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Examining the model dependence of the determination of kinetic freeze-out temperature and transverse flow velocity in small collision system

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Abstract

The transverse momentum distributions of the identified particles produced in small collision systems at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) have been analyzed by four models. The first two models utilize the blast-wave model with different statistics. The last two models employ certain linear correspondences based on different distributions. The four models describe the experimental data measured by the Pioneering High Energy Nuclear Interaction eXperiment, Solenoidal Tracker at RHIC, and A Large Ion Collider Experiment collaborations equally well. It is found that both the kinetic freeze-out temperature and transverse flow velocity in the central collisions are comparable with those in the peripheral collisions. With the increase of collision energy from that of the RHIC to that of the LHC, the considered quantities typically do not decrease. Comparing with the central collisions, the proton–proton collisions are closer to the peripheral collisions.

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References

  1. J. Cleymans, H. Oeschler, K. Redlich et al., Comparison of chemical freeze-out criteria in heavy-ion collisions. Phys. Rev. C 73, 034905 (2006). https://doi.org/10.1103/PhysRevC.73.034905

    Article  Google Scholar 

  2. A. Andronic, P. Braun-Munzinger, J. Stachel, Hadron production in central nucleus–nucleus collisions at chemical freeze-out. Nucl. Phys. A 772, 167 (2006). https://doi.org/10.1016/j.nuclphysa.2006.03.012

    Article  Google Scholar 

  3. A. Andronic, P. Braun-Munzinger, J. Stachel, Thermal hadron production in relativistic nuclear collisions. Acta Phys. Pol. B 40, 1005 (2009). arXiv:0901.2909 [nucl-th]

    Google Scholar 

  4. A. Andronic, P. Braun-Munzinger, J. Stachel, The horn, the hadron mass spectrum and the QCD phase diagram—the statistical model of hadron production in central nucleus-nucleus collisions. Nucl. Phys. A 834, 237c (2010). https://doi.org/10.1016/j.nuclphysa.2009.12.048

    Article  Google Scholar 

  5. S. Chatterjee, S. Das, L. Kumar et al., Freeze-out parameters in heavy-ion collisions at AGS, SPS, RHIC, and LHC energies. Adv. High Energy Phys. 2015, 349013 (2015). https://doi.org/10.1155/2015/349013

    Article  Google Scholar 

  6. E. Schnedermann, J. Sollfrank, U. Heinz, Thermal phenomenology of hadrons from 200\(A\) GeV S+S collisions. Phys. Rev. C 48, 2462 (1993). https://doi.org/10.1103/PhysRevC.48.2462

    Article  Google Scholar 

  7. B.I. Abelev et al., (STAR Collaboration), Systematic measurements of identified particle spectra in pp, d+Au, and Au+Au collisions at the STAR detector. Phys. Rev. C 79, 034909 (2009). https://doi.org/10.1103/PhysRevC.79.034909

  8. B.I. Abelev et al., (STAR Collaboration), Identified particle production, azimuthal anisotropy, and interferometry measurements in Au+Au collisions at \(\sqrt{s_{\text{NN}}}=\) 9.2 GeV. Phys. Rev. C 81, 024911 (2010). https://doi.org/10.1103/PhysRevC.81.024911

  9. Z.B. Tang, Y.C. Xu, L.J. Ruan et al., Spectra and radial flow in relativistic heavy ion collisions with Tsallis statistics in a blast-wave description. Phys. Rev. C 79, 051901(R) (2009). https://doi.org/10.1103/PhysRevC.79.051901

    Article  Google Scholar 

  10. S. Takeuchi, K. Murase, T. Hirano et al., Effects of hadronic rescattering on multistrange hadrons in high-energy nuclear collisions. Phys. Rev. C 92, 044907 (2015). https://doi.org/10.1103/PhysRevC.92.044907

    Article  Google Scholar 

  11. H. Heiselberg, A.M. Levy, Elliptic flow and Hanbury–Brown–Twiss in noncentral nuclear collisions. Phys. Rev. C 59, 2716 (1999). https://doi.org/10.1103/PhysRevC.59.2716

    Article  Google Scholar 

  12. U.W. Heinz, Lecture Notes for Lectures Presented at the 2nd CERN-Latin-American School of High-Energy Physics, June 1–14, 2003 (San Miguel Regla, Mexico, 2004). arXiv:hep-ph/0407360

    Google Scholar 

  13. R. Russo, Measurement of \(D^+\) meson production in p–Pb collisions with the ALICE detector, Ph.D. thesis (Universita degli Studi di Torino, Italy, 2015). arXiv:1511.04380 [nucl-ex]

  14. H.-L. Lao, F.-H. Liu, B.-C. Li, Kinetic freeze-out temperatures in central and peripheral collisions: which one is larger? Nucl. Sci. Tech. 29, 82 (2018). https://doi.org/10.1007/s41365-018-0425-x

    Article  Google Scholar 

  15. 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. Eur. Phys. J. A 52, 102 (2016). https://doi.org/10.1140/epja/i2016-16102-6

    Article  Google Scholar 

  16. H.-L. Lao, H.-R. Wei, F.-H. Liu, An evidence of mass-dependent differential kinetic freeze-out scenario observed in Pb–Pb collisions at 2.76 TeV. Eur. Phys. J. A 52, 203 (2016). https://doi.org/10.1140/epja/i2016-16203-2

    Article  Google Scholar 

  17. 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. J. Phys. G 43, 125102 (2016). https://doi.org/10.1088/0954-3899/43/12/125102

    Article  Google Scholar 

  18. 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

    Article  Google Scholar 

  19. H. Zheng, L.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

    Article  Google Scholar 

  20. A. Adare et al., (PHENIX Collaboration), Spectra and ratios of identified particles in Au+Au and d+Au collisions at \(\sqrt{s_{\text{ NN}}}=\) 200 GeV. Phys. Rev. C 88, 024906 (2013). https://doi.org/10.1103/PhysRevC.88.024906

  21. J. Adams et al., (STAR Collaboration), Identified hadron spectra at large transverse momentum in p+p and d+Au collisions at \(\sqrt{s_{\text{ NN}}}=\) 200 GeV. Phys. Lett. B 637, 161 (2006). https://doi.org/10.1016/j.physletb.2006.04.032

    Article  Google Scholar 

  22. G. Agakishiev et al., (STAR Collaboration), Identified hadron compositions in p+p and Au+Au collisions at high transverse momenta at \(\sqrt{s_{\text{ NN}}}=\) 200 GeV. Phys. Rev. Lett. 108, 072302 (2012). https://doi.org/10.1103/PhysRevLett.108.072302

  23. J. Adams, (STAR Collaboration), Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at \(\sqrt{s_{\text{ NN}}}=\) 200 GeV. Phys. Lett. B 616, 8 (2005). https://doi.org/10.1016/j.physletb.2005.04.041

    Article  Google Scholar 

  24. J. Adam et al., (ALICE Collaboration), Multiplicity dependence of charged pion, kaon, and (anti)proton production at large transverse momentum in p–Pb collisions at \(\sqrt{s_{\text{ NN}}}=\) 5.02 TeV. Phys. Lett. B 760, 720 (2016). https://doi.org/10.1016/j.physletb.2016.07.050

    Article  Google Scholar 

  25. B. Abelev et al., (ALICE Collaboration), Production of charged pions, kaons and protons at large transverse momenta in \(pp\) and Pb–Pb collisions at \(\sqrt{s_{\text{ NN}}}=\) 2.76 TeV. Phys. Lett. B 736, 196 (2014). https://doi.org/10.1016/j.physletb.2014.07.011

    Article  Google Scholar 

  26. R. Odorico, Does a transverse energy trigger actually trigger on large-\(p_T\) jets? Phys. Lett. B 118, 151 (1982). https://doi.org/10.1016/0370-2693(82)90620-7

    Article  Google Scholar 

  27. G. Arnison et al., (UA1 Collaboration), Transverse momentum spectra for charged particles at the CERN proton–antiproton collider. Phys. Lett. B 118, 167 (1982). https://doi.org/10.1016/0370-2693(82)90623-2

    Article  Google Scholar 

  28. T. Mizoguchi, M. Biyajima, N. Suzuki, Analyses of whole transverse momentum distributions in \({\rm p}{\bar{p}}\) and pp collisions by using a modified version of Hagedorn’s formula. Int. J. Mod. Phys. A 32, 1750057 (2017). https://doi.org/10.1142/S0217751X17500579

    Article  Google Scholar 

  29. http://www.phenix.bnl.gov/WWW/show_plot.php.html, quoted from ref. [19] (which shows the web page) in P. Guptaroy, G. Sau, S.K. Biswas, S. Bhattacharyya, Understanding the characteristics of multiple production of light hadrons in Cu+Cu interactions at various RHIC energies: a model-based analysis. Nuovo Cimento B 125, 1071 (2010). 10.1393/ncb/i2010-10913-4, arXiv:0907.2008v2 [hep-ph]

  30. B.I. Abelev et al., (STAR Collaboration), Spectra of identified high-\(p_T\) \(\pi ^{\pm }\) and p(\(\rm \bar{p}\)) in Cu+Cu collisions at \(\sqrt{s_{\text{ NN}}}=\) 200 GeV. Phys. Rev. C 81, 054907 (2010). https://doi.org/10.1103/PhysRevC.81.054907

  31. E.K.G. Sarkisyan, A.S. Sakharov, Multihadron production features in different reactions. AIP Conf. Proc. 828, 35 (2006). https://doi.org/10.1063/1.2197392

    Article  Google Scholar 

  32. E.K.G. Sarkisyan, A.S. Sakharov, Relating multihadron production in hadronic and nuclear collisions. Eur. Phys. J. C 70, 533 (2010). https://doi.org/10.1140/epjc/s10052-010-1493-1

    Article  Google Scholar 

  33. A.N. Mishra, R. Sahoo, E.K.G. Sarkisyan, Effective-energy budget in multiparticle production in nuclear collisions. Eur. Phys. J. C 74, 3147 (2014). https://doi.org/10.1140/epjc/s10052-015-3275-2. and Erratum. Eur. Phys. J. C 75 70 (2015). https://doi.org/10.1140/epjc/s10052-014-3147-1

  34. E.K.G. Sarkisyan, A.N. Mishra, R. Sahoo et al., Multihadron production dynamics exploring the energy balance in hadronic and nuclear collisions. Phys. Rev. D 93, 054046 (2016). https://doi.org/10.1103/PhysRevD.93.054046 and Addendum. Phys. Rev. D 93, 079904 (2016). https://doi.org/10.1103/PhysRevD.93.079904

  35. E.K.G. Sarkisyan, A.N. Mishra, R. Sahoo et al., Centrality dependence of midrapidity density from GeV to TeV heavy-ion collisions in the effective-energy universality picture of hadroproduction. Phys. Rev. D 94, 011501(R) (2016). https://doi.org/10.1103/PhysRevD.94.011501

    Article  Google Scholar 

  36. C. Patrignani et al., (Particle data group), Review of particle physics. Chin. Phys. C 40, 100001 (2016). https://doi.org/10.1088/1674-1137/40/10/100001

    Article  Google Scholar 

  37. F.-H. Liu, Y.-Q. Gao, B.-C. Li, Comparing two-Boltzmann distribution and Tsallis statistics of particle transverse momentums in collisions at LHC energies. Eur. Phys. J. A 50, 123 (2014). https://doi.org/10.1140/epja/i2014-14123-9

    Article  Google Scholar 

  38. A.N. Tawfik, Axiomatic nonextensive statistics at NICA energies. Eur. Phys. J. A 52, 253 (2016). https://doi.org/10.1140/epja/i2016-16253-4

    Article  Google Scholar 

  39. A.N. Tawfik, H. Yassin, E.R.A. Elyazeed, On thermodynamic self-consistency of generic axiomatic-nonextensive statistics. Chin. Phys. C 41, 053107 (2017). https://doi.org/10.1088/1674-1137/41/5/053107

    Article  Google Scholar 

  40. A.N. Tawfik, Lattice QCD thermodynamics and RHIC-BES particle production within generic nonextensive statistics. Phys. Part. Nucl. Lett. (PEPAN) 15, 199 (2018). https://doi.org/10.1134/S1547477118030196

    Article  Google Scholar 

  41. J.D. Bjorken, Highly relativistic nucleus–nucleus collisions: the central rapidity region. Phys. Rev. D 27, 140 (1983). https://doi.org/10.1103/PhysRevD.27.140

    Article  Google Scholar 

  42. K. Okamoto, C. Nonaka, A new relativistic viscous hydrodynamics code and its application to the Kelvin–Helmholtz instability in high-energy heavy-ion collisions. Eur. Phys. J. C 77, 383 (2017). https://doi.org/10.1140/epjc/s10052-017-4944-0

    Article  Google Scholar 

  43. H.C. Song, Y. Zhou, K. Gajdošová, Collective flow and hydrodynamics in large and small systems at the LHC. Nucl. Sci. Tech. 28, 99 (2017). https://doi.org/10.1007/s41365-017-0245-4

    Article  Google Scholar 

  44. S. Das (for the STAR Collaboration), Identified particle production and freeze-out properties in heavy-ion collisions at RHIC beam energy scan program. EPJ Web Conf. 90, 08007 (2015). https://doi.org/10.1051/epjconf/20159008007

    Article  Google Scholar 

  45. S. Das (for the STAR Collaboration), Centrality dependence of freeze-out parameters from the beam energy scan at STAR. Nucl. Phys. A 904–905, 891c (2013). https://doi.org/10.1016/j.nuclphysa.2013.02.158

    Article  Google Scholar 

  46. L. Adamczyk et al., (STAR Collaboration), Bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program. Phys. Rev. C 96, 044904 (2017). https://doi.org/10.1103/PhysRevC.96.044904

  47. X.F. Luo, Exploring the QCD phase structure with beam energy scan in heavy-ion collisions. Nucl. Phys. A 956, 75 (2016). https://doi.org/10.1016/j.nuclphysa.2016.03.025

    Article  Google Scholar 

  48. C. Markert (for the STAR Collaboration), Resonance production in heavy-ion collisions at STAR. J. Phys. G 35, 044029 (2008). https://doi.org/10.1088/0954-3899/35/4/044029

    Article  Google Scholar 

  49. I. Melo, B. Tomášik, Reconstructing the final state of Pb+Pb collisions at \(\sqrt{s_{\text{ NN}}}=\) 2.76. TeV. J. Phys. G 43, 015102 (2016). https://doi.org/10.1088/0954-3899/43/1/015102

    Article  Google Scholar 

  50. A. Iordanova, (for the STAR Collaboration), Strangeness and bulk freeze-out properties at RHIC. J. Phys. G 35, 044008 (2008). https://doi.org/10.1088/0954-3899/35/4/044008

    Article  Google Scholar 

  51. A. Iordanova, (for the STAR Collaboration), O. Barannikova, R. Hollis, System size dependence of freeze-out properties at RHIC. Int. J. Mod. Phys. E 16, 1800 (2007). https://doi.org/10.1142/S0218301307007027

  52. A. Ortiz, G. Bencédi, H. Bello, Revealing the source of the radial flow patterns in proton–proton collisions using hard probes. J. Phys. G 44, 065001 (2017). https://doi.org/10.1088/1361-6471/aa6594

    Article  Google Scholar 

  53. S.S. Adler et al., (PHENIX Collaboration), Identified charged particle spectra and yields in Au+Au collisions at \(\sqrt{s_{NN}}=\) 200 GeV. Phys. Rev. C 69, 034909 (2004). https://doi.org/10.1103/PhysRevC.69.034909

  54. S. Chatterjee, B. Mohanty, R. Singh, Freezeout hypersurface at energies available at the CERN large hadron collider from particle spectra: flavor and centrality dependence. Phys. Rev. C 92, 024917 (2015). https://doi.org/10.1103/PhysRevC.92.024917

    Article  Google Scholar 

  55. Z.B. Tang, L. Yi, L.J. Ruan et al., The statistical origin of constituent-quark scaling in the QGP hadronization. Chin. Phys. Lett. 30, 031201 (2013). https://doi.org/10.1088/0256-307X/30/3/031201

    Article  Google Scholar 

  56. K. Jiang, Y.Y. Zhu, W.T. Liu et al., Onset of radial flow in p+p collisions. Phys. Rev. C 91, 024910 (2015). https://doi.org/10.1103/PhysRevC.91.024910

    Article  Google Scholar 

  57. B. De, Non-extensive statistics and understanding particle production and kinetic freeze-out process from \(p_T\)-spectra at 2.76 TeV. Eur. Phys. J. A 50, 138 (2014). https://doi.org/10.1140/epja/i2014-14138-2

    Article  Google Scholar 

  58. D. Thakur, S. Tripathy, P. Garg, et al., Proceedings of the 11th Workshop on Particle Correlations and Femtoscopy (WPCF 2015), Nov. 3–7 2015, (Warsaw, Poland, 2016). arXiv:1603.04971 [hep-ph]

  59. D. Thakur, S. Tripathy, P. Garg et al., Indication of a differential freeze-out in proton-proton and heavy-ion collisions at RHIC and LHC energies. Adv. High Energy Phys. 2016, 4149352 (2016). https://doi.org/10.1155/2016/4149352

    Article  Google Scholar 

  60. X.-G. Deng, Y.-G. Ma, Electromagnetic field effects on nucleon transverse momentum for heavy ion collisions around 100 A MeV. Nucl. Sci. Tech. 28, 182 (2017). https://doi.org/10.1007/s41365-017-0337-1

    Article  MathSciNet  Google Scholar 

  61. K. Hattori, X.-G. Huang, Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions. Nucl. Sci. Tech. 28, 26 (2017). https://doi.org/10.1007/s41365-016-0178-3

    Article  Google Scholar 

  62. W.-Z. Jiang, R.-Y. Yang, S.-N. Wei, Strangeness to increase the density of finite nuclear systems in constraining the high-density nuclear equation of state. Nucl. Sci. Tech. 28, 180 (2017). https://doi.org/10.1007/s41365-017-0333-5

    Article  Google Scholar 

  63. X.-F. Luo, N. Xu, Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview. Nucl. Sci. Tech. 28, 112 (2017). https://doi.org/10.1007/s41365-017-0257-0

    Article  Google Scholar 

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Acknowledgements

We highly appreciate the communications with Dr. Muhammad Waqas.

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Authors and Affiliations

  1. Institute of Theoretical Physics & State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, 030006, China

    Hai-Ling Lao, Fu-Hu Liu, Bao-Chun Li & Mai-Ying Duan

  2. Departments of Chemistry & Physics, Stony Brook University, Stony Brook, NY, 11794, USA

    Roy A. Lacey

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  1. Hai-Ling Lao
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Correspondence to Fu-Hu Liu.

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This work was supported by the National Natural Science Foundation of China (Nos. 11575103 and 11747319), the Shanxi Provincial Natural Science Foundation (No. 201701D121005), the Fund for Shanxi “1331 Project” Key Subjects Construction, and the US DOE (DE-FG02-87ER40331.A008).

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Lao, HL., Liu, FH., Li, BC. et al. Examining the model dependence of the determination of kinetic freeze-out temperature and transverse flow velocity in small collision system. NUCL SCI TECH 29, 164 (2018). https://doi.org/10.1007/s41365-018-0504-z

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