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Waqas M, AbdelKader A, Ajaz M, Tawfik A, Wazir Z, Haj Ismail A, Luo S, Khan H. Dependence of Freeze-Out Parameters on Collision Energies and Cross-Sections. UNIVERSE 2023; 9:44. [DOI: 10.3390/universe9010044] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
We analyzed the transverse momentum spectra (pT) reported by the NA61/SHINE and NA49 experiments in inelastic proton–proton (pp) and central Lead–Lead (Pb−Pb), Argon–Scandium (Ar−Sc), and Beryllium–Beryllium (Be−Be) 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 (βT), the kinetic freeze-out temperature (T0), and the kinetic freeze-out volume (V) from the pT spectra using the BGBW model. Furthermore, we also obtained the initial temperature (Ti) and the mean transverse momentum (<pT>) by the alternative method. We observed that T0 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.
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Affiliation(s)
- Muhammad Waqas
- School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan 442002, China
| | - 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 Ajaz
- Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
| | - Abdel Tawfik
- Faculty of Engineering, Future University in Egypt (FUE), Fifth Settlement, New Cairo 11835, Egypt
| | - Zafar Wazir
- Department of Physics, Ghazi University, Dera Ghazi Khan 32200, Pakistan
| | - Abd 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
| | - Shi Luo
- School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan 442002, China
- Collaborative Center for Optoelectronic Technology, Hubei University of Automotive Technology, Shiyan 442002, China
| | - Hafsa Khan
- Center for High Energy Physics, Punjab University, Lahore P.O. Box 54590, Pakistan
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Waqas M, Liu LM, Peng GX, Ajaz M, Haj Ismail AAK, Dawi E, Khubrani AM. Observation of non-homogeneous scenarios for different temperatures in hadron(nucleus)-nucleus collisions at RHIC and LHC energies. CHINESE JOURNAL OF PHYSICS 2022; 80:206-228. [DOI: 10.1016/j.cjph.2022.09.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Li LL, Haj Ismail AAK. Study of Bulk Properties of Strange Particles in Au+Au Collisions at sNN = 54.4 GeV. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1720. [PMID: 36554123 PMCID: PMC9777710 DOI: 10.3390/e24121720] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/08/2022] [Revised: 11/20/2022] [Accepted: 11/21/2022] [Indexed: 06/17/2023]
Abstract
We analyzed the transverse momentum pT spectra of various strange hadrons KS0, Λ(Λ¯) and Ξ-(Ξ¯+) at mid-rapidity (y) in different centrality intervals from Au+Au collisions at sNN= 54.4 GeV. The pT spectra of these strange hadrons are investigated by the Tsallis-like distribution, which satisfactorily fits the experimental data. The bulk properties of the medium produced in ultra-relativistic heavy-ion collisions at the kinetic freeze-out are reflected by measuring the hadron spectra. The effective temperature T, transverse flow velocity βT, and mean pT along with other parameters that are strongly dependent on centrality and particle specie are extracted. The effective temperature of multi-strange particle (Ξ-(Ξ¯+)) is larger as compared to singly-strange particles Λ(Λ¯) and KS0. Furthermore, the kinetic freeze-out temperature T, transverse flow velocity βT. and mean pT (⟨pT⟩) show a decreasing trend towards lower centrality, while the entropy parameter q increases from central to peripheral collisions. In addition, a positive correlation of ⟨pT⟩ and T and a negative correlation of q and T are also reported.
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Affiliation(s)
- Li-Li Li
- Department of Basic Sciences, Shanxi Agriculture University, Jinzhong 030801, China
| | - 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
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Li LL, Waqas M, Ajaz M, Khubrani AM, Yao H, Adil Khan M. Analyses of pp, Cu- Cu, Au- Au and Pb- Pb Collisions by Tsallis-Pareto Type Function at RHIC and LHC Energies. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1219. [PMID: 36141106 PMCID: PMC9498218 DOI: 10.3390/e24091219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Revised: 08/25/2022] [Accepted: 08/26/2022] [Indexed: 06/16/2023]
Abstract
The parameters revealing the collective behavior of hadronic matter extracted from the transverse momentum spectra of π+, π-, K+, K-, p, p¯, Ks0, Λ, Λ¯, Ξ or Ξ-, Ξ¯+ and Ω or Ω¯+ or Ω+Ω¯ produced in the most central and most peripheral gold-gold (Au-Au), copper-copper (Cu-Cu) and lead-lead (Pb-Pb) collisions at 62.4 GeV, 200 GeV and 2760 GeV, respectively, are reported. In addition to studying the nucleus-nucleus (AA) collisions, we analyzed the particles mentioned above produced in pp collisions at the same center of mass energies (62.4 GeV, 200 GeV and 2760 GeV) to compare with the most peripheral AA collisions. We used the Tsallis-Pareto type function to extract the effective temperature from the transverse momentum spectra of the particles. The effective temperature is slightly larger in a central collision than in a peripheral collision and is mass-dependent. The mean transverse momentum and the multiplicity parameter (N0) are extracted and have the same result as the effective temperature. All three extracted parameters in pp collisions are closer to the peripheral AA collisions at the same center of mass energy, revealing that the extracted parameters have the same thermodynamic nature. Furthermore, we report that the mean transverse momentum in the Pb-Pb collision is larger than that of the Au-Au and Cu-Cu collisions. At the same time, the latter two are nearly equal, which shows their comparatively strong dependence on energy and weak dependence on the size of the system. The multiplicity parameter, N0 in central AA, depends on the interacting system's size and is larger for the bigger system.
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Affiliation(s)
- Li-Li Li
- Department of Basic Sciences, Shanxi Agricultural University, Jinzhong 030801, China
| | - Muhammad Waqas
- School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Muhammad Ajaz
- Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
| | - Ahmed M. Khubrani
- Department of Physics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
| | - Hui Yao
- Department of Basic Sciences, Shanxi Agricultural University, Jinzhong 030801, China
| | - Muhammad Adil Khan
- Department of Physics, Islamia College Peshawar, Peshawar 25120, 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\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}$$p_T$$\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}$$\beta _T$$\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}$$T_{eff}$$\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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Excitation Function of Kinetic Freeze-Out Parameters at 6.3, 17.3, 31, 900 and 7000 GeV. UNIVERSE 2022. [DOI: 10.3390/universe8020138] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2022]
Abstract
The transverse momentum spectra of π+ (π−)(π++π−) at 6.3, 17.3, 31, 900 and 7000 GeV are analyzed by the blast-wave model with Tsallis statistics (TBW) in proton-proton collisions. We took the value of flow profile n0 = 1 and 2 in order to see the difference in the results of the extracted parameters in the two cases. Different rapidity slices at 31 GeV are also analyzed, and the values of the related parameters, such as kinetic freeze-out temperature, transverse flow velocity and kinetic freeze-out volume, are obtained. The above parameters rise with the increase of collision energy, while at 31 GeV, they decrease with increasing rapidity, except for the kinetic freeze-out volume, which increases. We also extracted the parameter q, which is an entropy-based parameter, and its rising trend is noticed with increasing collision energy, while at 31 GeV, no specific dependence of q is observed on rapidity. In addition, the multiplicity parameter N0 and mean transverse momentum are extracted, which increase with increasing collision energy and decrease with increasing rapidity. We notice that the kinetic freeze-out temperature and mean transverse momentum are slightly larger with n0 = 2, while the transverse flow velocity is larger in the case of n0 = 1, but the difference is very small and hence insignificant.
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Abstract
We analyzed the transverse momentum spectra of positively and negatively charged pions (π+ and π−), positively and negatively charged kaons (K+ and K−), protons and antiprotons (p and p¯), as well as ϕ produced in mid-(pseudo)rapidity region in central nucleus–nucleus (AA) collisions over a center-of-mass energy range from 2.16 to 2760 GeV per nucleon pair. The transverse momentum of the considered particle is regarded as the joint contribution of two participant partons which obey the modified Tsallis-like transverse momentum distribution and have random azimuths in superposition. The calculation of transverse momentum distribution of particles is performed by the Monte Carlo method and compared with the experimental data measured by international collaborations. The excitation functions of effective temperature and other parameters are obtained in the considered energy range. With the increase of collision energy, the effective temperature parameter increases quickly and then slowly. The boundary appears at around 5 GeV, which means the change of reaction mechanism and/or generated matter.
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Waqas M, Chen HM, Peng GX, Haj Ismail AAK, Ajaz M, Wazir Z, Shehzadi R, Jamal S, AbdelKader A. Study of Kinetic Freeze-Out Parameters as a Function of Rapidity in pp Collisions at CERN SPS Energies. ENTROPY 2021; 23:e23101363. [PMID: 34682087 PMCID: PMC8534419 DOI: 10.3390/e23101363] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Revised: 09/13/2021] [Accepted: 10/18/2021] [Indexed: 12/03/2022]
Abstract
We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton–proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were π+, π−, K+, K−, and p¯. We extracted the kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease.
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Affiliation(s)
- Muhammad Waqas
- School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China or (M.W.); (H.-M.C.)
| | - Huai-Min Chen
- School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China or (M.W.); (H.-M.C.)
| | - Guang-Xiong Peng
- School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China or (M.W.); (H.-M.C.)
- Correspondence: (G.-X.P.); (A.A.K.H.I.)
| | - Abd Al Karim Haj Ismail
- Department of Mathematics and Science, 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
- Correspondence: (G.-X.P.); (A.A.K.H.I.)
| | - Muhammad Ajaz
- Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan; (M.A.); (S.J.)
| | - Zafar Wazir
- Department of Physics, Ghazi University, Dera Ghazi Khan 32200, Pakistan;
| | - Ramoona Shehzadi
- Department of Physics, University of the Punjab, Lahore 54590, Pakistan;
| | - Sabiha Jamal
- Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan; (M.A.); (S.J.)
| | - Atef AbdelKader
- Department of Mathematics and Science, 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
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