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Waqas M, Haj Ismail A, Alrebdi HI, Ajaz M. Centrality and System Size Dependence among Freezeout Parameters and the Implications for EOS and QGP in High-Energy Collisions. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1586. [PMID: 38136466 PMCID: PMC10742792 DOI: 10.3390/e25121586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Revised: 11/22/2023] [Accepted: 11/24/2023] [Indexed: 12/24/2023]
Abstract
Utilizing the Modified Hagedorn function with embedded flow, we analyze the transverse momenta (pT) and transverse mass (mT) spectra of π+ in Au-Au, Cu-Cu, and d-Au collisions at sNN = 200 GeV across various centrality bins. Our study reveals the centrality and system size dependence of key freezeout parameters, including kinetic freezeout temperature (T0), transverse flow velocity (βT), entropy-related parameter (n), and kinetic freezeout volume (V). Specifically, T0 and n increase from central to peripheral collisions, while βT and V show the opposite trend. These parameters also exhibit system size dependence; T0 and βT are smaller in larger collision systems, whereas V is larger. Importantly, central collisions correspond to a stiffer Equation of State (EOS), characterized by larger βT and smaller T0, while peripheral collisions indicate a softer EOS. These insights are crucial for understanding the properties of Quark-Gluon Plasma (QGP) and offer valuable constraints for Quantum Chromodynamics (QCD) models at high temperatures and densities.
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Affiliation(s)
- Muhammad Waqas
- School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan 442002, China
| | - Abd Haj Ismail
- College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates
| | - Haifa I. Alrebdi
- Department of Physics, College of Science, Prince Nourah Bint Abdulrahman Univeristy, P.O.Box 84428, Riyadh 11671, Saudi Arabia
| | - Muhammad Ajaz
- Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
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Ajaz M, Haj Ismail AAK, Ullah Mian M, Khan R, Shehzadi R, Adil Khan M, AbdelKader A, Waqas M, Dawi EA, Tabassam U. Charged Particles Transverse Momentum and Pseudorapidity Distribution in Hadronic Collisions at LHC Energies. ENTROPY (BASEL, SWITZERLAND) 2023; 25:452. [PMID: 36981340 PMCID: PMC10099715 DOI: 10.3390/e25030452] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Revised: 02/28/2023] [Accepted: 03/03/2023] [Indexed: 06/18/2023]
Abstract
We present an analysis of the pseudorapidity η and transverse momentum pT distributions of charged hadrons in pp collisions for the kinematic range of 0<pT<4 GeV/c and |η|<2.4 at 0.9, 2.36, and 7 TeV. Charged particles are produced in pp collision using several Monte Carlo event generators (Pythia Simple, Vincia, Dire showers, Sibyll2.3d, QGSJETII-04, EPOS-LHC) and compared with CMS data at LHC. It is observed that the Simple parton showers can explain the CMS data very well for pT>1 GeV/c at 0.9 and 2.36 TeV within the experimental errors, while Dire overshoots and Vicia undershoots the data by 50% each. At 7 TeV, the Dire module presents a good prediction, whereas the Simple and Vincia modules underestimate the data within 30% and 50%. Comparing the Simple module of the Pythia model and the predictions of the CRMC models with the experimental data shows that at 0.9 TeV, EPOS-LHC has better results than the others. At 2.36 GeV, the cosmic rays Monte Carlo (CRMC) models have better prediction than the Simple module of Pythia at low pT, while QGSJETII-04 predicts well at high pT. QGSJETII-04 and EPOS-LHC have closer results than the Pythia-Simple and Sibyll2.3d at 7 TeV. In the case of the pseudorapidity distributions, only the Pythia-Simple reproduced the experimental measurements at all energies. The Dire module overestimates, while Vincia underestimates the data in decreasing order of discrepancy (20%, 12%, 5%) with energy. All CRMC models underestimate the data over the entire η range at all energies by 20%. The angular ordering of partons and the parton fragmentation could be possible reasons for this deviation. Furthermore, we used the two-component standard distribution to fit the pT spectra to the experimental data and extracted the effective temperature (Teff) and the multiplicity parameter (N0). It is observed that Teff increases with the increase in the center of mass energy. The fit yielded 0.20368±0.01, 0.22348±0.011, and 0.24128±0.012 GeV for 0.9, 2.36, and 7 TeV, respectively. This shows that the system at higher energies freezes out earlier than lower ones because they quickly attain the equilibrium state.
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Affiliation(s)
- Muhammad Ajaz
- Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
| | - Abd Al Karim Haj Ismail
- College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates
- Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates
| | - Mateen Ullah Mian
- Department of Physics, Islamia College Peshawar, Peshawar 25120, Pakistan
| | - Rashid Khan
- Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
| | - Ramoona Shehzadi
- Department of Physics, University of the Punjab, Lahore 54590, Pakistan
| | - Muhammad Adil Khan
- Department of Physics, Islamia College Peshawar, Peshawar 25120, Pakistan
| | - Atef AbdelKader
- College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates
- Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates
| | - Muhammad Waqas
- School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan 442002, China
| | - Elmuez A. Dawi
- College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates
- Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates
| | - Uzma Tabassam
- Department of Physics, COMSATS University Islamabad, Islamabad 44000, Pakistan
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Ajaz M, Haj Ismail AAK, Waqas M, Suleymanov M, AbdelKader A, Suleymanov R. Pseudorapidity dependence of the bulk properties of hadronic medium in pp collisions at 7 TeV. Sci Rep 2022; 12:8142. [PMID: 35581273 PMCID: PMC9114398 DOI: 10.1038/s41598-022-11685-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 04/22/2022] [Indexed: 11/17/2022] Open
Abstract
The measured charged particle \documentclass[12pt]{minimal}
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\begin{document}$$p_T$$\end{document}pT spectra in proton-proton collisions obtained by the CMS experiment at CERN is compared with the simulation results of EPOS–LHC and Pythia8.24 models at 7 TeV center-of-mass energy. The Pythia8.24 model describes the experimental data very well, particularly in the high \documentclass[12pt]{minimal}
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\begin{document}$$p_T$$\end{document}pT region. The model also predicts the \documentclass[12pt]{minimal}
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\begin{document}$$p_T$$\end{document}pT spectra for \documentclass[12pt]{minimal}
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\begin{document}$$|$$\end{document}|\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}η\documentclass[12pt]{minimal}
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\begin{document}$$|$$\end{document}| < 2.4 at 0 \documentclass[12pt]{minimal}
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\begin{document}$$\le $$\end{document}≤\documentclass[12pt]{minimal}
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\begin{document}$$p_T$$\end{document}pT\documentclass[12pt]{minimal}
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\begin{document}$$\le $$\end{document}≤ 6 \documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV/}c$$\end{document}GeV/c. The EPOS–LHC model underpredicts the \documentclass[12pt]{minimal}
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\begin{document}$$p_T$$\end{document}pT spectra from 0.1 to 2 \documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV/}c$$\end{document}GeV/c in all \documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}η bins for about 20% and the \documentclass[12pt]{minimal}
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\begin{document}$$p_T$$\end{document}pT spectrum from 0.1 to 4.2 \documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV/}c$$\end{document}GeV/c for \documentclass[12pt]{minimal}
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\begin{document}$$|$$\end{document}|\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}η\documentclass[12pt]{minimal}
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\begin{document}$$|$$\end{document}| < 2.4 by about 15% while reasonably predicts well for \documentclass[12pt]{minimal}
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\begin{document}$$p_T$$\end{document}pT > 4.2 \documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV/}c$$\end{document}GeV/c within the experimental errors. Furthermore, to get information about collective properties of the hadronic matter, modified Hagedorn function with embedded transverse flow velocity and thermodynamically consistent Tsallis distribution functions are used to fit the experimental data and simulated results. The values of \documentclass[12pt]{minimal}
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\begin{document}$$\chi ^2/ndf$$\end{document}χ2/ndf show that the functions fit the data and simulation results well. The parameter extracted by the functions: \documentclass[12pt]{minimal}
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\begin{document}$$\beta _T$$\end{document}βT, \documentclass[12pt]{minimal}
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\begin{document}$$T_0$$\end{document}T0, and \documentclass[12pt]{minimal}
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\begin{document}$$T_{eff}$$\end{document}Teff decreases with increasing \documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}η. The decrease in \documentclass[12pt]{minimal}
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\begin{document}$$\beta _T$$\end{document}βT with increasing \documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}η is due to the large energy deposition in lower rapidity bins producing rapid expansion due to large pressure gradient resulting quick expansion of the fireball. Similarly, large energy transfer in the lower pseudo-rapidity bin results in higher degree of excitation of the system which results larger values of \documentclass[12pt]{minimal}
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\begin{document}$$T_0$$\end{document}T0 and \documentclass[12pt]{minimal}
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\begin{document}$$T_{eff}$$\end{document}Teff. The values of the fit constant \documentclass[12pt]{minimal}
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\begin{document}$$N_0$$\end{document}N0 increase with \documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}η where the values of \documentclass[12pt]{minimal}
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\begin{document}$$N_0$$\end{document}N0 extracted from Pythia8.24 are closer to the data than the EPOS–LHC model. The Pythia8.24 model has better prediction than the EPOS–LHC model which might be connected to its flow-like features and color re-connections resulting from different Parton interactions in the initial and final state.
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Affiliation(s)
- Muhammad Ajaz
- Department of physics, Abdul Wali Khan University Mardan, Mardan, 23200, Pakistan
| | - Abd Al Karim Haj Ismail
- College of Humanities and Sciences, Ajman University, Ajman, 346, United Arab Emirates. .,Nonlinear Dynamic Research Center (NDRC), Ajman University, Ajman, 346, United Arab Emirates.
| | - Muhammad Waqas
- School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, China.
| | | | - Atef AbdelKader
- College of Humanities and Sciences, Ajman University, Ajman, 346, United Arab Emirates.,Nonlinear Dynamic Research Center (NDRC), Ajman University, Ajman, 346, United Arab Emirates
| | - Rustam Suleymanov
- Institute of Physics, National Academy of Sciences, Baku, Azerbaijan
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