Dietel, P. Dillenseger, R. Divià, D. Di Bari, S. Di Liberto, A. Di Mauro, P. Di Nezza, Ø. Djuvsland, A. Dobrin, T. Dobrowolski, D. D. Gimenez, B. Dönigus, O. Dordic, S. Dørheim, A. K. Dubey, A. Dubla, L. Ducroux, P. Dupieux, A. K. D. Majumdar, T. E. Hilden, R. J. Ehlers, D. Elia, H. Engel, B. Erazmus, H. A. Erdal, D. Eschweiler, B. Espagnon, M. Esposito, M. Estienne, S. Esumi, D. Evans, S. Evdokimov, D. Fabris, J. Faivre, D. Falchieri, A. Fantoni, M. Fasel, D. Fehlker, L. Feldkamp, D. Felea, A. Feliciello, G. Feofilov, J. Ferencei, A. F. Téllez, E. G. Ferreiro, A. Ferretti, A. Festanti, J. Figiel, M. A. S. Figueredo, S. Filchagin, D. Finogeev, F. M. Fionda, E. M. Fiore, E. Floratos, M. Floris, S. Foertsch, P. Foka, S. Fokin, E. Fragiacomo, A. Francescon, U. Frankenfeld, U. Fuchs, C. Furget, A. Furs, M. F. Girard, J. J. Gaardhøje, M. Gagliardi, A. M. Gago, M. Gallio, D. R. Gangadharan, P. Ganoti, C. Gao, C. Garabatos, E. Garcia-Solis, C. Gargiulo, I. Garishvili, J. Gerhard, M. Germain, A. Gheata, M. Gheata, B. Ghidini, P. Ghosh, S. K. Ghosh, P. Gianotti, P. Giubellino, E. Gladysz-Dziadus, P. Glässel, A. G. Ramirez, P. González-Zamora, S. Gorbunov, L. Görlich, S. Gotovac, L. K. Graczykowski, A. Grelli, A. Grigoras, C. Grigoras, V. Grigoriev, A. Grigoryan, S. Grigoryan, B. Grinyov, N. Grion, J. F. Grosse-Oetringhaus, J.-Y. Grossiord, R. Grosso, F. Guber, R. Guernane, B. Guerzoni, M. Guilbaud, K. Gulbrandsen, H. Gulkanyan, M. Gumbo, T. Gunji, A. Gupta, R. Gupta, K. H. Khan, R. Haake, Ø. Haaland, C. Hadjidakis, M. Haiduc, H. Hamagaki, G. Hamar, L. D. Hanratty, A. Hansen, J. W. Harris, H. Hartmann, A. Harton, D. Hatzifotiadou, S. Hayashi, S. T. Heckel, M. Heide, H. Helstrup, A. Herghelegiu, G. H. Corral, B. A. Hess, K. F. Hetland, B. Hippolyte, J. Hladky, P. Hristov, M. Huang, T. J. Humanic, N. Hussain, T. Hussain, D. Hutter, D. S. Hwang, R. Ilkaev, I. Ilkiv, M. Inaba, G. M. Innocenti, C. Ionita, M. Ippolitov, M. Irfan, M. Ivanov, V. Ivanov, A. Jachołkowski, P. M. Jacobs, C. Jahnke, H. J. Jang, M. A. Janik, P. H. S. Y. Jayarathna, C. Jena, S. Jena, R. T. J. Bustamante, P. G. Jones, H. Jung, A. Jusko, V. Kadyshevskiy, P. Kalinak, A. Kalweit, J. Kamin, J. H. Kang, V. Kaplin, S. Kar, A. K. Uysal, O. Karavichev, T. Karavicheva, E. Karpechev, U. Kebschull, R. Keidel, D. L. D. Keijdener, M. S. V. N. Keil, M. M. Khan, P. Khan, S. A. Khan, A. Khanzadeev, Y. Kharlov, B. Kileng, B. Kim, D. W. Kim, D. J. Kim, J. S. Kim, M. Kim, S. Kim, T. Kim, S. Kirsch, I. Kisel, S. Kiselev, A. Kisiel, G. Kiss, J. L. Klay, J. Klein, C. Klein-Bösing, A. Kluge, M. L. Knichel, A. G. Knospe, C. Kobdaj, M. Kofarago, M. K. Köhler, T. Kollegger, A. Kolojvari, V. Kondratiev, N. Kondratyeva, A. Konevskikh, V. Kovalenko, M. Kowalski, S. Kox, G. K. Meethaleveedu, J. Kral, I. Králik, A. Kravčáková, M. Krelina, M. Kretz, M. Krivda, F. Krizek, E. Kryshen, M. Krzewicki, V. Kučera, Y. Kucheriaev, T. Kugathasan, C. Kuhn, P. G. Kuijer, I. Kulakov, J. Kumar, P. Kurashvili, A. Kurepin, A. B. Kurepin, A. Kuryakin, S. Kushpil, M. J. Kweon, Y. Kwon, P. L. de Guevara, C. L. Fernandes, I. Lakomov, R. Langoy, C. Lara, A. Lardeux, A. Lattuca, S. L. La Pointe, P. La Rocca, R. Lea, L. Leardini, G. R. Lee, I. Legrand, J. Lehnert, R. C. Lemmon, V. Lenti, E. Leogrande, M. Leoncino, I. L. Monzón, P. Lévai, S. Li, J. Lien, R. Lietava, S. Lindal, V. Lindenstruth, C. Lippmann, M. A. Lisa, H. M. Ljunggren, D. F. Lodato, P. I. Loenne, V. R. Loggins, V. Loginov, D. Lohner, C. Loizides, X. Lopez, E. L. Torres, X.-G. Lu, P. Luettig, M. Lunardon, G. Luparello, R. Ma, A. Maevskaya, M. Mager, D. P. Mahapatra, S. M. Mahmood, A. Maire, R. D. Majka, M. Malaev, I. M. Cervantes, L. Malinina, D. Mal’Kevich, P. Malzacher, A. Mamonov, L. Manceau, V. Manko, F. Manso, V. Manzari, M. Marchisone, J. Mareš, G. V. Margagliotti, A. Margotti, A. Marín, C. Markert, M. Marquard, I. Martashvili, N. A. Martin, P. Martinengo, M. I. Martínez, G. M. García, J. M. Blanco, Y. Martynov, A. Mas, S. Masciocchi, M. Masera, A. Masoni, L. Massacrier, A. Mastroserio, A. Matyja, C. Mayer, J. Mazer, M. A. Mazzoni, F. Meddi, A. Menchaca-Rocha, E. Meninno, J. M. Pérez, M. Meres, Y. Miake, K. Mikhaylov, L. Milano, J. Milosevic, A. Mischke, A. N. Mishra, D. Miśkowiec, J. Mitra, C. M. Mitu, J. Mlynarz, N. Mohammadi, B. Mohanty, L. Molnar, L. M. Zetina, E. Montes, M. Morando, D. A. M. De Godoy, S. Moretto, A. Morreale, A. Morsch, V. Muccifora, E. Mudnic, D. Mühlheim, S. Muhuri, M. Mukherjee, H. Müller, M. G. Munhoz, S. Murray, L. Musa, J. Musinsky, B. K. Nandi, R. Nania, E. Nappi, C. Nattrass, K. Nayak, T. K. Nayak, S. Nazarenko, A. Nedosekin, M. Nicassio, M. Niculescu, J. Niedziela, B. S. Nielsen, S. Nikolaev, S. Nikulin, V. Nikulin, B. S. Nilsen, F. Noferini, P. Nomokonov, G. Nooren, J. Norman, A. Nyanin, J. Nystrand, H. Oeschler, S. Oh, S. K. Oh, A. Okatan, T. Okubo, L. Olah, J. Oleniacz, A. C. O. Da Silva, J. Onderwaater, C. Oppedisano, A. O. Velasquez, A. Oskarsson, J. Otwinowski, K. Oyama, M. Ozdemir, P. Sahoo, Y. Pachmayer, M. Pachr, P. Pagano, G. Paić, C. Pajares, S. K. Pal, A. Palmeri, D. Pant, V. Papikyan, G. S. Pappalardo, P. Pareek, W. J. Park, S. Parmar, A. Passfeld, D. I. Patalakha, V. Paticchio, B. Paul, T. Pawlak, T. Peitzmann, H. P. Da Costa, E. P. D. O. Filho, D. Peresunko, C. E. P. Lara, A. Pesci, V. Peskov, Y. Pestov, V. Petráček, M. Petran, M. Petris, M. Petrovici, C. Petta, S. Piano, M. Pikna, P. Pillot, O. Pinazza, L. Pinsky, D. B. Piyarathna, M. Płoskoń, M. Planinic, J. Pluta, S. Pochybova, P. L. M. Podesta-Lerma, M. G. Poghosyan, E. H. O. Pohjoisaho, B. Polichtchouk, N. Poljak, A. Pop, S. Porteboeuf-Houssais, J. Porter, B. Potukuchi, S. K. Prasad, R. Preghenella, F. Prino, C. A. Pruneau, I. Pshenichnov, M. Puccio, G. Puddu, P. Pujahari, V. Punin, J. Putschke, H. Qvigstad, A. Rachevski, S. Raha, S. Rajput, J. Rak, A. Rakotozafindrabe, L. Ramello, R. Raniwala, S. Raniwala, S. Räsänen, B. T. Rascanu, D. Rathee, A. W. Rauf, V. Razazi, K. F. Read, J. S. Real, K. Redlich, R. J. Reed, A. Rehman, P. Reichelt, M. Reicher, F. Reidt, R. Renfordt, A. R. Reolon, A. Reshetin, F. Rettig, J.-P. Revol, K. Reygers, V. Riabov, R. A. Ricci, T. Richert, M. Richter, P. Riedler, W. Riegler, F. Riggi, A. Rivetti, E. Rocco, M. R. Cahuantzi, A. R. Manso, K. Røed, E. Rogochaya, S. Rohni, D. Rohr, D. Röhrich, R. Romita, F. Ronchetti, L. Ronflette, P. Rosnet, A. Rossi, F. Roukoutakis, A. Roy, C. Roy, P. Roy, A. J. R. Montero, R. Rui, R. Russo, E. Ryabinkin, Y. Ryabov, A. Rybicki, S. Sadovsky, K. Šafařík, B. Sahlmuller, R. Sahoo, P. K. Sahu, J. Saini, S. Sakai, C. A. Salgado, J. Salzwedel, S. Sambyal, V. Samsonov, X. S. Castro, F. J. S. Rodríguez, L. Šándor, A. Sandoval, M. Sano, G. Santagati, D. Sarkar, E. Scapparone, F. Scarlassara, R. P. Scharenberg, C. Schiaua, R. Schicker, C. Schmidt, H. R. Schmidt, S. Schuchmann, J. Schukraft, M. Schulc, T. Schuster, Y. Schutz, K. Schwarz, K. Schweda, G. Scioli, E. Scomparin, R. Scott, G. Segato, J. E. Seger, Y. Sekiguchi, I. Selyuzhenkov, K. Senosi, J. Seo, E. Serradilla, A. Sevcenco, A. Shabetai, G. Shabratova, R. Shahoyan, A. Shangaraev, A. Sharma, N. Sharma, S. Sharma, K. Shigaki, K. Shtejer, Y. Sibiriak, S. Siddhanta, T. Siemiarczuk, D. Silvermyr, C. Silvestre, G. Simatovic, R. Singaraju, R. Singh, S. Singha, V. Singhal, B. C. Sinha, T. Sinha, B. Sitar, M. Sitta, T. B. Skaali, K. Skjerdal, M. Slupecki, N. Smirnov, R. J. M. Snellings, C. Søgaard, R. Soltz, J. Song, M. Song, F. Soramel, S. Sorensen, M. Spacek, E. Spiriti, I. Sputowska, M. Spyropoulou-Stassinaki, B. K. Srivastava, J. Stachel, I. Stan, G. Stefanek, M. Steinpreis, E. Stenlund, G. Steyn, J. H. Stiller, D. Stocco, M. Stolpovskiy, P. Strmen, A. A. P. Suaide, T. Sugitate, C. Suire, M. Suleymanov, R. Sultanov, M. Šumbera, T. J. M. Symons, A. Szabo, A. S. de Toledo, I. Szarka, A. Szczepankiewicz, M. Szymanski, J. Takahashi, M. A. Tangaro, J. D. T. Takaki, A. T. Peloni, A. T. Martinez, M. Tariq, M. G. Tarzila, A. Tauro, G. T. Muñoz, A. Telesca, K. Terasaki, C. Terrevoli, J. Thäder, D. Thomas, R. Tieulent, A. R. Timmins, A. Toia, V. Trubnikov, W. H. Trzaska, T. Tsuji, A. Tumkin, R. Turrisi, T. S. Tveter, K. Ullaland, A. Uras, G. L. Usai, M. Vajzer, M. Vala, L. V. Palomo, S. Vallero, P. V. Vyvre, J. Van Der Maarel, J. W. Van Hoorne, M. van Leeuwen, A. Vargas, M. Vargyas, R. Varma, M. Vasileiou, A. Vasiliev, V. Vechernin, M. Veldhoen, A. Velure, M. Venaruzzo, E. Vercellin, S. V. Limón, R. Vernet, M. Verweij, L. Vickovic, G. Viesti, J. Viinikainen, Z. Vilakazi, O. V. Baillie, A. Vinogradov, L. Vinogradov, Y. Vinogradov, T. Virgili, V. Vislavicius, Y. P. Viyogi, A. Vodopyanov, M. A. Völkl, K. Voloshin, S. A. Voloshin, G. Volpe, B. von Haller, I. Vorobyev, D. Vranic, J. Vrláková, B. Vulpescu, A. Vyushin, B. Wagner, J. Wagner, V. Wagner, M. Wang, Y. Wang, D. Watanabe, M. Weber, S. G. Weber, J. P. Wessels, U. Westerhoff, J. Wiechula, J. Wikne, M. Wilde, G. Wilk, J. Wilkinson, M. C. S. Williams, B. Windelband, M. Winn, C. G. Yaldo, Y. Yamaguchi, H. Yang, P. Yang, S. Yang, S. Yano, S. Yasnopolskiy, J. Yi, Z. Yin, I.-K. Yoo, I. Yushmanov, V. Zaccolo, C. Zach, A. Zaman, C. Zampolli, S. Zaporozhets, A. Zarochentsev, P. Závada, N. Zaviyalov, H. Zbroszczyk, I. S. Zgura, M. Zhalov, H. Zhang, X. Zhang, Y. Zhang, C. Zhao, N. Zhigareva, D. Zhou, F. Zhou, Y. Zhou, Z. Zhuo, H. Zhu, J. Zhu, X. Zhu, A. Zichichi, A. Zimmermann, M. B. Zimmermann, G. Zinovjev, Y. Zoccarato, M. Zyzak, "Production of ∑ 1385 ± and Ξ 1530 0 in proton–proton collisions at s = 7 TeV," The European Physical Journal C, vol. 75 no. 1,DOI: 10.1140/epjc/s10052-014-3191-x, 2015.

[42] R. L. Ray, A. Jentsch, "Phenomenological models of two-particle correlation distributions on transverse momentum in relativistic heavy-ion collisions," Physical Review C, vol. 99 no. 2, article 024911,DOI: 10.1103/PhysRevC.99.024911, 2019.

[43] The CMS Collaboration, S. Chatrchyan, V. Khachatryan, A. M. Sirunyan, A. Tumasyan, W. Adam, T. Bergauer, M. Dragicevic, J. Erö, C. Fabjan, M. Friedl, R. Frühwirth, V. M. Ghete, J. Hammer, M. Hoch, N. Hörmann, J. Hrubec, M. Jeitler, W. Kiesenhofer, M. Krammer, D. Liko, I. Mikulec, M. Pernicka, B. Rahbaran, C. Rohringer, H. Rohringer, R. Schöfbeck, J. Strauss, A. Taurok, F. Teischinger, P. Wagner, W. Waltenberger, G. Walzel, E. Widl, C.-E. Wulz, V. Mossolov, N. Shumeiko, J. S. Gonzalez, S. Bansal, L. Benucci, T. Cornelis, E. A. De Wolf, X. Janssen, S. Luyckx, T. Maes, L. Mucibello, S. Ochesanu, B. Roland, R. Rougny, M. Selvaggi, H. Van Haevermaet, P. Van Mechelen, N. Van Remortel, A. Van Spilbeeck, F. Blekman, S. Blyweert, J. D’Hondt, R. G. Suarez, A. Kalogeropoulos, M. Maes, A. Olbrechts, W. Van Doninck, P. Van Mulders, G. P. Van Onsem, I. Villella, O. Charaf, B. Clerbaux, G. De Lentdecker, V. Dero, A. P. R. Gay, G. H. Hammad, T. Hreus, A. Léonard, P. E. Marage, L. Thomas, C. V. Velde, P. Vanlaer, J. Wickens, V. Adler, K. Beernaert, A. Cimmino, S. Costantini, G. Garcia, M. Grunewald, B. Klein, J. Lellouch, A. Marinov, J. Mccartin, A. A. O. Rios, D. Ryckbosch, N. Strobbe, F. Thyssen, M. Tytgat, L. Vanelderen, P. Verwilligen, S. Walsh, E. Yazgan, N. Zaganidis, S. Basegmez, G. Bruno, L. Ceard, J. D. F. De Jeneret, C. Delaere, T. du Pree, D. Favart, L. Forthomme, A. Giammanco, G. Grégoire, J. Hollar, V. Lemaitre, J. Liao, O. Militaru, C. Nuttens, D. Pagano, A. Pin, K. Piotrzkowski, N. Schul, N. Beliy, T. Caebergs, E. Daubie, G. A. Alves, D. D. J. Damiao, T. Martins, M. E. Pol, M. H. G. Souza, W. L. A. Júnior, W. Carvalho, A. Custódio, E. M. Da Costa, C. D. O. Martins, S. F. De Souza, D. M. Figueiredo, L. Mundim, H. Nogima, V. Oguri, W. L. Prado Da Silva, A. Santoro, S. M. S. Do Amaral, L. S. Jorge, A. Sznajder, T. S. Anjos, C. A. Bernardes, F. A. Dias, T. R. F. P. Tomei, E. M. Gregores, C. Lagana, F. Marinho, P. G. Mercadante, S. F. Novaes, S. S. Padula, V. Genchev, P. Iaydjiev, S. Piperov, M. Rodozov, S. Stoykova, G. Sultanov, V. Tcholakov, R. Trayanov, M. Vutova, A. Dimitrov, R. Hadjiiska, A. Karadzhinova, V. Kozhuharov, L. Litov, B. Pavlov, P. Petkov, J. G. Bian, G. M. Chen, H. S. Chen, C. H. Jiang, D. Liang, S. Liang, X. Meng, J. Tao, J. Wang, J. Wang, X. Wang, Z. Wang, H. Xiao, M. Xu, J. Zang, Z. Zhang, C. Asawatangtrakuldee, Y. Ban, S. Guo, Y. Guo, W. Li, S. Liu, Y. Mao, S. J. Qian, H. Teng, S. Wang, B. Zhu, W. Zou, A. Cabrera, B. G. Moreno, A. F. O. Oliveros, J. C. Sanabria, N. Godinovic, D. Lelas, R. Plestina, D. Polic, I. Puljak, Z. Antunovic, M. Dzelalija, M. Kovac, V. Brigljevic, S. Duric, K. Kadija, J. Luetic, S. Morovic, A. Attikis, M. Galanti, J. Mousa, C. Nicolaou, F. Ptochos, P. A. Razis, M. Finger, M. Finger, Y. Assran, A. E. Kamel, S. Khalil, M. A. Mahmoud, A. Radi, A. Hektor, M. Kadastik, M. Müntel, M. Raidal, L. Rebane, A. Tiko, V. Azzolini, P. Eerola, G. Fedi, M. Voutilainen, S. Czellar, J. Härkönen, A. Heikkinen, V. Karimäki, R. Kinnunen, M. J. Kortelainen, T. Lampén, K. Lassila-Perini, S. Lehti, T. Lindén, P. Luukka, T. Mäenpää, T. Peltola, E. Tuominen, J. Tuominiemi, E. Tuovinen, D. Ungaro, L. Wendland, K. Banzuzi, A. Korpela, T. Tuuva, D. Sillou, M. Besancon, S. Choudhury, M. Dejardin, D. Denegri, B. Fabbro, J. L. Faure, F. Ferri, S. Ganjour, A. Givernaud, P. Gras, G. H. de Monchenault, P. Jarry, E. Locci, J. Malcles, M. Marionneau, L. Millischer, J. Rander, A. Rosowsky, I. Shreyber, M. Titov, S. Baffioni, F. Beaudette, L. Benhabib, L. Bianchini, M. Bluj, C. Broutin, P. Busson, C. Charlot, N. Daci, T. Dahms, L. Dobrzynski, S. Elgammal, R. G. de Cassagnac, M. Haguenauer, P. Miné, C. Mironov, C. Ochando, P. Paganini, D. Sabes, R. Salerno, Y. Sirois, C. Thiebaux, C. Veelken, A. Zabi, J.-L. Agram, J. Andrea, D. Bloch, D. Bodin, J.-M. Brom, M. Cardaci, E. C. Chabert, C. Collard, E. Conte, F. Drouhin, C. Ferro, J.-C. Fontaine, D. Gelé, U. Goerlach, S. Greder, P. Juillot, M. Karim, A.-C. Le Bihan, P. Van Hove, F. Fassi, D. Mercier, C. Baty, S. Beauceron, N. Beaupere, M. Bedjidian, O. Bondu, G. Boudoul, D. Boumediene, H. Brun, J. Chasserat, R. Chierici, D. Contardo, P. Depasse, H. El Mamouni, A. Falkiewicz, J. Fay, S. Gascon, M. Gouzevitch, B. Ille, T. Kurca, T. Le Grand, M. Lethuillier, L. Mirabito, S. Perries, V. Sordini, S. Tosi, Y. Tschudi, P. Verdier, S. Viret, D. Lomidze, G. Anagnostou, S. Beranek, M. Edelhoff, L. Feld, N. Heracleous, O. Hindrichs, R. Jussen, K. Klein, J. Merz, A. Ostapchuk, A. Perieanu, F. Raupach, J. Sammet, S. Schael, D. Sprenger, H. Weber, B. Wittmer, V. Zhukov, M. Ata, J. Caudron, E. Dietz-Laursonn, M. Erdmann, A. Güth, T. Hebbeker, C. Heidemann, K. Hoepfner, T. Klimkovich, D. Klingebiel, P. Kreuzer, D. Lanske, J. Lingemann, C. Magass, M. Merschmeyer, A. Meyer, M. Olschewski, P. Papacz, H. Pieta, H. Reithler, S. A. Schmitz, L. Sonnenschein, J. Steggemann, D. Teyssier, M. Weber, M. Bontenackels, V. Cherepanov, M. Davids, G. Flügge, H. Geenen, M. Geisler, W. H. Ahmad, F. Hoehle, B. Kargoll, T. Kress, Y. Kuessel, A. Linn, A. Nowack, L. Perchalla, O. Pooth, J. Rennefeld, P. Sauerland, A. Stahl, M. H. Zoeller, M. A. Martin, W. Behrenhoff, U. Behrens, M. Bergholz, A. Bethani, K. Borras, A. Cakir, A. Campbell, E. Castro, D. Dammann, G. Eckerlin, D. Eckstein, A. Flossdorf, G. Flucke, A. Geiser, J. Hauk, H. Jung, M. Kasemann, P. Katsas, C. Kleinwort, H. Kluge, A. Knutsson, M. Krämer, D. Krücker, E. Kuznetsova, W. Lange, W. Lohmann, B. Lutz, R. Mankel, I. Marfin, M. Marienfeld, I.-A. Melzer-Pellmann, A. B. Meyer, J. Mnich, A. Mussgiller, S. Naumann-Emme, J. Olzem, A. Petrukhin, D. Pitzl, A. Raspereza, P. M. R. Cipriano, M. Rosin, J. Salfeld-Nebgen, R. Schmidt, T. Schoerner-Sadenius, N. Sen, A. Spiridonov, M. Stein, J. Tomaszewska, R. Walsh, C. Wissing, C. Autermann, V. Blobel, S. Bobrovskyi, J. Draeger, H. Enderle, J. Erfle, U. Gebbert, M. Görner, T. Hermanns, R. S. Höing, K. Kaschube, G. Kaussen, H. Kirschenmann, R. Klanner, J. Lange, B. Mura, F. Nowak, N. Pietsch, C. Sander, H. Schettler, P. Schleper, E. Schlieckau, A. Schmidt, M. Schröder, T. Schum, H. Stadie, G. Steinbrück, J. Thomsen, C. Barth, J. Berger, T. Chwalek, W. De Boer, A. Dierlamm, G. Dirkes, M. Feindt, J. Gruschke, M. Guthoff, C. Hackstein, F. Hartmann, M. Heinrich, H. Held, K. H. Hoffmann, S. Honc, I. Katkov, J. R. Komaragiri, T. Kuhr, D. Martschei, S. Mueller, T. Müller, M. Niegel, O. Oberst, A. Oehler, J. Ott, T. Peiffer, G. Quast, K. Rabbertz, F. Ratnikov, N. Ratnikova, M. Renz, S. Röcker, C. Saout, A. Scheurer, P. Schieferdecker, F.-P. Schilling, M. Schmanau, G. Schott, H. J. Simonis, F. M. Stober, D. Troendle, J. Wagner-Kuhr, T. Weiler, M. Zeise, E. B. Ziebarth, G. Daskalakis, T. Geralis, S. Kesisoglou, A. Kyriakis, D. Loukas, I. Manolakos, A. Markou, C. Markou, C. Mavrommatis, E. Ntomari, L. Gouskos, T. J. Mertzimekis, A. Panagiotou, N. Saoulidou, E. Stiliaris, I. Evangelou, C. Foudas, P. Kokkas, N. Manthos, I. Papadopoulos, V. Patras, F. A. Triantis, A. Aranyi, G. Bencze, L. Boldizsar, C. Hajdu, P. Hidas, D. Horvath, A. Kapusi, K. Krajczar, F. Sikler, G. Vesztergombi, N. Beni, J. Molnar, J. Palinkas, Z. Szillasi, V. Veszpremi, J. Karancsi, P. Raics, Z. L. Trocsanyi, B. Ujvari, S. B. Beri, V. Bhatnagar, N. Dhingra, R. Gupta, M. Jindal, M. Kaur, J. M. Kohli, M. Z. Mehta, N. Nishu, L. K. Saini, A. Sharma, A. P. Singh, J. Singh, S. P. Singh, S. Ahuja, B. C. Choudhary, A. Kumar, A. Kumar, S. Malhotra, M. Naimuddin, K. Ranjan, V. Sharma, R. K. Shivpuri, S. Banerjee, S. Bhattacharya, S. Dutta, B. Gomber, S. Jain, S. Jain, R. Khurana, S. Sarkar, R. K. Choudhury, D. Dutta, S. Kailas, V. Kumar, A. K. Mohanty, L. M. Pant, P. Shukla, T. Aziz, S. Ganguly, M. Guchait, A. Gurtu, M. Maity, G. Majumder, K. Mazumdar, G. B. Mohanty, B. Parida, A. Saha, K. Sudhakar, N. Wickramage, S. Banerjee, S. Dugad, N. K. Mondal, H. Arfaei, H. Bakhshiansohi, S. M. Etesami, A. Fahim, M. Hashemi, H. Hesari, A. Jafari, M. Khakzad, A. Mohammadi, M. M. Najafabadi, S. P. Mehdiabadi, B. Safarzadeh, M. Zeinali, M. Abbrescia, L. Barbone, C. Calabria, S. S. Chhibra, A. Colaleo, D. Creanza, N. De Filippis, M. De Palma, L. Fiore, G. Iaselli, L. Lusito, G. Maggi, M. Maggi, N. Manna, B. Marangelli, S. My, S. Nuzzo, N. Pacifico, A. Pompili, G. Pugliese, F. Romano, G. Selvaggi, L. Silvestris, G. Singh, S. Tupputi, G. Zito, G. Abbiendi, A. C. Benvenuti, D. Bonacorsi, S. Braibant-Giacomelli, L. Brigliadori, P. Capiluppi, A. Castro, F. R. Cavallo, M. Cuffiani, G. M. Dallavalle, F. Fabbri, A. Fanfani, D. Fasanella, P. Giacomelli, C. Grandi, S. Marcellini, G. Masetti, M. Meneghelli, A. Montanari, F. L. Navarria, F. Odorici, A. Perrotta, F. Primavera, A. M. Rossi, T. Rovelli, G. Siroli, R. Travaglini, S. Albergo, G. Cappello, M. Chiorboli, S. Costa, R. Potenza, A. Tricomi, C. Tuve, G. Barbagli, V. Ciulli, C. Civinini, R. D’Alessandro, E. Focardi, S. Frosali, E. Gallo, S. Gonzi, M. Meschini, S. Paoletti, G. Sguazzoni, A. Tropiano, L. Benussi, S. Bianco, S. Colafranceschi, F. Fabbri, D. Piccolo, P. Fabbricatore, R. Musenich, A. Benaglia, F. De Guio, L. Di Matteo, S. Fiorendi, S. Gennai, A. Ghezzi, S. Malvezzi, R. A. Manzoni, A. Martelli, A. Massironi, D. Menasce, L. Moroni, M. Paganoni, D. Pedrini, S. Ragazzi, N. Redaelli, S. Sala, T. T. de Fatis, S. Buontempo, C. A. C. Montoya, N. Cavallo, A. De Cosa, O. Dogangun, F. Fabozzi, A. O. M. Iorio, L. Lista, M. Merola, P. Paolucci, P. Azzi, N. Bacchetta, P. Bellan, D. Bisello, A. Branca, R. Carlin, P. Checchia, T. Dorigo, U. Dosselli, F. Gasparini, U. Gasparini, A. Gozzelino, K. Kanishchev, S. Lacaprara, I. Lazzizzera, M. Margoni, M. Mazzucato, A. T. Meneguzzo, M. Michelotto, M. Nespolo, L. Perrozzi, N. Pozzobon, P. Ronchese, F. Simonetto, E. Torassa, M. Tosi, S. Vanini, P. Zotto, G. Zumerle, P. Baesso, U. Berzano, S. P. Ratti, C. Riccardi, P. Torre, P. Vitulo, C. Viviani, M. Biasini, G. M. Bilei, B. Caponeri, L. Fanò, P. Lariccia, A. Lucaroni, G. Mantovani, M. Menichelli, A. Nappi, F. Romeo, A. Santocchia, S. Taroni, M. Valdata, P. Azzurri, G. Bagliesi, T. Boccali, G. Broccolo, R. Castaldi, R. T. D’Agnolo, R. Dell’Orso, F. Fiori, L. Foà, A. Giassi, A. Kraan, F. Ligabue, T. Lomtadze, L. Martini, A. Messineo, F. Palla, F. Palmonari, A. Rizzi, A. T. Serban, P. Spagnolo, R. Tenchini, G. Tonelli, A. Venturi, P. G. Verdini, L. Barone, F. Cavallari, D. Del Re, M. Diemoz, C. Fanelli, D. Franci, M. Grassi, E. Longo, P. Meridiani, F. Micheli, S. Nourbakhsh, G. Organtini, F. Pandolfi, R. Paramatti, S. Rahatlou, M. Sigamani, L. Soffi, N. Amapane, R. Arcidiacono, S. Argiro, M. Arneodo, C. Biino, C. Botta, N. Cartiglia, R. Castello, M. Costa, N. Demaria, A. Graziano, C. Mariotti, S. Maselli, E. Migliore, V. Monaco, M. Musich, M. M. Obertino, N. Pastrone, M. Pelliccioni, A. Potenza, A. Romero, M. Ruspa, R. Sacchi, V. Sola, A. Solano, A. Staiano, A. V. Pereira, S. Belforte, F. Cossutti, G. D. Ricca, B. Gobbo, M. Marone, D. Montanino, A. Penzo, S. G. Heo, S. K. Nam, S. Chang, J. Chung, D. H. Kim, G. N. Kim, J. E. Kim, D. J. Kong, H. Park, S. R. Ro, D. C. Son, J. Y. Kim, Z. J. Kim, S. Song, H. Y. Jo, S. Choi, D. Gyun, B. Hong, M. Jo, H. Kim, T. J. Kim, K. S. Lee, D. H. Moon, S. K. Park, E. Seo, K. S. Sim, M. Choi, S. Kang, H. Kim, J. H. Kim, C. Park, I. C. Park, S. Park, G. Ryu, Y. Cho, Y. Choi, Y. K. Choi, J. Goh, M. S. Kim, B. Lee, J. Lee, S. Lee, H. Seo, I. Yu, M. J. Bilinskas, I. Grigelionis, M. Janulis, H. Castilla-Valdez, E. De La Cruz-Burelo, I. H. de La Cruz, R. Lopez-Fernandez, R. M. Villalba, J. Martínez-Ortega, A. Sánchez-Hernández, L. M. Villasenor-Cendejas, S. C. Moreno, F. V. Valencia, H. A. S. Ibarguen, E. C. Linares, A. M. Pineda, M. A. Reyes-Santos, D. Krofcheck, A. J. Bell, P. H. Butler, R. Doesburg, S. Reucroft, H. Silverwood, M. Ahmad, M. I. Asghar, H. R. Hoorani, S. Khalid, W. A. Khan, T. Khurshid, S. Qazi, M. A. Shah, M. Shoaib, G. Brona, M. Cwiok, W. Dominik, K. Doroba, A. Kalinowski, M. Konecki, J. Krolikowski, H. Bialkowska, B. Boimska, T. Frueboes, R. Gokieli, M. Górski, M. Kazana, K. Nawrocki, K. Romanowska-Rybinska, M. Szleper, G. Wrochna, P. Zalewski, N. Almeida, P. Bargassa, A. David, P. Faccioli, P. G. F. Parracho, M. Gallinaro, P. Musella, A. Nayak, J. Pela, P. Q. Ribeiro, J. Seixas, J. Varela, P. Vischia, S. Afanasiev, I. Belotelov, P. Bunin, M. Gavrilenko, I. Golutvin, I. Gorbunov, A. Kamenev, V. Karjavin, G. Kozlov, A. Lanev, P. Moisenz, V. Palichik, V. Perelygin, S. Shmatov, V. Smirnov, A. Volodko, A. Zarubin, S. Evstyukhin, V. Golovtsov, Y. Ivanov, V. Kim, P. Levchenko, V. Murzin, V. Oreshkin, I. Smirnov, V. Sulimov, L. Uvarov, S. Vavilov, A. Vorobyev, A. Vorobyev, Y. Andreev, A. Dermenev, S. Gninenko, N. Golubev, M. Kirsanov, N. Krasnikov, V. Matveev, A. Pashenkov, A. Toropin, S. Troitsky, V. Epshteyn, M. Erofeeva, V. Gavrilov, M. Kossov, A. Krokhotin, N. Lychkovskaya, V. Popov, G. Safronov, S. Semenov, V. Stolin, E. Vlasov, A. Zhokin, A. Belyaev, E. Boos, A. Ershov, A. Gribushin, O. Kodolova, V. Korotkikh, I. Lokhtin, A. Markina, S. Obraztsov, M. Perfilov, S. Petrushanko, L. Sarycheva, V. Savrin, A. Snigirev, I. Vardanyan, V. Andreev, M. Azarkin, I. Dremin, M. Kirakosyan, A. Leonidov, G. Mesyats, S. V. Rusakov, A. Vinogradov, I. Azhgirey, I. Bayshev, S. Bitioukov, V. Grishin, V. Kachanov, D. Konstantinov, A. Korablev, V. Krychkine, V. Petrov, R. Ryutin, A. Sobol, L. Tourtchanovitch, S. Troshin, N. Tyurin, A. Uzunian, A. Volkov, P. Adzic, M. Djordjevic, M. Ekmedzic, D. Krpic, J. Milosevic, M. Aguilar-Benitez, J. A. Maestre, P. Arce, C. Battilana, E. Calvo, M. Cerrada, M. C. Llatas, N. Colino, B. De La Cruz, A. D. Peris, C. D. Pardos, D. D. Vázquez, C. F. Bedoya, J. P. F. Ramos, A. Ferrando, J. Flix, M. C. Fouz, P. Garcia-Abia, O. G. Lopez, S. G. Lopez, J. M. Hernandez, M. I. Josa, G. Merino, J. P. Pelayo, I. Redondo, L. Romero, J. Santaolalla, M. S. Soares, C. Willmott, C. Albajar, G. Codispoti, J. F. de Trocóniz, J. Cuevas, J. F. Menendez, S. Folgueras, I. G. Caballero, L. L. Iglesias, J. M. V. Garcia, J. A. B. Cifuentes, I. J. Cabrillo, A. Calderon, S. H. Chuang, J. D. Campderros, M. Felcini, M. Fernandez, G. Gomez, J. G. Sanchez, C. Jorda, P. L. Pardo, A. L. Virto, J. Marco, R. Marco, C. M. Rivero, F. Matorras, F. J. M. Sanchez, J. P. Gomez, T. Rodrigo, A. Y. Rodríguez-Marrero, A. Ruiz-Jimeno, L. Scodellaro, M. S. Sanudo, I. Vila, R. V. Cortabitarte, D. Abbaneo, E. Auffray, G. Auzinger, P. Baillon, A. H. Ball, D. Barney, C. Bernet, W. Bialas, G. Bianchi, P. Bloch, A. Bocci, H. Breuker, K. Bunkowski, T. Camporesi, G. Cerminara, T. Christiansen, J. A. C. Perez, B. Curé, D. D’Enterria, A. De Roeck, S. Di Guida, M. Dobson, N. Dupont-Sagorin, A. Elliott-Peisert, B. Frisch, W. Funk, A. Gaddi, G. Georgiou, H. Gerwig, M. Giffels, D. Gigi, K. Gill, D. Giordano, M. Giunta, F. Glege, R. G.-R. Garrido, P. Govoni, S. Gowdy, R. Guida, L. Guiducci, M. Hansen, P. Harris, C. Hartl, J. Harvey, B. Hegner, A. Hinzmann, H. F. Hoffmann, V. Innocente, P. Janot, K. Kaadze, E. Karavakis, K. Kousouris, P. Lecoq, P. Lenzi, C. Lourenço, T. Mäki, M. Malberti, L. Malgeri, M. Mannelli, L. Masetti, G. Mavromanolakis, F. Meijers, S. Mersi, E. Meschi, R. Moser, M. U. Mozer, M. Mulders, E. Nesvold, M. Nguyen, T. Orimoto, L. Orsini, E. P. Cortezon, E. Perez, A. Petrilli, A. Pfeiffer, M. Pierini, M. Pimiä, D. Piparo, G. Polese, L. Quertenmont, A. Racz, W. Reece, J. R. Antunes, G. Rolandi, T. Rommerskirchen, C. Rovelli, M. Rovere, H. Sakulin, F. Santanastasio, C. Schäfer, C. Schwick, I. Segoni, A. Sharma, P. Siegrist, P. Silva, M. Simon, P. Sphicas, D. Spiga, M. Spiropulu, M. Stoye, A. Tsirou, G. I. Veres, P. Vichoudis, H. K. Wöhri, S. D. Worm, W. D. Zeuner, W. Bertl, K. Deiters, W. Erdmann, K. Gabathuler, R. Horisberger, Q. Ingram, H. C. Kaestli, S. König, D. Kotlinski, U. Langenegger, F. Meier, D. Renker, T. Rohe, J. Sibille, L. Bäni, P. Bortignon, M. A. Buchmann, B. Casal, N. Chanon, Z. Chen, A. Deisher, G. Dissertori, M. Dittmar, M. Dünser, J. Eugster, K. Freudenreich, C. Grab, P. Lecomte, W. Lustermann, P. M. R. del Arbol, N. Mohr, F. Moortgat, C. Nägeli, P. Nef, F. Nessi-Tedaldi, L. Pape, F. Pauss, M. Peruzzi, F. J. Ronga, M. Rossini, L. Sala, A. K. Sanchez, M.-C. Sawley, A. Starodumov, B. Stieger, M. Takahashi, L. Tauscher, A. Thea, K. Theofilatos, D. Treille, C. Urscheler, R. Wallny, H. A. Weber, L. Wehrli, J. Weng, E. Aguilo, C. Amsler, V. Chiochia, S. De Visscher, C. Favaro, M. I. Rikova, B. M. Mejias, P. Otiougova, P. Robmann, H. Snoek, M. Verzetti, Y. H. Chang, K. H. Chen, C. M. Kuo, S. W. Li, W. Lin, Z. K. Liu, Y. J. Lu, D. Mekterovic, R. Volpe, S. S. Yu, P. Bartalini, P. Chang, Y. H. Chang, Y. W. Chang, Y. Chao, K. F. Chen, C. Dietz, U. Grundler, W.-S. Hou, Y. Hsiung, K. Y. Kao, Y. J. Lei, R.-S. Lu, D. Majumder, E. Petrakou, X. Shi, J. G. Shiu, Y. M. Tzeng, X. Wan, M. Wang, A. Adiguzel, M. N. Bakirci, S. Cerci, C. Dozen, I. Dumanoglu, E. Eskut, S. Girgis, G. Gokbulut, I. Hos, E. E. Kangal, G. Karapinar, A. K. Topaksu, G. Onengut, K. Ozdemir, S. Ozturk, A. Polatoz, K. Sogut, D. S. Cerci, B. Tali, H. Topakli, D. Uzun, L. N. Vergili, M. Vergili, I. V. Akin, T. Aliev, B. Bilin, S. Bilmis, M. Deniz, H. Gamsizkan, A. M. Guler, K. Ocalan, A. Ozpineci, M. Serin, R. Sever, U. E. Surat, M. Yalvac, E. Yildirim, M. Zeyrek, M. Deliomeroglu, E. Gülmez, B. Isildak, M. Kaya, O. Kaya, S. Ozkorucuklu, N. Sonmez, L. Levchuk, F. Bostock, J. J. Brooke, E. Clement, D. Cussans, H. Flacher, R. Frazier, J. Goldstein, M. Grimes, G. P. Heath, H. F. Heath, L. Kreczko, S. Metson, D. M. Newbold, K. Nirunpong, A. Poll, S. Senkin, V. J. Smith, T. Williams, L. Basso, A. Belyaev, C. Brew, R. M. Brown, D. J. A. Cockerill, J. A. Coughlan, K. Harder, S. Harper, J. Jackson, B. W. Kennedy, E. Olaiya, D. Petyt, B. C. Radburn-Smith, C. H. Shepherd-Themistocleous, I. R. Tomalin, W. J. Womersley, R. Bainbridge, G. Ball, R. Beuselinck, O. Buchmuller, D. Colling, N. Cripps, M. Cutajar, P. Dauncey, G. Davies, M. D. Negra, W. Ferguson, J. Fulcher, D. Futyan, A. Gilbert, A. G. Bryer, G. Hall, Z. Hatherell, J. Hays, G. Iles, M. Jarvis, G. Karapostoli, L. Lyons, A.-M. Magnan, J. Marrouche, B. Mathias, R. Nandi, J. Nash, A. Nikitenko, A. Papageorgiou, M. Pesaresi, K. Petridis, M. Pioppi, D. M. Raymond, S. Rogerson, N. Rompotis, A. Rose, M. J. Ryan, C. Seez, P. Sharp, A. Sparrow, A. Tapper, S. Tourneur, M. V. Acosta, T. Virdee, S. Wakefield, N. Wardle, D. Wardrope, T. Whyntie, M. Barrett, M. Chadwick, J. E. Cole, P. R. Hobson, A. Khan, P. Kyberd, D. Leslie, W. Martin, I. D. Reid, P. Symonds, L. Teodorescu, M. Turner, K. Hatakeyama, H. Liu, T. Scarborough, C. Henderson, A. Avetisyan, T. Bose, E. C. Jarrin, C. Fantasia, A. Heister, J. St John, P. Lawson, D. Lazic, J. Rohlf, D. Sperka, L. Sulak, S. Bhattacharya, D. Cutts, A. Ferapontov, U. Heintz, S. Jabeen, G. Kukartsev, G. Landsberg, M. Luk, M. Narain, D. Nguyen, M. Segala, T. Sinthuprasith, T. Speer, K. V. Tsang, R. Breedon, G. Breto, M. C. D. L. B. Sanchez, M. Caulfield, S. Chauhan, M. Chertok, J. Conway, R. Conway, P. T. Cox, J. Dolen, R. Erbacher, M. Gardner, R. Houtz, W. Ko, A. Kopecky, R. Lander, O. Mall, T. Miceli, R. Nelson, D. Pellett, J. Robles, B. Rutherford, M. Searle, J. Smith, M. Squires, M. Tripathi, R. V. Sierra, V. Andreev, K. Arisaka, D. Cline, R. Cousins, J. Duris, S. Erhan, P. Everaerts, C. Farrell, J. Hauser, M. Ignatenko, C. Jarvis, C. Plager, G. Rakness, P. Schlein, J. Tucker, V. Valuev, M. Weber, J. Babb, R. Clare, J. Ellison, J. W. Gary, F. Giordano, G. Hanson, G. Y. Jeng, H. Liu, O. R. Long, A. Luthra, H. Nguyen, S. Paramesvaran, J. Sturdy, S. Sumowidagdo, R. Wilken, S. Wimpenny, W. Andrews, J. G. Branson, G. B. Cerati, S. Cittolin, D. Evans, F. Golf, A. Holzner, R. Kelley, M. Lebourgeois, J. Letts, I. Macneill, B. Mangano, S. Padhi, C. Palmer, G. Petrucciani, H. Pi, M. Pieri, R. Ranieri, M. Sani, I. Sfiligoi, V. Sharma, S. Simon, E. Sudano, M. Tadel, Y. Tu, A. Vartak, S. Wasserbaech, F. Würthwein, A. Yagil, J. Yoo, D. Barge, R. Bellan, C. Campagnari, M. D’Alfonso, T. Danielson, K. Flowers, P. Geffert, J. Incandela, C. Justus, P. Kalavase, S. A. Koay, D. Kovalskyi, V. Krutelyov, S. Lowette, N. Mccoll, V. Pavlunin, F. Rebassoo, J. Ribnik, J. Richman, R. Rossin, D. Stuart, W. To, J. R. Vlimant, C. West, A. Apresyan, A. Bornheim, J. Bunn, Y. Chen, E. Di Marco, J. Duarte, M. Gataullin, Y. Ma, A. Mott, H. B. Newman, C. Rogan, V. Timciuc, P. Traczyk, J. Veverka, R. Wilkinson, Y. Yang, R. Y. Zhu, B. Akgun, R. Carroll, T. Ferguson, Y. Iiyama, D. W. Jang, S. Y. Jun, Y. F. Liu, M. Paulini, J. Russ, H. Vogel, I. Vorobiev, J. P. Cumalat, M. E. Dinardo, B. R. Drell, C. J. Edelmaier, W. T. Ford, A. Gaz, B. Heyburn, E. L. Lopez, U. Nauenberg, J. G. Smith, K. Stenson, K. A. Ulmer, S. R. Wagner, S. L. Zang, L. Agostino, J. Alexander, A. Chatterjee, N. Eggert, L. K. Gibbons, B. Heltsley, W. Hopkins, A. Khukhunaishvili, B. Kreis, N. Mirman, G. N. Kaufman, J. R. Patterson, D. Puigh, A. Ryd, E. Salvati, W. Sun, W. D. Teo, J. Thom, J. Thompson, J. Vaughan, Y. Weng, L. Winstrom, P. Wittich, A. Biselli, G. Cirino, D. Winn, S. Abdullin, M. Albrow, J. Anderson, G. Apollinari, M. Atac, J. A. Bakken, L. A. T. Bauerdick, A. Beretvas, J. Berryhill, P. C. Bhat, I. Bloch, K. Burkett, J. N. Butler, V. Chetluru, H. W. K. Cheung, F. Chlebana, S. Cihangir, W. Cooper, D. P. Eartly, V. D. Elvira, S. Esen, I. Fisk, J. Freeman, Y. Gao, E. Gottschalk, D. Green, O. Gutsche, J. Hanlon, R. M. Harris, J. Hirschauer, B. Hooberman, H. Jensen, S. Jindariani, M. Johnson, U. Joshi, B. Klima, S. Kunori, S. Kwan, C. Leonidopoulos, D. Lincoln, R. Lipton, J. Lykken, K. Maeshima, J. M. Marraffino, S. Maruyama, D. Mason, P. McBride, T. Miao, K. Mishra, S. Mrenna, Y. Musienko, C. Newman-Holmes, V. O’Dell, J. Pivarski, R. Pordes, O. Prokofyev, T. Schwarz, E. Sexton-Kennedy, S. Sharma, W. J. Spalding, L. Spiegel, P. Tan, L. Taylor, S. Tkaczyk, L. Uplegger, E. W. Vaandering, R. Vidal, J. Whitmore, W. Wu, F. Yang, F. Yumiceva, J. C. Yun, D. Acosta, P. Avery, D. Bourilkov, M. Chen, S. Das, M. De Gruttola, G. P. Di Giovanni, D. Dobur, A. Drozdetskiy, R. D. Field, M. Fisher, Y. Fu, I. K. Furic, J. Gartner, S. Goldberg, J. Hugon, B. Kim, J. Konigsberg, A. Korytov, A. Kropivnitskaya, T. Kypreos, J. F. Low, K. Matchev, P. Milenovic, G. Mitselmakher, L. Muniz, R. Remington, A. Rinkevicius, M. Schmitt, B. Scurlock, P. Sellers, N. Skhirtladze, M. Snowball, D. Wang, J. Yelton, M. Zakaria, V. Gaultney, L. M. Lebolo, S. Linn, P. Markowitz, G. Martinez, J. L. Rodriguez, T. Adams, A. Askew, J. Bochenek, J. Chen, B. Diamond, S. V. Gleyzer, J. Haas, S. Hagopian, V. Hagopian, M. Jenkins, K. F. Johnson, H. Prosper, S. Sekmen, V. Veeraraghavan, M. Weinberg, M. M. Baarmand, B. Dorney, M. Hohlmann, H. Kalakhety, I. Vodopiyanov, M. R. Adams, I. M. Anghel, L. Apanasevich, Y. Bai, V. E. Bazterra, R. R. Betts, J. Callner, R. Cavanaugh, C. Dragoiu, L. Gauthier, C. E. Gerber, D. J. Hofman, S. Khalatyan, G. J. Kunde, F. Lacroix, M. Malek, C. O’Brien, C. Silkworth, C. Silvestre, D. Strom, N. Varelas, U. Akgun, E. A. Albayrak, B. Bilki, W. Clarida, F. Duru, S. Griffiths, C. K. Lae, E. McCliment, J.-P. Merlo, H. Mermerkaya, A. Mestvirishvili, A. Moeller, J. Nachtman, C. R. Newsom, E. Norbeck, J. Olson, Y. Onel, F. Ozok, S. Sen, E. Tiras, J. Wetzel, T. Yetkin, K. Yi, B. A. Barnett, B. Blumenfeld, S. Bolognesi, A. Bonato, C. Eskew, D. Fehling, G. Giurgiu, A. V. Gritsan, Z. J. Guo, G. Hu, P. Maksimovic, S. Rappoccio, M. Swartz, N. V. Tran, A. Whitbeck, P. Baringer, A. Bean, G. Benelli, O. Grachov, R. P. K. Iii, M. Murray, D. Noonan, S. Sanders, R. Stringer, G. Tinti, J. S. Wood, V. Zhukova, A. F. Barfuss, T. Bolton, I. Chakaberia, A. Ivanov, S. Khalil, M. Makouski, Y. Maravin, S. Shrestha, I. Svintradze, J. Gronberg, D. Lange, D. Wright, A. Baden, M. Boutemeur, B. Calvert, S. C. Eno, J. A. Gomez, N. J. Hadley, R. G. Kellogg, M. Kirn, T. Kolberg, Y. Lu, A. C. Mignerey, A. Peterman, K. Rossato, P. Rumerio, A. Skuja, J. Temple, M. B. Tonjes, S. C. Tonwar, E. Twedt, B. Alver, G. Bauer, J. Bendavid, W. Busza, E. Butz, I. A. Cali, M. Chan, V. Dutta, G. G. Ceballos, M. Goncharov, K. A. Hahn, Y. Kim, M. Klute, Y.-J. Lee, W. Li, P. D. Luckey, T. Ma, S. Nahn, C. Paus, D. Ralph, C. Roland, G. Roland, M. Rudolph, G. S. F. Stephans, F. Stöckli, K. Sumorok, K. Sung, D. Velicanu, E. A. Wenger, R. Wolf, B. Wyslouch, S. Xie, M. Yang, Y. Yilmaz, A. S. Yoon, M. Zanetti, S. I. Cooper, P. Cushman, B. Dahmes, A. De Benedetti, G. Franzoni, A. Gude, J. Haupt, S. C. Kao, K. Klapoetke, Y. Kubota, J. Mans, N. Pastika, V. Rekovic, R. Rusack, M. Sasseville, A. Singovsky, N. Tambe, J. Turkewitz, L. M. Cremaldi, R. Godang, R. Kroeger, L. Perera, R. Rahmat, D. A. Sanders, D. Summers, E. Avdeeva, K. Bloom, S. Bose, J. Butt, D. R. Claes, A. Dominguez, M. Eads, P. Jindal, J. Keller, I. Kravchenko, J. Lazo-Flores, H. Malbouisson, S. Malik, G. R. Snow, U. Baur, A. Godshalk, I. Iashvili, S. Jain, A. Kharchilava, A. Kumar, S. P. Shipkowski, K. Smith, Z. Wan, G. Alverson, E. Barberis, D. Baumgartel, M. Chasco, D. Trocino, D. Wood, J. Zhang, A. Anastassov, A. Kubik, N. Mucia, N. Odell, R. A. Ofierzynski, B. Pollack, A. Pozdnyakov, M. Schmitt, S. Stoynev, M. Velasco, S. Won, L. Antonelli, D. Berry, A. Brinkerhoff, M. Hildreth, C. Jessop, D. J. Karmgard, J. Kolb, K. Lannon, W. Luo, S. Lynch, N. Marinelli, D. M. Morse, T. Pearson, R. Ruchti, J. Slaunwhite, N. Valls, M. Wayne, M. Wolf, J. Ziegler, B. Bylsma, L. S. Durkin, C. Hill, P. Killewald, K. Kotov, T. Y. Ling, M. Rodenburg, C. Vuosalo, G. Williams, N. Adam, E. Berry, P. Elmer, D. Gerbaudo, V. Halyo, P. Hebda, J. Hegeman, A. Hunt, E. Laird, D. L. Pegna, P. Lujan, D. Marlow, T. Medvedeva, M. Mooney, J. Olsen, P. Piroué, X. Quan, A. Raval, H. Saka, D. Stickland, C. Tully, J. S. Werner, A. Zuranski, J. G. Acosta, X. T. Huang, A. Lopez, H. Mendez, S. Oliveros, J. E. R. Vargas, A. Zatserklyaniy, E. Alagoz, V. E. Barnes, D. Benedetti, G. Bolla, L. Borrello, D. Bortoletto, M. De Mattia, A. Everett, L. Gutay, Z. Hu, M. Jones, O. Koybasi, M. Kress, A. T. Laasanen, N. Leonardo, V. Maroussov, P. Merkel, D. H. Miller, N. Neumeister, I. Shipsey, D. Silvers, A. Svyatkovskiy, M. V. Marono, H. D. Yoo, J. Zablocki, Y. Zheng, S. Guragain, N. Parashar, A. Adair, C. Boulahouache, V. Cuplov, K. M. Ecklund, F. J. M. Geurts, B. P. Padley, R. Redjimi, J. Roberts, J. Zabel, B. Betchart, A. Bodek, Y. S. Chung, R. Covarelli, P. de Barbaro, R. Demina, Y. Eshaq, A. Garcia-Bellido, P. Goldenzweig, Y. Gotra, J. Han, A. Harel, D. C. Miner, G. Petrillo, W. Sakumoto, D. Vishnevskiy, M. Zielinski, A. Bhatti, R. Ciesielski, L. Demortier, K. Goulianos, G. Lungu, S. Malik, C. Mesropian, S. Arora, O. Atramentov, A. Barker, J. P. Chou, C. Contreras-Campana, E. Contreras-Campana, D. Duggan, D. Ferencek, Y. Gershtein, R. Gray, E. Halkiadakis, D. Hidas, D. Hits, A. Lath, S. Panwalkar, M. Park, R. Patel, A. Richards, K. Rose, S. Salur, S. Schnetzer, C. Seitz, S. Somalwar, R. Stone, S. Thomas, G. Cerizza, M. Hollingsworth, S. Spanier, Z. C. Yang, A. York, R. Eusebi, W. Flanagan, J. Gilmore, T. Kamon, V. Khotilovich, R. Montalvo, I. Osipenkov, Y. Pakhotin, A. Perloff, J. Roe, A. Safonov, T. Sakuma, S. Sengupta, I. Suarez, A. Tatarinov, D. Toback, N. Akchurin, C. Bardak, J. Damgov, P. R. Dudero, C. Jeong, K. Kovitanggoon, S. W. Lee, T. Libeiro, P. Mane, Y. Roh, A. Sill, I. Volobouev, R. Wigmans, E. Appelt, E. Brownson, D. Engh, C. Florez, W. Gabella, A. Gurrola, M. Issah, W. Johns, P. Kurt, C. Maguire, A. Melo, P. Sheldon, B. Snook, S. Tuo, J. Velkovska, M. W. Arenton, M. Balazs, S. Boutle, S. Conetti, B. Cox, B. Francis, S. Goadhouse, J. Goodell, R. Hirosky, A. Ledovskoy, C. Lin, C. Neu, J. Wood, R. Yohay, S. Gollapinni, R. Harr, P. E. Karchin, C. K. K. Don, P. Lamichhane, M. Mattson, C. Milstène, A. Sakharov, M. Anderson, M. Bachtis, D. Belknap, J. N. Bellinger, J. Bernardini, D. Carlsmith, M. Cepeda, S. Dasu, J. Efron, E. Friis, L. Gray, K. S. Grogg, M. Grothe, R. Hall-Wilton, M. Herndon, A. Hervé, P. Klabbers, J. Klukas, A. Lanaro, C. Lazaridis, J. Leonard, R. Loveless, A. Mohapatra, I. Ojalvo, G. A. Pierro, I. Ross, A. Savin, W. H. Smith, J. Swanson, "Study of high- p T charged particle suppression in PbPb compared to pp collisions at s NN = 2.76 TeV," The European Physical Journal C, vol. 72 no. 3,DOI: 10.1140/epjc/s10052-012-1945-x, 2012.

[44] C. Tsallis, "Possible generalization of Boltzmann-Gibbs statistics," Journal of Statistical Physics, vol. 52 no. 1-2, pp. 479-487, DOI: 10.1007/BF01016429, 1988.

[45] B. I. Abelev, J. Adams, M. M. Aggarwal, Z. Ahammed, J. Amonett, B. D. Anderson, M. Anderson, D. Arkhipkin, G. S. Averichev, Y. Bai, J. Balewski, O. Barannikova, L. S. Barnby, J. Baudot, S. Bekele, V. V. Belaga, A. Bellingeri-Laurikainen, R. Bellwied, F. Benedosso, S. Bhardwaj, A. Bhasin, A. K. Bhati, H. Bichsel, J. Bielcik, J. Bielcikova, L. C. Bland, S. L. Blyth, B. E. Bonner, M. Botje, J. Bouchet, A. V. Brandin, A. Bravar, T. P. Burton, M. Bystersky, R. V. Cadman, X. Z. Cai, H. Caines, M. C. B. Sánchez, J. Castillo, O. Catu, D. Cebra, Z. Chajecki, P. Chaloupka, S. Chattopadhyay, H. F. Chen, J. H. Chen, J. Cheng, M. Cherney, A. Chikanian, W. Christie, J. P. Coffin, T. M. Cormier, M. R. Cosentino, J. G. Cramer, H. J. Crawford, D. Das, S. Das, S. Dash, M. Daugherity, M. M. . Moura, T. G. Dedovich, M. DePhillips, A. A. Derevschikov, L. Didenko, T. Dietel, P. Djawotho, S. M. Dogra, W. J. Dong, X. Dong, J. E. Draper, F. Du, V. B. Dunin, J. C. Dunlop, M. R. D. Mazumdar, V. Eckardt, W. R. Edwards, L. G. Efimov, V. Emelianov, J. Engelage, G. Eppley, B. Erazmus, M. Estienne, P. Fachini, R. Fatemi, J. Fedorisin, K. Filimonov, P. Filip, E. Finch, V. Fine, Y. Fisyak, J. Fu, C. A. Gagliardi, L. Gaillard, M. S. Ganti, V. Ghazikhanian, P. Ghosh, J. E. Gonzalez, Y. G. Gorbunov, H. Gos, O. Grebenyuk, D. Grosnick, S. M. Guertin, K. S. F. F. Guimaraes, A. Gupta, T. D. Gutierrez, B. Haag, T. J. Hallman, A. Hamed, J. W. Harris, W. He, M. Heinz, T. W. Henry, S. Hepplemann, B. Hippolyte, A. Hirsch, E. Hjort, A. M. Hoffman, G. W. Hoffmann, M. J. Horner, H. Z. Huang, S. L. Huang, E. W. Hughes, T. J. Humanic, G. Igo, P. Jacobs, W. W. Jacobs, P. Jakl, F. Jia, H. Jiang, P. G. Jones, E. G. Judd, S. Kabana, K. Kang, J. Kapitan, M. Kaplan, D. Keane, A. Kechechyan, V. Y. Khodyrev, B. C. Kim, J. Kiryluk, A. Kisiel, E. M. Kislov, S. R. Klein, A. Kocoloski, D. D. Koetke, T. Kollegger, M. Kopytine, L. Kotchenda, V. Kouchpil, K. L. Kowalik, M. Kramer, P. Kravtsov, V. I. Kravtsov, K. Krueger, C. Kuhn, A. I. Kulikov, A. Kumar, A. A. Kuznetsov, M. A. C. Lamont, J. M. Landgraf, S. Lange, S. LaPointe, F. Laue, J. Lauret, A. Lebedev, R. Lednicky, C. H. Lee, S. Lehocka, M. J. LeVine, C. Li, Q. Li, Y. Li, G. Lin, X. Lin, S. J. Lindenbaum, M. A. Lisa, F. Liu, H. Liu, J. Liu, L. Liu, Z. Liu, T. Ljubicic, W. J. Llope, H. Long, R. S. Longacre, W. A. Love, Y. Lu, T. Ludlam, D. Lynn, G. L. Ma, J. G. Ma, Y. G. Ma, D. Magestro, D. P. Mahapatra, R. Majka, L. K. Mangotra, R. Manweiler, S. Margetis, C. Markert, L. Martin, H. S. Matis, Y. A. Matulenko, C. J. McClain, T. S. McShane, Y. Melnick, A. Meschanin, J. Millane, M. L. Miller, N. G. Minaev, S. Mioduszewski, C. Mironov, A. Mischke, D. K. Mishra, J. Mitchell, B. Mohanty, L. Molnar, C. F. Moore, D. A. Morozov, M. G. Munhoz, B. K. Nandi, C. Nattrass, T. K. Nayak, J. M. Nelson, P. K. Netrakanti, L. V. Nogach, S. B. Nurushev, G. Odyniec, A. Ogawa, V. Okorokov, M. Oldenburg, D. Olson, M. Pachr, S. K. Pal, Y. Panebratsev, S. Y. Panitkin, A. I. Pavlinov, T. Pawlak, T. Peitzmann, V. Perevoztchikov, C. Perkins, W. Peryt, S. C. Phatak, R. Picha, M. Planinic, J. Pluta, N. Poljak, N. Porile, J. Porter, A. M. Poskanzer, M. Potekhin, E. Potrebenikova, B. V. K. S. Potukuchi, D. Prindle, C. Pruneau, J. Putschke, G. Rakness, R. Raniwala, S. Raniwala, R. L. Ray, S. V. Razin, J. Reinnarth, D. Relyea, F. Retiere, A. Ridiger, H. G. Ritter, J. B. Roberts, O. V. Rogachevskiy, J. L. Romero, A. Rose, C. Roy, L. Ruan, M. J. Russcher, R. Sahoo, T. Sakuma, S. Salur, J. Sandweiss, M. Sarsour, P. S. Sazhin, J. Schambach, R. P. Scharenberg, N. Schmitz, K. Schweda, J. Seger, I. Selyuzhenkov, P. Seyboth, A. Shabetai, E. Shahaliev, M. Shao, M. Sharma, W. Q. Shen, S. S. Shimanskiy, E. Sichtermann, F. Simon, R. N. Singaraju, N. Smirnov, R. Snellings, G. Sood, P. Sorensen, J. Sowinski, J. Speltz, H. M. Spinka, B. Srivastava, A. Stadnik, T. D. S. Stanislaus, R. Stock, A. Stolpovsky, M. Strikhanov, B. Stringfellow, A. A. P. Suaide, E. Sugarbaker, M. Sumbera, Z. Sun, B. Surrow, M. Swanger, T. J. M. Symons, A. S. . Toledo, A. Tai, J. Takahashi, A. H. Tang, T. Tarnowsky, D. Thein, J. H. Thomas, A. R. Timmins, S. Timoshenko, M. Tokarev, T. A. Trainor, S. Trentalange, R. E. Tribble, O. D. Tsai, J. Ulery, T. Ullrich, D. G. Underwood, G. V. Buren, N. Kolk, M. . Leeuwen, A. M. V. Molen, R. Varma, I. M. Vasilevski, A. N. Vasiliev, R. Vernet, S. E. Vigdor, V. P. Viyogi, S. Vokal, S. A. Voloshin, W. T. Waggoner, F. Wang, G. Wang, J. S. Wang, X. L. Wang, Y. Wang, J. W. Watson, J. C. Webb, G. D. Westfall, A. Wetzler, C. Whitten, H. Wieman, S. W. Wissink, R. Witt, J. Wood, J. Wu, N. Xu, Q. H. Xu, Z. Xu, P. Yepes, I. K. Yoo, V. I. Yurevich, W. Zhan, H. Zhang, W. M. Zhang, Y. Zhang, Z. P. Zhang, Y. Zhao, C. Zhong, R. Zoulkarneev, Y. Zoulkarneeva, A. N. Zubarev, J. X. Zuo, "Strange particle production in p + p collisions at s = 200 GeV," Physical Review C, vol. 75 no. 6, article 064901,DOI: 10.1103/PhysRevC.75.064901, 2007.

[46] T. S. Biró, G. Purcsel, K. Urmössy, "Non-extensive approach to quark matter," The European Physical Journal A, vol. 40 no. 3,DOI: 10.1140/epja/i2009-10806-6, 2009.

[47] R. Odorico, "Does a transverse energy trigger actually trigger on large-P T jets?," Physics Letters B, vol. 118 no. 1-3, pp. 151-154, DOI: 10.1016/0370-2693(82)90620-7, 1982.

[48] G. Arnison, A. Astbury, B. Aubert, C. Bacci, R. Bernabei, A. Bézaguet, R. Böck, T. J. V. Bowcock, M. Calvetti, T. Carroll, P. Catz, S. Centro, F. Ceradini, S. Cittolin, A. M. Cnops, C. Cochet, J. Colas, M. Corden, D. Dallman, S. D'Angelo, M. DeBeer, M. Della Negra, M. Demoulin, D. Denegri, D. DiBitonto, L. Dobryznski, J. D. Dowell, M. Edwards, K. Eggert, E. Eisenhandler, N. Ellis, P. Erhard, H. Faissner, G. Fontaine, J. P. Fournier, R. Frey, R. Frühwirth, J. Garvey, S. Geer, C. Ghesquière, P. Ghez, K. L. Giboni, W. R. Gibson, Y. Giraud-Heraud, A. Givernaud, A. Gonidec, G. Grayer, P. Gutierrez, R. Haidan, T. Hansl-Kozanecka, W. J. Haynes, L. O. Hertzberger, C. Hodges, D. Hoffmann, H. Hoffmann, D. J. Holthuizen, R. J. Homer, A. Honma, W. Jank, P. I. P. Kalmus, V. Karimaki, R. Keeler, I. Kenyon, A. Kernan, R. Kinnunen, H. Kowalski, W. Kozanecki, D. Kryn, F. Lacava, J. P. Laugier, J. P. Lees, H. Lehmann, R. Leuchs, A. Leveque, D. Linglin, E. Locci, T. Markiewicz, G. Maurin, T. McMahon, J. P. Mendiburu, M. N. Minard, M. Moricca, F. Muller, A. K. Nandi, L. Naumann, A. Norton, A. Orkin-Lecourtois, L. Paoluzi, G. Piano Mortari, M. Pimiä, A. Placci, E. Radermacher, J. Ransdell, H. Reithler, J. P. Revol, J. Rich, M. Rijsenbeek, C. Roberts, C. Rubbia, B. Sadoulet, G. Sajot, G. Salvi, G. Salvini, J. Sass, J. Saudraix, A. Savoy-Navarro, D. Schinzel, W. Scott, T. P. Shah, M. Spiro, J. Strauss, K. Sumorok, F. Szoncso, C. Tao, G. Thompson, J. Timmer, E. Tscheslog, J. Tuominiemi, J. P. Vialle, J. Vrana, V. Vuillemin, H. Wahl, P. Watkins, J. Wilson, M. Yvert, E. Zurfluh, "Transverse momentum spectra for charged particles at the CERN proton-antiproton collider," Physics Letters B, vol. 118 no. 1-3, pp. 167-172, DOI: 10.1016/0370-2693(82)90623-2, 1982.

[49] T. Mizoguchi, M. Biyajima, N. Suzuki, "Analyses of whole transverse momentum distributions in p p ¯ and pp collisions by using a modified version of Hagedorn’s formula," International Journal of Modern Physics A, vol. 32 no. 11, article 1750057,DOI: 10.1142/S0217751X17500579, 2017.

[50] M. Suleymanov, "The meaning behind observed p T regions at the LHC energies," International Journal of Modern Physics E, vol. 27 no. 1, article 1850008,DOI: 10.1142/S0218301318500088, 2018.

[51] L. J. Gutay, A. S. Hirsch, R. P. Scharenberg, B. K. Srivastava, C. Pajares, "De-confinement in small systems: clustering of color sources in high multiplicity p ¯ p collisions at s = 1.8 TeV," International Journal of Modern Physics E, vol. 24 no. 12, article 1550101,DOI: 10.1142/S0218301315501013, 2015.

[52] A. S. Hirsch, C. Pajares, R. P. Scharenberg, B. K. Srivastava, "De-confinement in high multiplicity proton-proton collisions at LHC energies," . 2018, https://arxiv.org/abs/1803.02301

[53] P. Sahoo, S. De, S. K. Tiwari, R. Sahoo, "Energy and centrality dependent study of deconfinement phase transition in a color string percolation approach at RHIC energies," The European Physical Journal A, vol. 54 no. 8,DOI: 10.1140/epja/i2018-12571-9, 2018.

[54] J. Cleymans, "The physics case for the s N N ≈ 10 GeV region," . 2017, http://arxiv.org/abs/1711.02882

[55] B. Abelev, J. Adam, D. Adamová, A. M. Adare, M. M. Aggarwal, G. Aglieri Rinella, M. Agnello, A. G. Agocs, A. Agostinelli, Z. Ahammed, N. Ahmad, A. Ahmad Masoodi, S. A. Ahn, S. U. Ahn, M. Ajaz, A. Akindinov, D. Aleksandrov, B. Alessandro, A. Alici, A. Alkin, E. Almaráz Aviña, J. Alme, T. Alt, V. Altini, S. Altinpinar, I. Altsybeev, C. Andrei, A. Andronic, V. Anguelov, J. Anielski, C. Anson, T. Antičić, F. Antinori, P. Antonioli, L. Aphecetche, H. Appelshäuser, N. Arbor, S. Arcelli, A. Arend, N. Armesto, R. Arnaldi, T. Aronsson, I. C. Arsene, M. Arslandok, A. Asryan, A. Augustinus, R. Averbeck, T. C. Awes, J. Äystö, M. D. Azmi, M. Bach, A. Badalà, Y. W. Baek, R. Bailhache, R. Bala, A. Baldisseri, F. Baltasar Dos Santos Pedrosa, J. Bán, R. C. Baral, R. Barbera, F. Barile, G. G. Barnaföldi, L. S. Barnby, V. Barret, J. Bartke, M. Basile, N. Bastid, S. Basu, B. Bathen, G. Batigne, B. Batyunya, C. Baumann, I. G. Bearden, H. Beck, N. K. Behera, I. Belikov, F. Bellini, R. Bellwied, E. Belmont-Moreno, G. Bencedi, S. Beole, I. Berceanu, A. Bercuci, Y. Berdnikov, D. Berenyi, A. A. E. Bergognon, D. Berzano, L. Betev, A. Bhasin, A. K. Bhati, J. Bhom, L. Bianchi, N. Bianchi, J. Bielčík, J. Bielčíková, A. Bilandzic, S. Bjelogrlic, F. Blanco, F. Blanco, D. Blau, C. Blume, M. Boccioli, S. Böttger, A. Bogdanov, H. Bøggild, M. Bogolyubsky, L. Boldizsár, M. Bombara, J. Book, H. Borel, A. Borissov, F. Bossú, M. Botje, E. Botta, E. Braidot, P. Braun-Munzinger, M. Bregant, T. Breitner, T. A. Broker, T. A. Browning, M. Broz, R. Brun, E. Bruna, G. E. Bruno, D. Budnikov, H. Buesching, S. Bufalino, P. Buncic, O. Busch, Z. Buthelezi, D. Caffarri, X. Cai, H. Caines, E. Calvo Villar, P. Camerini, V. Canoa Roman, G. Cara Romeo, F. Carena, W. Carena, N. Carlin Filho, F. Carminati, A. Casanova Díaz, J. Castillo Castellanos, J. F. Castillo Hernandez, E. A. R. Casula, V. Catanescu, C. Cavicchioli, C. Ceballos Sanchez, J. Cepila, P. Cerello, B. Chang, S. Chapeland, J. L. Charvet, S. Chattopadhyay, S. Chattopadhyay, M. Cherney, C. Cheshkov, B. Cheynis, V. Chibante Barroso, D. D. Chinellato, P. Chochula, M. Chojnacki, S. Choudhury, P. Christakoglou, C. H. Christensen, P. Christiansen, T. Chujo, S. U. Chung, C. Cicalo, L. Cifarelli, F. Cindolo, J. Cleymans, F. Colamaria, D. Colella, A. Collu, G. Conesa Balbastre, Z. Conesa del Valle, M. E. Connors, G. Contin, J. G. Contreras, T. M. Cormier, Y. Corrales Morales, P. Cortese, I. Cortés Maldonado, M. R. Cosentino, F. Costa, M. E. Cotallo, E. Crescio, P. Crochet, E. Cruz Alaniz, R. Cruz Albino, E. Cuautle, L. Cunqueiro, A. Dainese, A. Danu, K. Das, I. Das, S. Das, D. Das, S. Dash, A. Dash, S. de, G. O. V. de Barros, A. de Caro, G. de Cataldo, J. de Cuveland, A. de Falco, D. de Gruttola, H. Delagrange, A. Deloff, N. de Marco, E. Dénes, S. de Pasquale, A. Deppman, G. D. Erasmo, R. de Rooij, M. A. Diaz Corchero, D. di Bari, T. Dietel, C. di Giglio, S. di Liberto, A. di Mauro, P. di Nezza, R. Divià, Ø. Djuvsland, A. Dobrin, T. Dobrowolski, B. Dönigus, O. Dordic, O. Driga, A. K. Dubey, A. Dubla, L. Ducroux, P. Dupieux, A. K. Dutta Majumdar, D. Elia, D. Emschermann, H. Engel, B. Erazmus, H. A. Erdal, B. Espagnon, M. Estienne, S. Esumi, D. Evans, G. Eyyubova, D. Fabris, J. Faivre, D. Falchieri, A. Fantoni, M. Fasel, R. Fearick, D. Fehlker, L. Feldkamp, D. Felea, A. Feliciello, B. Fenton-Olsen, G. Feofilov, A. Fernández Téllez, A. Ferretti, A. Festanti, J. Figiel, M. A. S. Figueredo, S. Filchagin, D. Finogeev, F. M. Fionda, E. M. Fiore, E. Floratos, M. Floris, S. Foertsch, P. Foka, S. Fokin, E. Fragiacomo, A. Francescon, U. Frankenfeld, U. Fuchs, C. Furget, M. Fusco Girard, J. J. Gaardhøje, M. Gagliardi, A. Gago, M. Gallio, D. R. Gangadharan, P. Ganoti, C. Garabatos, E. Garcia-Solis, C. Gargiulo, I. Garishvili, J. Gerhard, M. Germain, C. Geuna, A. Gheata, M. Gheata, B. Ghidini, P. Ghosh, P. Gianotti, M. R. Girard, P. Giubellino, E. Gladysz-Dziadus, P. Glässel, R. Gomez, E. G. Ferreiro, L. H. González-Trueba, P. González-Zamora, S. Gorbunov, A. Goswami, S. Gotovac, L. K. Graczykowski, R. Grajcarek, A. Grelli, A. Grigoras, C. Grigoras, V. Grigoriev, S. Grigoryan, A. Grigoryan, B. Grinyov, N. Grion, P. Gros, J. F. Grosse-Oetringhaus, J. Y. Grossiord, R. Grosso, F. Guber, R. Guernane, B. Guerzoni, M. Guilbaud, K. Gulbrandsen, H. Gulkanyan, T. Gunji, R. Gupta, A. Gupta, R. Haake, Ø. Haaland, C. Hadjidakis, M. Haiduc, H. Hamagaki, G. Hamar, B. H. Han, L. D. Hanratty, A. Hansen, Z. Harmanová-Tóthová, J. W. Harris, M. Hartig, A. Harton, D. Hatzifotiadou, S. Hayashi, A. Hayrapetyan, S. T. Heckel, M. Heide, H. Helstrup, A. Herghelegiu, G. Herrera Corral, N. Herrmann, B. A. Hess, K. F. Hetland, B. Hicks, B. Hippolyte, Y. Hori, P. Hristov, I. Hřivnáčová, M. Huang, T. J. Humanic, D. S. Hwang, R. Ichou, R. Ilkaev, I. Ilkiv, M. Inaba, E. Incani, G. M. Innocenti, P. G. Innocenti, M. Ippolitov, M. Irfan, C. Ivan, M. Ivanov, A. Ivanov, V. Ivanov, O. Ivanytskyi, A. Jachołkowski, P. M. Jacobs, H. J. Jang, M. A. Janik, R. Janik, P. H. S. Y. Jayarathna, S. Jena, D. M. Jha, R. T. Jimenez Bustamante, P. G. Jones, H. Jung, A. Jusko, A. B. Kaidalov, S. Kalcher, P. Kaliňák, T. Kalliokoski, A. Kalweit, J. H. Kang, V. Kaplin, A. Karasu Uysal, O. Karavichev, T. Karavicheva, E. Karpechev, A. Kazantsev, U. Kebschull, R. Keidel, M. M. Khan, K. H. Khan, P. Khan, S. A. Khan, A. Khanzadeev, Y. Kharlov, B. Kileng, T. Kim, J. S. Kim, D. J. Kim, S. Kim, M. Kim, B. Kim, M. Kim, D. W. Kim, J. H. Kim, S. Kirsch, I. Kisel, S. Kiselev, A. Kisiel, J. L. Klay, J. Klein, C. Klein-Bösing, M. Kliemant, A. Kluge, M. L. Knichel, A. G. Knospe, M. K. Köhler, T. Kollegger, A. Kolojvari, M. Kompaniets, V. Kondratiev, N. Kondratyeva, A. Konevskikh, V. Kovalenko, M. Kowalski, S. Kox, G. Koyithatta Meethaleveedu, J. Kral, I. Králik, F. Kramer, A. Kravčáková, T. Krawutschke, M. Krelina, M. Kretz, M. Krivda, F. Krizek, M. Krus, E. Kryshen, M. Krzewicki, Y. Kucheriaev, T. Kugathasan, C. Kuhn, P. G. Kuijer, I. Kulakov, J. Kumar, P. Kurashvili, A. Kurepin, A. B. Kurepin, A. Kuryakin, S. Kushpil, V. Kushpil, H. Kvaerno, M. J. Kweon, Y. Kwon, P. Ladrón de Guevara, I. Lakomov, R. Langoy, S. L. la Pointe, C. Lara, A. Lardeux, P. la Rocca, R. Lea, M. Lechman, K. S. Lee, G. R. Lee, S. C. Lee, I. Legrand, J. Lehnert, R. C. Lemmon, M. Lenhardt, V. Lenti, H. León, I. León Monzón, H. León Vargas, P. Lévai, S. Li, J. Lien, R. Lietava, S. Lindal, V. Lindenstruth, C. Lippmann, M. A. Lisa, H. M. Ljunggren, D. F. Lodato, P. I. Loenne, V. R. Loggins, V. Loginov, D. Lohner, C. Loizides, K. K. Loo, X. Lopez, E. López Torres, G. Løvhøiden, X. G. Lu, P. Luettig, M. Lunardon, J. Luo, G. Luparello, C. Luzzi, R. Ma, K. Ma, D. M. Madagodahettige-Don, A. Maevskaya, M. Mager, D. P. Mahapatra, A. Maire, M. Malaev, I. Maldonado Cervantes, L. Malinina, D. Mal'Kevich, P. Malzacher, A. Mamonov, L. Manceau, L. Mangotra, V. Manko, F. Manso, N. Manukyan, V. Manzari, Y. Mao, M. Marchisone, J. Mareš, G. V. Margagliotti, A. Margotti, A. Marín, C. Markert, M. Marquard, I. Martashvili, N. A. Martin, P. Martinengo, M. I. Martínez, A. Martínez Davalos, G. Martínez García, Y. Martynov, A. Mas, S. Masciocchi, M. Masera, A. Masoni, L. Massacrier, A. Mastroserio, A. Matyja, C. Mayer, J. Mazer, M. A. Mazzoni, F. Meddi, A. Menchaca-Rocha, J. Mercado Pérez, M. Meres, Y. Miake, K. Mikhaylov, L. Milano, J. Milosevic, A. Mischke, A. N. Mishra, D. Miśkowiec, C. Mitu, S. Mizuno, J. Mlynarz, B. Mohanty, L. Molnar, L. Montaño Zetina, M. Monteno, E. Montes, T. Moon, M. Morando, D. A. Moreira de Godoy, S. Moretto, A. Morreale, A. Morsch, V. Muccifora, E. Mudnic, S. Muhuri, M. Mukherjee, H. Müller, M. G. Munhoz, S. Murray, L. Musa, J. Musinsky, B. K. Nandi, R. Nania, E. Nappi, C. Nattrass, T. K. Nayak, S. Nazarenko, A. Nedosekin, M. Nicassio, M. Niculescu, B. S. Nielsen, T. Niida, S. Nikolaev, V. Nikolic, S. Nikulin, V. Nikulin, B. S. Nilsen, M. S. Nilsson, F. Noferini, P. Nomokonov, G. Nooren, A. Nyanin, A. Nyatha, C. Nygaard, J. Nystrand, A. Ochirov, H. Oeschler, S. K. Oh, S. Oh, J. Oleniacz, A. C. Oliveira da Silva, C. Oppedisano, A. Ortiz Velasquez, A. Oskarsson, P. Ostrowski, J. Otwinowski, K. Oyama, K. Ozawa, Y. Pachmayer, M. Pachr, F. Padilla, P. Pagano, G. Paić, F. Painke, C. Pajares, S. K. Pal, A. Palaha, A. Palmeri, V. Papikyan, G. S. Pappalardo, W. J. Park, A. Passfeld, B. Pastirčák, D. I. Patalakha, V. Paticchio, B. Paul, A. Pavlinov, T. Pawlak, T. Peitzmann, H. Pereira da Costa, E. Pereira de Oliveira Filho, D. Peresunko, C. E. Pérez Lara, D. Perrino, W. Peryt, A. Pesci, V. Peskov, Y. Pestov, V. Petráček, M. Petran, M. Petris, P. Petrov, M. Petrovici, C. Petta, S. Piano, M. Pikna, P. Pillot, O. Pinazza, L. Pinsky, N. Pitz, D. B. Piyarathna, M. Planinic, M. Płoskoń, J. Pluta, T. Pocheptsov, S. Pochybova, P. L. M. Podesta-Lerma, M. G. Poghosyan, K. Polák, B. Polichtchouk, N. Poljak, A. Pop, S. Porteboeuf-Houssais, V. Pospíšil, B. Potukuchi, S. K. Prasad, R. Preghenella, F. Prino, C. A. Pruneau, I. Pshenichnov, G. Puddu, V. Punin, M. Putiš, J. Putschke, H. Qvigstad, A. Rachevski, A. Rademakers, T. S. Räihä, J. Rak, A. Rakotozafindrabe, L. Ramello, A. Ramírez Reyes, S. Raniwala, R. Raniwala, S. S. Räsänen, B. T. Rascanu, D. Rathee, K. F. Read, J. S. Real, K. Redlich, R. J. Reed, A. Rehman, P. Reichelt, M. Reicher, R. Renfordt, A. R. Reolon, A. Reshetin, F. Rettig, J. P. Revol, K. Reygers, L. Riccati, R. A. Ricci, T. Richert, M. Richter, P. Riedler, W. Riegler, F. Riggi, M. Rodríguez Cahuantzi, A. Rodriguez Manso, K. Røed, E. Rogochaya, D. Rohr, D. Röhrich, R. Romita, F. Ronchetti, P. Rosnet, S. Rossegger, A. Rossi, C. Roy, P. Roy, A. J. Rubio Montero, R. Rui, R. Russo, E. Ryabinkin, A. Rybicki, S. Sadovsky, K. Šafařík, R. Sahoo, P. K. Sahu, J. Saini, H. Sakaguchi, S. Sakai, D. Sakata, C. A. Salgado, J. Salzwedel, S. Sambyal, V. Samsonov, X. Sanchez Castro, L. Šándor, A. Sandoval, M. Sano, G. Santagati, R. Santoro, J. Sarkamo, E. Scapparone, F. Scarlassara, R. P. Scharenberg, C. Schiaua, R. Schicker, H. R. Schmidt, C. Schmidt, S. Schuchmann, J. Schukraft, T. Schuster, Y. Schutz, K. Schwarz, K. Schweda, G. Scioli, E. Scomparin, R. Scott, P. A. Scott, G. Segato, I. Selyuzhenkov, S. Senyukov, J. Seo, S. Serci, E. Serradilla, A. Sevcenco, A. Shabetai, G. Shabratova, R. Shahoyan, S. Sharma, N. Sharma, S. Rohni, K. Shigaki, K. Shtejer, Y. Sibiriak, E. Sicking, S. Siddhanta, T. Siemiarczuk, D. Silvermyr, C. Silvestre, G. Simatovic, G. Simonetti, R. Singaraju, R. Singh, S. Singha, V. Singhal, T. Sinha, B. C. Sinha, B. Sitar, M. Sitta, T. B. Skaali, K. Skjerdal, R. Smakal, N. Smirnov, R. J. M. Snellings, C. Søgaard, R. Soltz, H. Son, J. Song, M. Song, C. Soos, F. Soramel, I. Sputowska, M. Spyropoulou-Stassinaki, B. K. Srivastava, J. Stachel, I. Stan, G. Stefanek, M. Steinpreis, E. Stenlund, G. Steyn, J. H. Stiller, D. Stocco, M. Stolpovskiy, P. Strmen, A. A. P. Suaide, M. A. Subieta Vásquez, T. Sugitate, C. Suire, R. Sultanov, M. Šumbera, T. Susa, T. J. M. Symons, A. Szanto de Toledo, I. Szarka, A. Szczepankiewicz, M. Szymański, J. Takahashi, M. A. Tangaro, J. D. Tapia Takaki, A. Tarantola Peloni, A. Tarazona Martinez, A. Tauro, G. Tejeda Muñoz, A. Telesca, A. ter Minasyan, C. Terrevoli, J. Thäder, D. Thomas, R. Tieulent, A. R. Timmins, D. Tlusty, A. Toia, H. Torii, L. Toscano, V. Trubnikov, D. Truesdale, W. H. Trzaska, T. Tsuji, A. Tumkin, R. Turrisi, T. S. Tveter, J. Ulery, K. Ullaland, J. Ulrich, A. Uras, G. M. Urciuoli, G. L. Usai, M. Vajzer, M. Vala, L. Valencia Palomo, P. Vande Vyvre, M. van Leeuwen, L. Vannucci, A. Vargas, R. Varma, M. Vasileiou, A. Vasiliev, V. Vechernin, M. Veldhoen, M. Venaruzzo, E. Vercellin, S. Vergara, R. Vernet, M. Verweij, L. Vickovic, G. Viesti, J. Viinikainen, Z. Vilakazi, O. Villalobos Baillie, L. Vinogradov, Y. Vinogradov, A. Vinogradov, T. Virgili, Y. P. Viyogi, A. Vodopyanov, M. A. Völkl, S. Voloshin, K. Voloshin, G. Volpe, B. von Haller, I. Vorobyev, D. Vranic, J. Vrláková, B. Vulpescu, A. Vyushin, V. Wagner, B. Wagner, R. Wan, Y. Wang, M. Wang, D. Wang, Y. Wang, K. Watanabe, M. Weber, J. P. Wessels, U. Westerhoff, J. Wiechula, J. Wikne, M. Wilde, A. Wilk, G. Wilk, M. C. S. Williams, B. Windelband, L. Xaplanteris Karampatsos, C. G. Yaldo, Y. Yamaguchi, H. Yang, S. Yang, S. Yasnopolskiy, J. Yi, Z. Yin, I. K. Yoo, J. Yoon, W. Yu, X. Yuan, I. Yushmanov, V. Zaccolo, C. Zach, C. Zampolli, S. Zaporozhets, A. Zarochentsev, P. Závada, N. Zaviyalov, H. Zbroszczyk, P. Zelnicek, I. S. Zgura, M. Zhalov, X. Zhang, H. Zhang, Y. Zhou, F. Zhou, D. Zhou, J. Zhu, J. Zhu, X. Zhu, H. Zhu, A. Zichichi, A. Zimmermann, G. Zinovjev, Y. Zoccarato, M. Zynovyev, M. Zyzak, "Centrality dependence of π , K , and p production in Pb-Pb collisions at s N N = 2.76 TeV," Physical Review C, vol. 88 no. 4, article 044910,DOI: 10.1103/PhysRevC.88.044910, 2013.

[56] L. Kumar, "Systematics of kinetic freeze-out properties in high energy collisions from STAR," Nuclear Physics A, vol. 931, pp. 1114-1119, DOI: 10.1016/j.nuclphysa.2014.08.085, 2014.

[57] A. Khuntia, H. Sharma, S. K. Tiwari, R. Sahoo, J. Cleymans, "Radial flow and differential freeze-out in proton-proton collisions at s = 7 TeV at the LHC," The European Physical Journal A, vol. 55,DOI: 10.1140/epja/i201912669-6, 2019.

[58] P. F. Kolb, U. Heinz, "Hydrodynamic description of ultrarelativistic heavy-ion collisions," Quark-Gluon Plasma 3,DOI: 10.1142/5029, 2004.

[59] D. Thakur, S. Tripathy, P. Garg, R. Sahoo, J. Cleymans, "Indication of a differential freeze-out in proton-proton and heavy-ion collisions at RHIC and LHC energies," Advances in High Energy Physics, vol. 2016,DOI: 10.1155/2016/4149352, 2016.

[60] P.-P. Yang, M.-Y. Duan, F.-H. Liu, R. Sahoo, "Multiparticle production and initial quasi-temperature from proton induced carbon collisions at p L a b = 31 GeV/ c," , . https://arxiv.org/abs/1903.04008