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Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions

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A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "High Energy Nuclear and Particle Physics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 13164

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Special Issue Editors

Prof. Dr. Khusniddin Olimov

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Guest Editor

Physical-Technical Institute of Uzbekistan Academy of Sciences, Tashkent 100084, Uzbekistan
Interests: high-energy proton–proton and heavy-ion collisions; phenomenological analysis of transverse momentum and (pseudo)rapidity distributions of particles; chemical and kinetic freeze-out of particles; non-extensive statistical distributions; equilibration, thermalization and evolution of collision system

Prof. Dr. Fu-Hu Liu

E-Mail Website
Guest Editor

Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
Interests: statistics in high-energy heavy-ion physics; multiparticle production and collective phenomena; properties of chemical and kinetic freeze-outs; electron–positron collisions
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Kosim Olimov

E-Mail Website
Guest Editor

Physical-Technical Institute of Uzbekistan Academy of Sciences, Tashkent 100084, Uzbekistan
Interests: high-energy nuclear collisions; relativistic nuclear collisions; fragmentation of nuclei; processes of multiparticle production; production of resonances in relativistic nuclear collisions

Special Issue Information

Dear Colleagues,

Collectivity plays an important role in all branches of physics, including high-energy physics. Many collective phenomena, such as collective flow, strangeness enhancement, charmonium suppression, jet quenching and others, have been observed so far in high-energy heavy-ion as well as proton–proton collisions. At high-energy heavy-ion collisions, the ordinary nuclear (hadronic) matter gets squeezed and “melts” into the state of Quark–gluon plasma (QGP) at high enough energy density and temperature. This short-lived QGP state of almost free quarks and gluons is believed to have occupied the Universe within a few microseconds after the so-called “Big Bang”, thought to be the starting point in the creation of the Universe. Modern experiments with the Large Hadron Collider (LHC, Switzerland) and Relativistic Heavy-Ion Collider (RHIC, USA) aim to create QGP in high-energy heavy-ion collisions and investigate in detail its various properties. The observations of different QGP signatures in high-multiplicity proton–proton collisions at high energies, including strong similarity and resemblance of collective properties of high-multiplicity proton–proton collisions to those of heavy ions, also show the importance and necessity of further investigations of high-energy proton–proton collisions. Because of the extremely short life time of QGP formation and its evolution, we cannot “detect” and measure its properties directly. Physicists obtain valuable information about the formation, properties and evolution of this hot and dense matter from analysis of properties and spectra of produced particles—“hot” direct photons, pions, kaons, protons and antiprotons, and other particles and resonances consisting of heavy quarks. To extract the parameters and properties of collectivity, it is extremely important and useful to analyze the transverse momentum as well as (pseudo)rapidity distributions of particles produced in high-energy collisions, using efficient phenomenological models based on laws of statistical physics, thermodynamics, and hydrodynamics.

In this Special Issue, we aim to collect original articles and review papers, related to the analysis of any kind of collectivity and collective properties, such as collective flow, strangeness and multistrangeness enhancement, production and suppression of heavy resonances, jet production and quenching, system equilibration and thermalization, and others, in high-energy proton–proton and heavy-ion collisions.

We look forward to receiving your valuable contributions.

With kind regards,

Prof. Dr. Khusniddin Olimov
Prof. Dr. Fu-Hu Liu
Prof. Dr. Kosim Olimov
Guest Editors

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Keywords

Collective flow
Chemical and kinetic freeze-out of particles
System equilibration and thermalization
Strangeness enhancement
Production and suppression of heavy resonances
Jet production and quenching
QGP formation and evolution
Non-extensive statistical (Tsallis) distributions
High-energy proton–proton and heavy-ion collisions

Published Papers (11 papers)

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Research

17 pages, 525 KiB

Open AccessArticle

Space–Time Structure of Particle Emission and Femtoscopy Scales in Ultrarelativistic Heavy-Ion Collisions

by Yuri Sinyukov, Volodymyr Shapoval and Musfer Adzhymambetov

Universe 2023, 9(10), 433; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9100433 - 28 Sep 2023

Cited by 1 | Viewed by 1069

Abstract

The analysis of the spatiotemporal picture of particle radiation in relativistic heavy-ion collisions in terms of correlation femtoscopy scales, emission, and source functions allows one to probe the character of the evolution of the system created in the collision. Realistic models, such as the integrated hydrokinetic model (iHKM), used in the present work, are able to simulate the entire evolution process of strongly interacting matter produced in high-energy nuclear collisions. The mentioned model describes all the stages of the system’s evolution, including thermalisation and hydrodynamisation, which can help researchers figure out the specific details of the process and better understand the formation mechanisms of certain observables. In the current paper, we investigated the behaviour of the pion and kaon interferometry radii and their connection with emission functions in ultrarelativistic heavy-ion collisions at the Large Hadron Collider within iHKM. We focused on the study of the emission time scales at different energies for both particle species (pions and kaons) aiming to gain deeper insight into relation of these scales and the peculiarities of the mentioned system’s collective expansion and decay with the experimentally observed femtoscopy radii. One of our main interests was the problem of the total system’s lifetime estimation based on the femtoscopy analysis. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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23 pages, 904 KiB

Open AccessArticle

Search for Super-Deformed Identical Bands in the A = 190 Mass Region on the Basis of Level Spin

by Poonam Jain, Yogesh Kumar, Vinod Kumar and Pargin Bangotra

Universe 2023, 9(8), 362; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9080362 - 03 Aug 2023

Viewed by 800

Abstract

The systematic study of Super-Deformed (SD) bands in the

A = 190

The systematic study of Super-Deformed (SD) bands in the

A = 190

mass region has been performed. We observed a large number of pairs of SD bands, with different mass numbers, having transition energies nearly equal (within 3 keV) and having identical dynamic moments of inertia. The bands having nearly equal transitions energies and other parameters are called identical bands. We have performed detailed analysis and found 16 pairs of Super-Deformed Identical Bands (SDIBs) whose

E_{γ}

energies and moment of inertia are in good agreement with each other. The modified Variable Moment of Inertia (VMI) model is applied to 16 pairs of SDIBs to estimate the band spins by fitting the two parameters

J_{0}

and C. We found that out of 16 pairs, the band-head spin is consistent with moment of inertia and transition energies for four pairs. For another seven pairs, the transition energies and moment of inertia are identical, but originate from levels with different spins. The remaining five pairs have the identical energy but spins are either increasing or decreasing by one unit in the pair. Secondly, the

N_{p} N_{n}

scheme is applied to verify the existence of SDIBs. The parameters deduced from the

N_{p} N_{n}

scheme are also in good agreement for the mentioned case. The study indicates that each pair of conjugate nuclei have nearly identical spin, moment of inertia (dynamic) and gamma transition energy. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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13 pages, 426 KiB

Open AccessArticle

Excitation Functions of Related Temperatures of η and η⁰ Emission Sources from Squared Momentum Transfer Spectra in High-Energy Collisions

by Qi Wang, Fu-Hu Liu and Khusniddin K. Olimov

Universe 2023, 9(7), 342; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9070342 - 23 Jul 2023

Viewed by 722

Abstract

The squared momentum transfer spectra of

η

and

η^{0}

, produced in high-energy photon–proton (

γ p

)

\to η (η^{0}) + p

processes in electron–proton (

e p

) collisions performed at CEBAF, NINA, CEA, SLAC, DESY, and [...] Read more.

The squared momentum transfer spectra of

η

and

η^{0}

, produced in high-energy photon–proton (

γ p

)

\to η (η^{0}) + p

processes in electron–proton (

e p

) collisions performed at CEBAF, NINA, CEA, SLAC, DESY, and WLS are analyzed. The Monte Carlo calculations are used in the analysis of the squared momentum transfer spectra, where the transfer undergoes from the incident

γ

to emitted

η (η^{0})

or equivalently from the target proton to emitted proton. In the calculations, the Erlang distribution and Tsallis–Levy function are used to describe the transverse momentum (

p_{T}

) spectra of emitted particles. Our results show that the average transverse momentum (

⟨ p_{T} ⟩

), the initial-state temperature (

T_{i}

), and the final-state temperature (

T_{0}

) roughly decrease from the lower center-of-mass energy (W) to the higher one in the concerned energy range of a few GeV, which is different from the excitation function from heavy-ion collisions in the similar energy range. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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11 pages, 301 KiB

Open AccessCommunication

Study of Isothermal Compressibility and Speed of Sound in the Hadronic Matter Formed in Heavy-Ion Collision Using Unified Formalism

by Shubhangi Jain, Rohit Gupta and Satyajit Jena

Universe 2023, 9(4), 170; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9040170 - 30 Mar 2023

Cited by 3 | Viewed by 790

Abstract

The thermodynamical quantities and response functions are useful to describe the particle production in heavy-ion collisions as they reveal crucial information about the produced system. While the study of isothermal compressibility provides an inference about the viscosity of the medium, speed of sound helps in understanding the equation of state. With an aim towards understanding the system produced in the heavy-ion collision, we have made an attempt to study isothermal compressibility and speed of sound as function of charged particle multiplicity in heavy-ion collisions at

\sqrt{s_{N N}}

2.76

TeV,

5.02

TeV, and

5.44

TeV using unified formalism. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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22 pages, 495 KiB

Open AccessArticle

The Theoretical Description of the Transverse Momentum Spectra: A Unified Model

by Rohit Gupta, Anjaly Menon, Shubhangi Jain and Satyajit Jena

Universe 2023, 9(2), 111; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9020111 - 20 Feb 2023

Cited by 1 | Viewed by 1084

Abstract

Analysis of transverse momentum distributions is a useful tool to understand the dynamics of relativistic particles produced in high-energy collisions. Finding a proper distribution function to approximate the spectra is a vastly developing area of research in particle physics. In this work, we have provided a detailed theoretical description of the unified statistical framework in high-energy physics. We have tested the applicability of this framework on experimental data by analyzing the transverse momentum spectra of pion produced in heavy-ion collision at RHIC and LHC. We have also attempted to explain the transverse momentum spectra of charged hadrons formed in pp collision at different energies using the unified statistical framework. This formalism has been proved to nicely explain the spectra of particles produced in soft processes as well as hard scattering processes in a consistent manner. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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11 pages, 340 KiB

Open AccessArticle

Some Aspects of Persistent Homology Analysis on Phase Transition: Examples in an Effective QCD Model with Heavy Quarks

by Hayato Antoku and Kouji Kashiwa

Universe 2023, 9(2), 82; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9020082 - 03 Feb 2023

Cited by 2 | Viewed by 976

Abstract

Recently, persistent homology analysis has been used to investigate phase structure. In this study, we apply persistent homology analysis to the QCD effective model with heavy quarks at finite imaginary chemical potential; i.e., the Potts model with the suitably tuned external field. Since we try to obtain a deeper understanding of the relationship between persistent homology and phase transition in QCD, we consider the imaginary chemical potential because the clear phase transition, which is closely related to the confinement-deconfinement transition, exists. In the actual analysis, we employ the point-cloud approach to consider persistent homology. In addition, we investigate the fluctuation of persistent diagrams to obtain additional information on the relationship between the spatial topology and the phase transition. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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13 pages, 3884 KiB

Open AccessArticle

On Statistical Fluctuations in Collective Flows

by Wei-Liang Qian, Kai Lin, Chong Ye, Jin Li, Yu Pan and Rui-Hong Yue

Universe 2023, 9(2), 67; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9020067 - 27 Jan 2023

Cited by 1 | Viewed by 919

Abstract

In relativistic heavy-ion collisions, event-by-event fluctuations are known to have non-trivial implications. Even though the probability distribution is geometrically isotropic for the initial conditions, the anisotropic

ε_{n}

still differs from zero owing to the statistical fluctuations in the energy profile. On the [...] Read more.

ε_{n}

still differs from zero owing to the statistical fluctuations in the energy profile. On the other hand, the flow harmonics extracted from the hadron spectrum using the multi-particle correlators are inevitably subjected to non-vanishing variance due to the finite number of hadrons emitted in individual events. As one aims to extract information on the fluctuations in the initial conditions via flow harmonics and their fluctuations, finite multiplicity may play a role in interfering with such an effort. In this study, we explore the properties and impacts of such fluctuations in the initial and final states, which both notably appear to be statistical ones originating from the finite number of quanta of the underlying system. We elaborate on the properties of the initial-state eccentricities for the smooth and event-by-event fluctuating initial conditions and their distinct impacts on the resulting flow harmonics. Numerical simulations are performed. The possible implications of the present study are also addressed. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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11 pages, 478 KiB

Open AccessArticle

Dependence of Freeze-Out Parameters on Collision Energies and Cross-Sections

by Muhammad Waqas, Atef AbdelKader, Muhammad Ajaz, Abdel Nasser Tawfik, Zafar Wazir, Abd Al Karim Haj Ismail, Shi Jun Luo and Hafsa Zar Khan

Universe 2023, 9(1), 44; https://0-doi-org.brum.beds.ac.uk/10.3390/universe9010044 - 10 Jan 2023

Cited by 2 | Viewed by 1178

Abstract

We analyzed the transverse momentum spectra (

p_{T}

) reported by the NA61/SHINE and NA49 experiments in inelastic proton–proton (

p p

) and central Lead–Lead (

P b - P b

), Argon–Scandium (

A r - S c

), and [...] Read more.

We analyzed the transverse momentum spectra (

p_{T}

) reported by the NA61/SHINE and NA49 experiments in inelastic proton–proton (

p p

) and central Lead–Lead (

P b - P b

), Argon–Scandium (

A r - S c

), and Beryllium–Beryllium (

B e - B e

) collisions with the Blast-wave model with Boltzmann–Gibbs (BWBG) statistics. The BGBW model was in good agreement with the experimental data. We were able to extract the transverse flow velocity (

β_{T}

), the kinetic freeze-out temperature (

T_{0}

), and the kinetic freeze-out volume (V) from the

p_{T}

spectra using the BGBW model. Furthermore, we also obtained the initial temperature (

T_{i}

) and the mean transverse momentum (<

p_{T}

>) by the alternative method. We observed that

T_{0}

increases with increasing collision energy and collision cross-section, representing the colliding system’s size. The transverse flow velocity was observed to remain invariant with increasing collision energy, while it showed a random change with different collision cross-sections. In the same way, the kinetic freeze-out volume and mean transverse momentum increased with an increase in collision energy or collision cross-section. The same behavior was also seen in the freeze-out temperature, which increased with increasing collision cross-sections. At chemical freeze-out, we also determined both the chemical potential and temperature and compared these with the hadron resonance gas model (HRG) and different experimental data. We report that there is an excellent agreement with the HRG model and various experiments, which reveals the ability of the fit function to manifest features of the chemical freeze-out. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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18 pages, 3499 KiB

Open AccessArticle

Simultaneous Analysis of Midrapidity

p_{T}

Spectra of Identified Particle Species in Pb + Pb Collisions at

\sqrt{s_{n n}}

= 2.76 TeV Using Tsallis Distribution with Transverse Flow

by Khusniddin K. Olimov, Igor A. Lebedev, Anastasiya I. Fedosimova, Fu-Hu Liu, Shakhnoza Z. Kanokova, Maratbek Z. Shodmonov and Boburbek J. Tukhtaev

Universe 2022, 8(12), 655; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8120655 - 13 Dec 2022

Cited by 3 | Viewed by 1300

Abstract

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons in ten groups of centrality of Pb + Pb collisions at

\sqrt{s_{n n}}

= 2.76 TeV, measured by the ALICE Collaboration, have been analyzed successfully using both thermodynamically consistent [...] Read more.

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons in ten groups of centrality of Pb + Pb collisions at

\sqrt{s_{n n}}

= 2.76 TeV, measured by the ALICE Collaboration, have been analyzed successfully using both thermodynamically consistent and non-consistent Tsallis distribution functions with transverse flow. The collision centrality dependencies of the extracted parameters of two kinds of Tsallis functions with transverse flow have been investigated. The significantly different behavior (growth rates) of ⟨β_T⟩ in regions

⟨ N_{p a r t} ⟩

< 71 and

⟨ N_{p a r t} ⟩

> 71 with the temperature T₀ becoming constant in region

⟨ N_{p a r t} ⟩

> 71 has been observed. This could indicate that

⟨ N_{p a r t} ⟩

= 71 ± 5 (corresponding to

⟨ d N_{c h} / d η ⟩

= 205 ± 15) is a threshold border value of collision centrality for crossover phase transition from the dense hadronic state to the QGP state (or a mixed state of QGP and hadrons) in Pb + Pb collisions at

\sqrt{s_{n n}}

= 2.76 TeV. This conjecture is supported further by the observed, significantly different correlations between T₀ and

⟨ β_{T} ⟩

parameters in the corresponding

⟨ β_{T} ⟩

< 0.44 and

⟨ β_{T} ⟩

> 0.44 ranges. The strong positive linear correlation between non-extensivity parameter q for pions and kaons, between q for pions and (anti)protons, and between q for kaons and (anti)protons has been obtained. The parameter q for all studied particle species has proven to be strongly anticorrelated with the average transverse flow velocity, ⟨β_T⟩. Quite a large positive linear correlation has been obtained between the q of the studied particle species and temperature parameter T₀. Analysis of q versus

⟨ N_{p a r t} ⟩

dependencies for the studied particle species suggests that the highly thermalized and equilibrated QGP is produced in central Pb + Pb collisions at

\sqrt{s_{n n}}

= 2.76 TeV with

⟨ N_{p a r t} ⟩

> 160. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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23 pages, 3630 KiB

Open AccessFeature PaperArticle

Centrality-Dependent Chemical Potentials of Light Hadrons and Quarks Based on p_T Spectrum and Particle Yield Ratio in Au-Au Collisions at RHIC Energies

by Xing-Wei He, Hua-Rong Wei, Bi-Hai Hong, Hong-Yu Wu, Wei-Ting Zhu and Feng-Min Wu

Universe 2022, 8(8), 420; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8080420 - 12 Aug 2022

Viewed by 1101

Abstract

We analyze the

p_{T}

spectra of

π^{\pm}

K^{\pm}

, p, and

\bar{p}

produced in different centralities’ Au-Au collisions at different collision energies from 7.7 to 62.4 GeV using a two-component Erlang distribution in the framework of a [...] Read more.

We analyze the

p_{T}

spectra of

π^{\pm}

K^{\pm}

, p, and

\bar{p}

produced in different centralities’ Au-Au collisions at different collision energies from 7.7 to 62.4 GeV using a two-component Erlang distribution in the framework of a multi-source thermal model. The fitting results are consistent with the experimental data, and the yield ratios of negative to positive particles are obtained from the normalization constants. Based on the yield ratios, the chemical potentials of light hadrons (

π

, K, and p) and quarks (u, d, and s) are extracted. This study shows that only the yield ratios of p decrease with the increase in centrality. The logarithms of these yield ratios in the same centrality show obvious linear dependence on

1 / \sqrt{s_{N N}}

. The extracted chemical potentials (the absolute magnitude for

π

) of light hadrons and quarks decrease with the increase in energy. The curves of chemical potential vs. energy for all centralities derived from the linear fits of the logarithms of the yield ratio as a function of energy have their maximum (the absolute magnitude for

π

) at the same energy of 3.526 GeV, which is possibly the critical energy of phase transition from a liquid-like hadron state to a gas-like quark state in the collision system. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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22 pages, 3942 KiB

Open AccessArticle

Analysis of Midrapidity

p_{T}

Distributions of Identified Charged Particles in Pb + Pb Collisions at

\sqrt{s_{n n}}

= 5.02 TeV Using Tsallis Distribution with Embedded Transverse Flow

by Khusniddin K. Olimov, Fu-Hu Liu, Anastasiya I. Fedosimova, Igor A. Lebedev, Airton Deppman, Kobil A. Musaev, Maratbek Z. Shodmonov and Boburbek J. Tukhtaev

Universe 2022, 8(8), 401; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8080401 - 29 Jul 2022

Cited by 7 | Viewed by 1624

Abstract

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at

\sqrt{s_{n n}}

= 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are [...] Read more.

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at

\sqrt{s_{n n}}

= 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are successfully analyzed using combined minimum χ² fits with a thermodynamically non-consistent, as well as thermodynamically consistent, Tsallis function with transverse flow. The extracted non-extensivity parameter q decreases systematically for all considered particle species with increasing Pb + Pb collision centrality, suggesting an increase in the degree of system thermalization with an increase in collision centrality. The results for q suggest quite a large degree of thermalization of quark–gluon plasma (QGP) created in central Pb + Pb collisions at

\sqrt{s_{n n}}

= 5.02 TeV with the average number of participant nucleons

⟨ N_{p a r t} ⟩

> 160. The obtained significantly different growth rates of transverse flow velocity,

⟨ β_{T} ⟩

, in regions

⟨ N_{p a r t} ⟩

< 71 ± 7 and

⟨ N_{p a r t} ⟩

> 71 ± 7 with the temperature parameter T₀ remaining constant within uncertainties in region

⟨ N_{p a r t} ⟩

> 71 ± 7 probably indicates that

⟨ N_{p a r t} ⟩

≈ 71 ± 7 (corresponding to

⟨ d N_{c h} / d η ⟩

≈ 251 ± 20) is a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Pb + Pb collisions at

\sqrt{s_{n n}}

= 5.02 TeV. The threshold border value for transverse flow velocity

⟨ β_{T} ⟩

≈ 0.46 ± 0.03 (corresponding to

⟨ N_{p a r t} ⟩

≈ 71 ± 7), estimated by us in Pb + Pb collisions at

\sqrt{s_{n n}}

= 5.02 TeV, agrees well with the corresponding border value

⟨ β_{T} ⟩

≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at

\sqrt{s_{n n}}

= 5.44 TeV, and with almost constant

⟨ β_{T} ⟩

values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, GA, USA) in central Au + Au collisions in the

\sqrt{s_{n n}}

= 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T₀ and

⟨ β_{T} ⟩

parameters are found to be greatly different in regions

⟨ β_{T} ⟩

< 0.46 and

⟨ β_{T} ⟩

> 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at

\sqrt{s_{n n}}

= 5.02 TeV. Full article

(This article belongs to the Special Issue Collectivity in High-Energy Proton-Proton and Heavy-Ion Collisions)

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