Abstract
To determine the center of mass energy at which ordinary matter undergoes a transition to hot and dense matter, we employed a combination of the blast wave model and Tsallis statistics. Specifically, we analyzed the transverse momentum spectra of resonance particles (in this case, \(K^{*0}\)) produced in different centrality intervals during Au–Au collisions at various energies ranging from \(\sqrt{s_{NN}}= 7.7\) to 39 GeV. Our findings include the phase transition from hadronic matter to the quark-gluon plasma (QGP), and a quick expansion of the system at higher energies and in more central collisions, and disclose the fact that the central collision system, as well as the systems with higher center of mass energies, are easy to be in equilibrium. Our observations indicate a phase transition occurring from ordinary hadronic matter to the quark-gluon plasma (QGP) state in the final stages of collisions but not in the initial stages. Besides, we presented the correlation of \(T_0\) with various parameters and reported the higher excitation degree of the fireball and its rapid expansion. Our results can provide further insights into the role of the fluctuations in thermal excitation and collective expansion.
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Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data used to support the findings of this study are included within the article and are cited in relevant places within the text as references.]
References
B. Liu, M. Toro, G.Y. Shao, V. Greco, C.W. Shen, Z.H. Li, Hadron-quark phase coexistence in a hybrid MIT-Bag model. Eur. Phys. J. A 47, 104 (2011). https://doi.org/10.1140/epja/i2011-11104-6. arXiv:1105.0555 [nucl-th]
H. Satz, R. Stock, Quark matter: the beginning. Nucl. Phys. A 956, 898–901 (2016). https://doi.org/10.1016/j.nuclphysa.2016.06.002
H. Bohr, H.B. Nielsen, Hadron production from a boiling quark soup. Nucl. Phys. B 128, 275–293 (1977). https://doi.org/10.1016/0550-3213(77)90032-3
C.P. Robert, G. Casella, Monte Carlo Statistical Methods, 2nd edn. (Springer Press, New York, 2004)
Z.w. Lin, M. Gyulassy, Open charm as a probe of preequilibrium dynamics in nuclear collisions. Phys. Rev. C 51 (1995), 2177–2187 [erratum: Phys. Rev. C 52 (1995), 440] https://doi.org/10.1103/PhysRevC.52.440arXiv:nucl-th/9409007 [nucl-th]
F. Karsch, D. Kharzeev, K. Tuchin, Universal properties of bulk viscosity near the QCD phase transition. Phys. Lett. B 663, 217–221 (2008). https://doi.org/10.1016/j.physletb.2008.01.080. arXiv:0711.0914 [hep-ph]
D. Kharzeev, K. Tuchin, Bulk viscosity of QCD matter near the critical temperature. JHEP 09, 093 (2008). https://doi.org/10.1088/1126-6708/2008/09/093. arXiv:0705.4280 [hep-ph]
M. Cacciari, P. Nason, R. Vogt, QCD predictions for charm and bottom production at RHIC. Phys. Rev. Lett. 95, 122001 (2005). https://doi.org/10.1103/PhysRevLett.95.122001. arXiv:hep-ph/0502203 [hep-ph]
M.A. Stephanov, QCD phase diagram and the critical point. Prog. Theor. Phys. Suppl. 153, 139–156 (2004). https://doi.org/10.1142/S0217751X05027965. arXiv:hep-ph/0402115 [hep-ph]
A. Barducci, R. Casalbuoni, S. De Curtis, R. Gatto, G. Pettini, Chiral phase transitions in QCD for finite temperature and density. Phys. Rev. D 41, 1610 (1990). https://doi.org/10.1103/PhysRevD.41.1610
M. Tokarev, A. Kechechyan, I. Zborovský, Validation of \(z\)-scaling for negative particle production in \(Au\) + \(Au\) collisions from BES-I at STAR. Nucl. Phys. A 993, 121646 (2020). https://doi.org/10.1016/j.nuclphysa.2019.121646
G. Odyniec, for the STAR Collaboration, PoS CORFU2018, 151 (2018)
L. Kumar, Review of recent results from the RHIC beam energy scan. Mod. Phys. Lett. A 28, 1330033 (2013). https://doi.org/10.1142/S0217732313300334. arXiv:1311.3426 [nucl-ex]
L. Kumar, STAR Results from the RHIC Beam Energy Scan-I, Nucl. Phys. A 904-905 (2013), 256c–263c https://doi.org/10.1016/j.nuclphysa.2013.01.070arXiv:1211.1350 [nucl-ex]
L. Adamczyk et al. [STAR], Bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program. Phys. Rev. C 964, 044904 (2017). https://doi.org/10.1103/PhysRevC.96.044904arXiv:1701.07065 [nucl-ex]
F. Becattini, J. Manninen, M. Gazdzicki, Energy and system size dependence of chemical freeze-out in relativistic nuclear collisions. Phys. Rev. C 73, 044905 (2006). https://doi.org/10.1103/PhysRevC.73.044905. arXiv:hep-ph/0511092 [hep-ph]
J. Cleymans, K. Redlich, Chemical and thermal freezeout parameters from 1-A/GeV to 200-A/GeV. Phys. Rev. C 60, 054908 (1999). https://doi.org/10.1103/PhysRevC.60.054908. arXiv:nucl-th/9903063 [nucl-th]
A. Andronic, P. Braun-Munzinger, J. Stachel, Hadron production in central nucleus-nucleus collisions at chemical freeze-out. Nucl. Phys. A 772, 167–199 (2006). https://doi.org/10.1016/j.nuclphysa.2006.03.012. arXiv:nucl-th/0511071 [nucl-th]
E. Laermann, O. Philipsen, The Status of lattice QCD at finite temperature. Ann. Rev. Nucl. Part. Sci. 53, 163–198 (2003). https://doi.org/10.1146/annurev.nucl.53.041002.110609. arXiv:hep-ph/0303042 [hep-ph]
Q. Wang, F.H. Liu, K.K. Olimov, Initial-state temperature of light meson emission source from squared momentum transfer spectra in high-energy collisions. Front. Phys. 9, 792039 (2021). https://doi.org/10.3389/fphy.2021.792039. arXiv:2111.04486 [hep-ph]
Q. Wang, F.H. Liu, K.K. Olimov, Initial- and final-state temperatures of emission source from differential cross-section in squared momentum transfer in high-energy collisions. Adv. High Energy Phys. 2021, 6677885 (2021). https://doi.org/10.1155/2021/6677885. arXiv:2104.14271 [hep-ph]
Q. Wang, F.H. Liu, Excitation function of initial temperature of heavy flavor quarkonium emission source in high energy collisions. Adv. High Energy Phys. 2020, 5031494 (2020). https://doi.org/10.1155/2020/5031494. arXiv:2005.04940 [hep-ph]
L.N. Gao, F.H. Liu, B.C. Li, Rapidity dependent transverse momentum spectra of heavy quarkonia produced in small collision systems at the LHC. Adv. High Energy Phys. 2019, 6739315 (2019). https://doi.org/10.1155/2019/6739315. arXiv:1901.05823 [hep-ph]
M. Waqas, L.M. Liu, G.X. Peng, M. Ajaz, A.A.K. Haj Ismail, E.A. Dawi, A.M. Khubrani, Observation of non-homogeneous scenarios for different temperatures in hadron (nucleus)-nucleus collisions at RHIC and LHC energies. Chin. J. Phys. 80, 206–228 (2022). https://doi.org/10.1016/j.cjph.2022.09.016
T. Hirano, K. Tsuda, Collective flow and two-pion correlations from a relativistic hydrodynamic model with early chemical freeze-out. Phys. Rev. C 66(5), 054905 (2002)
U. Heinz, G. Kestin, Universal chemical freeze-out as a phase transition signature. arXiv preprint arXiv:nucl-th/0612105 (2006)
P. Braun-Munzinger, Chemical equilibration and the hadron-QGP phase transition. arXiv preprint arXiv:nucl-ex/0007021 (2000)
J. Adam et al. [STAR], Centrality and transverse momentum dependence of \(D^0\)-meson production at mid-rapidity in Au+Au collisions at \({\sqrt{s_{\rm NN}} = {\rm 200\,GeV}}\). Phys. Rev. C 993, 034908, (2019) https://doi.org/10.1103/PhysRevC.99.034908arXiv:1812.10224 [nucl-ex]
M. Ajaz, A.M. Khubrani, M. Waqas, A.A.K. Haj Ismail, E.A. Dawi, Collective properties of hadrons in comparison of models prediction in pp collisions at 7 TeV. Results Phys. 36, 105433 (2022). https://doi.org/10.1016/j.rinp.2022.105433
J. Gu, C. Li, Q. Wang, W. Zhang, H. Zheng, J. Phys. G 49(11), 115101 (2022). https://doi.org/10.1088/1361-6471/ac9074. arXiv:2201.02091 [nucl-th]
B.C. Li, Y.Z. Wang, F.H. Liu, Formulation of transverse mass distributions in Au–Au collisions at \(\sqrt{s_{NN}}\)=200 GeV/nucleon. Phys. Lett. B 725, 352–356 (2013). https://doi.org/10.1016/j.physletb.2013.07.043. arXiv:1402.6023 [hep-ph]
J.X. Sun, L.L. Liu, E.Q. Wang, F.H. Liu, Charged particle pseudorapidity distributions in high energy p-anti-p or p–p collisions and the improved multi-source thermal model. Indian J. Phys. 87, 177–184 (2013). https://doi.org/10.1007/s12648-012-0193-0
M. Waqas, H.M. Chen, G.X. Peng, A.A.K.H. Ismail, M. Ajaz, Z. Wazir, R. Shehzadi, S. Jamal, A. AbdelKader, Study of kinetic freeze-out parameters as a function of rapidity in pp collisions at CERN SPS energies. Entropy 23(10), 1363 (2021). https://doi.org/10.3390/e23101363. arXiv:2109.05831 [hep-ph]
M. Waqas, G.X. Peng, Z. Wazir, H. Lao, Analysis of kinetic freeze-out temperature and transverse flow velocity in nucleus–nucleus and proton–proton collisions at same center-of-mass energy. Int. J. Mod. Phys. E 30(08), 2150061 (2021). https://doi.org/10.1142/S0218301321500610. arXiv:2107.11613 [hep-ph]
L.J. Gutay, A.S. Hirsch, C. Pajares, R.P. Scharenberg, B.K. Srivastava, De-Confinement in small systems: clustering of color sources in high multiplicity \({\bar{p}}\)p collisions at \(\sqrt{s}\)= 1.8 TeV. Int. J. Mod. Phys. E 24(12), 1550101 (2015). https://doi.org/10.1142/S0218301315501013. arXiv:1504.08270 [nucl-ex]
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. Eur. Phys. J. A 54(8), 136 (2018). https://doi.org/10.1140/epja/i2018-12571-9. arXiv:1803.08280 [hep-ph]
R.P. Scharenberg, B.K. Srivastava, C. Pajares, Exploring the initial stage of high multiplicity proton-proton collisions by determining the initial temperature of the quark–gluon plasma. Phys. Rev. D 100(11), 114040 (2019). https://doi.org/10.1103/PhysRevD.100.114040. arXiv:1803.02301 [hep-ph]
M. Waqas, F.H. Liu, R.Q. Wang, I. Siddique, Eur. Phys. J. A 56(7), 188 (2020). https://doi.org/10.1140/epja/s10050-020-00192-y. arXiv:2007.00825 [hep-ph]
M. Waqas, F.H. Liu, S. Fakhraddin, M.A. Rahim, Possible scenarios for single, double, or multiple kinetic freeze-out in high energy collisions. Indian J. Phys. 93(10), 1329–1343 (2019). https://doi.org/10.1007/s12648-019-01396-9. arXiv:1806.04312 [nucl-th]
M. Waqas, G.X. Peng, F.H. Liu, An evidence of triple kinetic freezeout scenario observed in all centrality intervals in Cu–Cu, Au–Au and Pb–Pb collisions at high energies. J. Phys. G 48(7), 075108 (2021). https://doi.org/10.1088/1361-6471/abdd8d. arXiv:2101.07971 [hep-ph]
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? Nucl. Sci. Tech. 29(6), 82 (2018). https://doi.org/10.1007/s41365-018-0425-x. arXiv:1703.04944 [nucl-th]
M.S. Abdallah [STAR], et al., \(K*0\) production in Au+Au collisions at sNN=7.7, 11.5, 14.5, 19.6, 27, and 39 GeV from the RHIC beam energy scan. Phys. Rev. C 1073, 034907 (2023). https://doi.org/10.1103/PhysRevC.107.034907. arXiv:2210.02909 [nucl-ex]
J. Cleymans, D. Worku, Relativistic thermodynamics: transverse momentum distributions in high-energy physics. Eur. Phys. J. A 48, 160 (2012). https://doi.org/10.1140/epja/i2012-12160-0. arXiv:1203.4343 [hep-ph]
E. Schnedermann, J. Sollfrank, U.W. Heinz, Thermal phenomenology of hadrons from 200-A/GeV S+S collisions. Phys. Rev. C 48, 2462–2475 (1993). https://doi.org/10.1103/PhysRevC.48.2462. arXiv:nucl-th/9307020 [nucl-th]
B.I. Abelev et al. [STAR], Identified particle production, azimuthal anisotropy, and interferometry measurements in Au+Au collisions at s(NN)**(1/2) = 9.2- GeV. Phys. Rev. C 81, 024911 (2010). https://doi.org/10.1103/PhysRevC.81.024911. arXiv:0909.4131 [nucl-ex]
B.I. Abelev et al., Systematic measurements of identified particle spectra in \(p p, d^+\) Au and Au+Au collisions from STAR. Phys. Rev. C 79, 034909 (2009). https://doi.org/10.1103/PhysRevC.79.034909. arXiv:0808.2041 [nucl-ex]
Z. Tang, Y. Xu, L. Ruan, G. van Buren, F. Wang, Z. Xu, Spectra and radial flow at RHIC with Tsallis statistics in a Blast-Wave description. Phys. Rev. C 79, 051901 (2009). https://doi.org/10.1103/PhysRevC.79.051901. arXiv:0812.1609 [nucl-ex]
R. Hagedorn, Multiplicities, \(p_T\) distributions and the expected hadron \(\longrightarrow\) quark-gluon phase tranistion. Riv. Nuovo Cimento 6, 1 (1983)
H. Zheng, L. Zhu, Comparing the Tsallis distribution with and without thermodynamical description in \(p+p\) collisions. Adv. High Energy Phys. 2016, 9632126 (2016). https://doi.org/10.1155/2016/9632126. arXiv:1512.03555 [nucl-th]
P. P. Yang, M. Y. Duan, F. H. Liu, R. Sahoo, Analysis of identified particle transverse momentum spectra produced in pp, p–Pb and Pb–Pb Collisions at the LHC using TP-like function. Symmetry 14(8), 1530 (2022). https://doi.org/10.3390/sym14081530. arXiv:2112.13223 [hep-ph]
R. Odorico, Does a transverse energy trigger actually trigger on large-PT jets? Phys. Lett. B 118, 151 (1982)
T. Mizoguchi, M. Biyajima, N. Suzuki, Analyses of whole transverse momentum distributions in p\({{\bar{p}}}\) and pp collisions by using a modified version of Hagedorn’s formula. Int. J. Mod. Phys. A 32, 1750057 (2017)
G. Arnison et al., Transverse momentum spectra for charged particles at the CERN proton-antiproton collider (UA1 Collaboration). Phys. Lett. B 118, 167 (1982)
M. Petrovici, C. Andrei, I. Berceanu, A. Bercuci, A. Herghelegiu, A. Pop, Recent results and open questions on collective type phenomena from A-A to pp collisions. AIP Conf. Proc. 1645, 52 (2015)
H. Zheng, L.L. Zhu, Comparing the Tsallis distribution with and without tthermodynamical description in p + p collisions. Adv. High Energy Phys. (2016). https://doi.org/10.1155/2016/9632126
B. Abelev et al., Production of \(K^*(892)^0\) and \(\phi (1020)\) in \(pp\) collisions at \(\sqrt{s}=7\) TeV. Eur. Phys. J. C 72, 2183 (2012). https://doi.org/10.1140/epjc/s10052-012-2183-y. arXiv:1208.5717 [hep-ex]
K.K. Olimov, I.A. Lebedev, B.J. Tukhtaev, A.I. Fedosimova, F.H. Liu, S.A. Khudoyberdieva, S.Z. Kanokova, Int. J. Mod. Phys. E 32(12), 2350066 (2023). https://doi.org/10.1142/S0218301323500660
L.L. Li, F.H. Liu, Eur. Phys. J. A 54(10), 169 (2018). https://doi.org/10.3847/1538-4365/aada4a. arXiv:1809.03881 [hep-ph]
M. Waqas, G.X. Peng, R.Q. Wang, M. Ajaz, A.A.K.H. Ismail, Eur. Phys. J. Plus 136(10), 1082 (2021). https://doi.org/10.1140/epjp/s13360-021-02089-1. arXiv:2110.09505 [nucl-th]
M.A. Stankiewicz, Entropy in the thermal model, arXiv:nucl-th/0509058 [nucl-th]
M. Waqas, B.C. Li, Kinetic freeze-out temperature and transverse flow velocity in Au–Au collisions at RHIC-BES energies. Adv. High Energy Phys. 2020, 1787183 (2020). https://doi.org/10.1155/2020/1787183. arXiv:1909.11339 [hep-ph]
Acknowledgements
Under grant number BK202313, the Hubei University of Automotive Technology, Shiyan, China, is supporting this work. The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, Saudi Arabia for funding this research work through the project number “-NBU-FFR -2024-2225-03”. We would also like to acknowledge the support of Ajman University Internal Research Grant No. [DRGS Ref. 2023-IRG-HBS-13].
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Waqas, M., Ajaz, M., Saidani, T. et al. Initial and final state temperature of \(K^{*0}\) in Beam Energy Scan of Au–Au collisions at RHIC energies. Eur. Phys. J. Plus 139, 415 (2024). https://doi.org/10.1140/epjp/s13360-024-05227-7
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DOI: https://doi.org/10.1140/epjp/s13360-024-05227-7