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Second virial coefficients of light nuclear clusters and their chemical freeze-out in nuclear collisions

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Abstract

Here we develop a new strategy to analyze the chemical freeze-out of light (anti)nuclei produced in high energy collisions of heavy atomic nuclei within an advanced version of the hadron resonance gas model. It is based on two different, but complementary approaches to model the hard-core repulsion between the light nuclei and hadrons. The first approach is based on an approximate treatment of the equivalent hard-core radius of a roomy nuclear cluster and pions, while the second approach is rigorously derived here using a self-consistent treatment of classical excluded volumes of light (anti)nuclei and hadrons. By construction, in a hadronic medium dominated by pions, both approaches should give the same results. Employing this strategy to the analysis of hadronic and light (anti)nuclei multiplicities measured by ALICE at \(\sqrt{s_{NN}} =2.76\) TeV and by STAR at \(\sqrt{s_{NN}} =200\) GeV, we got rid of the existing ambiguity in the description of light (anti)nuclei data and determined the chemical freeze-out parameters of nuclei with high accuracy and confidence. At ALICE energy the nuclei are frozen prior to the hadrons at the temperature \(T = 175.1^{+2.3}_{-3.9}\) MeV, while at STAR energy there is a single freeze-out of hadrons and nuclei at the temperature \(T = 167.2 \pm 3.9\) MeV. We argue that the found chemical freeze-out volumes of nuclei can be considered as the volumes of quark-gluon bags that produce the nuclei at the moment of hadronization.

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References

  1. W. Ebeling, D. Blaschke, R. Redmer, H. Reinholz, G. Röpke, J. Phys. A 42, 214033 (2009)

    ADS  Google Scholar 

  2. G. Röpke, D. Blaschke, T. Döppner, C. Lin, W.D. Kraeft, R. Redmer, H. Reinholz, Phys. Rev. E 99(3), 033201 (2019)

    ADS  Google Scholar 

  3. D. Blaschke, H. Grigorian, G. Röpke, Particles 3(2), 477 (2020)

    Google Scholar 

  4. S. Typel, G. Röpke, T. Klähn, D. Blaschke, H.H. Wolter, Phys. Rev. C 81, 015803 (2010)

    ADS  Google Scholar 

  5. M. Hempel, K. Hagel, J. Natowitz, G. Röpke, S. Typel, Phys. Rev. C 91(4), 045805 (2015)

    ADS  Google Scholar 

  6. G. Röpke, Phys. Rev. C 101(6), 064310 (2020)

    ADS  Google Scholar 

  7. J.M. Lattimer, F.D. Swesty, Nucl. Phys. A 535, 331 (1991)

    ADS  Google Scholar 

  8. H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, Nucl. Phys. A 637, 435 (1998)

    ADS  Google Scholar 

  9. M. Hempel, J. Schaffner-Bielich, S. Typel, G. Röpke, Phys. Rev. C 84, 055804 (2011)

    ADS  Google Scholar 

  10. G. Röpke, N.-U. Bastian, D. Blaschke, T. Klähn, S. Typel , H. H. Wolter, Nucl. Phys. A 897, 70 (2013), arXiv:1209.0212 [nucl-th]

  11. N.U.F. Bastian, D. Blaschke, T. Fischer, G. Röpke, Universe 4, 67 (2018). (and references therein)

    ADS  Google Scholar 

  12. S. Mrowczynski, Acta Phys. Polon. B 48, 707 (2017)

    ADS  Google Scholar 

  13. K.J. Sun, L.W. Chen, C.M. Ko, Z. Xu, Phys. Lett. B 774, 103 (2017)

    ADS  Google Scholar 

  14. K.J. Sun, L.W. Chen, C.M. Ko, J. Pu, Z. Xu, Phys. Lett. B 781, 499–504 (2018)

    ADS  Google Scholar 

  15. K.J. Sun, C.M. Ko, B. Dönigus, Phys. Lett. B 792, 132–137 (2019)

    ADS  Google Scholar 

  16. V. Vovchenko, B. Dönigus, H. Stoecker, Phys. Lett. B 785, 171 (2018)

    ADS  Google Scholar 

  17. F. Bellini, A.P. Kalweit, Phys. Rev. C 99(5), 054905 (2019)

    ADS  Google Scholar 

  18. F. Bellini, K. Blum, A. P. Kalweit , M. Puccio, arXiv:2007.01750 [nucl-th]

  19. Y. Cai, T.D. Cohen, B.A. Gelman, Y. Yamauchi, Phys. Rev. C 100(2), 024911 (2019)

    ADS  Google Scholar 

  20. J. Aichelin, E. Bratkovskaya, A. Le Fèvre, V. Kireyeu, V. Kolesnikov, Y. Leifels, V. Voronyuk, G. Coci, Phys. Rev. C 101(4), 044905 (2020)

    ADS  Google Scholar 

  21. D. Oliinychenko, talk given at XXVIIIth Conference “Quark Matter 2019“, arXiv:2003.05476v1 [hep-ph] (and references therein)

  22. S. Mrowczynski, arXiv:2004.07029v1 [nucl-th] and references therein

  23. D. Blaschke, A.V. Friesen, Y.B. Ivanov, Y.L. Kalinovsky, M. Kozhevnikova, S. Liebing, A. Radzhabov, G. Röpke, arXiv:2004.01159 [hep-ph]

  24. D. Blaschke, G. Röpke, Y. Ivanov, M. Kozhevnikova, S. Liebing, Springer Proc. Phys. 250, 183 (2020)

    Google Scholar 

  25. D.R. Oliinychenko, K.A. Bugaev, A.S. Sorin, Ukr. J. Phys. 58, 211 (2013)

    Google Scholar 

  26. K.A. Bugaev, D.R. Oliinychenko, A.S. Sorin, G.M. Zinovjev, Eur. Phys. J. A 49, 30 (2013)

    Google Scholar 

  27. K.A. Bugaev et al., Europhys. Lett. 104, 22002 (2013)

    ADS  Google Scholar 

  28. K.A. Bugaev, A.I. Ivanytskyi, D.R. Oliinychenko, E.G. Nikonov, V.V. Sagun, G.M. Zinovjev, Ukr. J. Phys. 60, 181 (2015)

    Google Scholar 

  29. V.V. Sagun, Ukr. J. Phys. 59, 755 (2014)

    Google Scholar 

  30. K.A. Bugaev et al., Phys. Part. Nucl. Lett. 12, 238 (2015)

    ADS  Google Scholar 

  31. K.A. Bugaev et al., Eur. Phys. J. A 52, 175 (2016)

    ADS  Google Scholar 

  32. K.A. Bugaev et al., Eur. Phys. J. A 52, 227 (2016)

    ADS  Google Scholar 

  33. K.A. Bugaev et al., Phys. Part. Nucl. Lett. 15, 210 (2018)

    Google Scholar 

  34. K.A. Bugaev et al., EPJ Web of Conferences 204, 03001 (2019)

  35. A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl. Phys. A 772, 167 (2006). (and references therein)

    ADS  Google Scholar 

  36. V.V. Sagun, A.I. Ivanytskyi, K.A. Bugaev, I.N. Mishustin, Nucl. Phys. A 924, 24 (2014)

    ADS  Google Scholar 

  37. V.V. Sagun et al., Eur. Phys. J. A 54, 100 (2018)

    ADS  Google Scholar 

  38. K.A. Bugaev et al., Nucl. Phys. A 970, 133 (2018)

    ADS  Google Scholar 

  39. K.A. Bugaev, Eur. Phys. J. A 55, 215 (2019)

    ADS  Google Scholar 

  40. N. S. Yakovenko, K. A. Bugaev, L.V. Bravina , E. E. Zabrodin, arXiv:1910.04889 [nucl-th]

  41. S. Bazak, S. Mrowczynski, Eur. Phys. J. A 56(7), 193 (2020)

    ADS  Google Scholar 

  42. STAR Collaboration (B. I. Abelev et al.), Science 328, 58 (2010)

  43. STAR Collaboration (H. Agakishiev et al.), Nature 473, 58 (2011)

  44. STAR Collaboration (J. Adam et al.), Phys. Rev. C 99, 064905 (2019)

  45. ALICE Collaboration (J. Adam et al.), Phys. Rev. C 93, 024917 (2016)

  46. ALICE Collaboration (L. Ramonaet al.), AIP Conf. Proc. 1701, (1) 080009 (2016)

  47. ALICE Collaboration (J. Adam et al.), Phys. Lett. B 754, 360 (2016)

  48. R. Venugopalan, M. Prakash, Nucl. Phys. A 546, 718 (1992)

    ADS  Google Scholar 

  49. E. Shuryak, J.M. Torres-Rincon, Phys. Rev. C 100, 024903 (2019). (and references therein)

    ADS  Google Scholar 

  50. E. Shuryak, J.M. Torres-Rincon, Phys. Rev. C 101(3), 034914 (2020)

    ADS  Google Scholar 

  51. L.M. Satarov, M.N. Dmitriev, I.N. Mishustin, Phys. At. Nucl. 72, 1390 (2009)

    Google Scholar 

  52. K.A. Bugaev, A.I. Ivanytskyi, V.V. Sagun, E.G. Nikonov, G.M. Zinovjev, Ukr. J. Phys. 63, 863 (2018). (and references therein)

    Google Scholar 

  53. K.A. Bugaev, Nucl. Phys. A 606, 559 (1996)

    ADS  Google Scholar 

  54. K.A. Bugaev, Phys. Rev. Lett. 90, 252301 (2003). (and references therein)

    ADS  Google Scholar 

  55. R. Hagedorn, Nuovo Cim. Suppl. 3, 147 (1965)

    Google Scholar 

  56. S. Chatterjee et al., Adv. High Energy Phys. 2015, 349013 (2015). (and references therein)

    Google Scholar 

  57. J. Cleymans, S. Kabana, I. Kraus, H. Oeschler, K. Redlich, N. Sharma, Phys. Rev. C 84, 054916 (2011)

    ADS  Google Scholar 

  58. J. Stachel, A. Andronic, P. Braun-Munzinger, K. Redlich, J. Phys. Conf. Ser. 509, 012019 (2014)

    Google Scholar 

  59. A. Andronic, P. Braun-Munzinger, K. Redlich, J. Stachel, Nature 561(7723), 321–330 (2018)

    ADS  Google Scholar 

  60. K.A. Bugaev et al., J. Phys. Conf. Ser. 1390, 012038 (2019)

    Google Scholar 

  61. P. Braun-Munzinger, B. Dönigus, Nucl. Phys. A 987, 144 (2019). (and references therein)

    ADS  Google Scholar 

  62. B. E. Grinyuk et al., (2020). arXiv:2004.05481v1 [hep-ph]

  63. A. Bohr, B. Mottelson, Nuclear Structure, vol. 1 (Benjamin, New York, 1969)

    MATH  Google Scholar 

  64. I. Angeli, K. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)

    ADS  Google Scholar 

  65. H. Nemura, Y. Suzuki, Y. Fujiwara, C. Nakamoto, Prog. Theor. Phys. 103, 929 (2000). arXiv:nucl-th/9912065

  66. J. Rafelski, Phys. Lett. B 62, 333 (1991)

    ADS  Google Scholar 

  67. E. Beth, G. Uhlenbeck, Physica 4, 915 (1937)

    ADS  Google Scholar 

  68. J. Hüfner, S.P. Klevansky, P. Zhuang, H. Voss, Ann. Phys. 234, 225 (1994)

    ADS  Google Scholar 

  69. A. Wergieluk, D. Blaschke, Y.L. Kalinovsky, A. Friesen, Phys. Part. Nucl. Lett. 10, 660 (2013)

    Google Scholar 

  70. D. Blaschke, M. Buballa, A. Dubinin, G. Röpke, D. Zablocki, Ann. Phys. 348, 228 (2014)

    ADS  Google Scholar 

  71. D. Blaschke, A. Dubinin, A. Radzhabov, A. Wergieluk, Phys. Rev. D 96(9), 094008 (2017)

    Google Scholar 

  72. D. Blaschke, A. Dubinin, L. Turko, arXiv:1611.09845v2 [hep-ph]

  73. D. Blaschke, A. Dubinin, L. Turko, Acta Phys. Polon. Supp. 10, 473 (2017)

    Google Scholar 

  74. G. Baym, Phys. Rev. 127, 1391 (1962)

    ADS  MathSciNet  Google Scholar 

  75. B. Vanderheyden, G. Baym, J. Stat. Phys. 93, 843 (1998)

    ADS  Google Scholar 

  76. K.A. Bugaev, P.T. Reuter, Ukr. J. Phys. 52, 489 (2007). (and references therein)

    Google Scholar 

  77. K. Huang, Statistical Mechanics (Wiley, New York, 1967)

    Google Scholar 

  78. L.M. Satarov, K.A. Bugaev, I.N. Mishustin, Phys. Rev. C 91, 055203 (2015)

    ADS  Google Scholar 

  79. V. Vovchenko, H. Stöcker, J. Phys. G 44, 055103 (2017)

    ADS  Google Scholar 

  80. J.P. Hansen, I.R. McDonald, Theory of Simple Fluids (Academic Press, Amsterdam, 2006)

    Google Scholar 

  81. A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn, V.F. Weisskopf, Phys. Rev. D 9, 3471 (1974)

    ADS  MathSciNet  Google Scholar 

  82. B. Abelev et al., [ALICE Collaboration], Phys. Rev. C 88, 044910 (2013)

  83. B. B. Abelev et al. [ALICE Collaboration], Phys. Lett. B 728 (2014) (216: Erratum: [Phys. Lett. B 734 (2014) 409])

  84. B.B. Abelev et al., [ALICE Collaboration], Phys. Rev. Lett. 111, 222301 (2013)

  85. B.B. Abelev et al., [ALICE Collaboration], Phys. Rev. C 91, 024609 (2015)

  86. A. Andronic, P. Braun-Munzinger, K. Redlich, J. Stachel, J. Phys. Conf. Ser. 779, 012012 (2017)

    Google Scholar 

  87. Wuppertal-Budapest Collaboration (S. Borsanyi et al.), JHEP 1009, 073 (2010)

  88. HotQCD Collaboration (A. Bazavov et al.), Phys. Rev. D 90, 094503 (2014)

  89. A. Bazavov et al., HotQCD. Phys. Lett. B 795, 15 (2019)

    ADS  MathSciNet  Google Scholar 

  90. J. Adams et al., Phys. Rev. Lett. 92, 112301 (2004)

    ADS  Google Scholar 

  91. J. Adams et al., Phys. Lett. B 612, 181 (2005)

    ADS  Google Scholar 

  92. A. Billmeier et al., J. Phys. G 30, S363 (2004)

    Google Scholar 

  93. A. Andronic, P. Braun-Munzinger, J. Stachel, H. Stoecker, Phys. Lett. B 697, 203 (2011)

    ADS  Google Scholar 

  94. X. Xu, R. Rapp, Eur. Phys. J. A 55, 68 (2019). arXiv:1809.04024v2 [nucl-th] (and references therein)

  95. G. F. Chapline , A. K. Kerman, MIT-CTP-695 (1978)

  96. L.G. Moretto, K.A. Bugaev, J.B. Elliott, L. Phair, Europhys. Lett. 76, 402 (2006). (LBNL preprint 56898)

    ADS  MathSciNet  Google Scholar 

  97. K. Gallmeister , C. Greiner, arXiv:2007.08258 [hep-ph]

  98. VYu. Naboka, IuA Karpenko, YuM Sinyukov, Phys. Rev. C 93, 024902 (2016)

    ADS  Google Scholar 

  99. S. Sombun et al., Phys. Rev. C 99, 014901 (2019)

    ADS  Google Scholar 

  100. Y. Yamamoto, T. Furumoto, N. Yasutake, T.A. Rijken, Eur. Phys. J. A 52(2), 19 (2016)

    ADS  Google Scholar 

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Acknowledgements

The authors are thankful to Dmytro Oliinychenko for brining to our attention Ref. [44] and for illuminating discussions, and to Grigory Nigmatkulov and Ivan Yakimenko for the valuable comments. K.A.B. and G.M.Z. acknowledge support from the NAS of Ukraine by its priority project “Fundamental properties of the matter in the relativistic collisions of nuclei and in the early Universe” (No. 0120U100935). V.V.S. and O.I.I. are thankful for the support by the Fundação para a Ciência e Tecnologia (FCT), Portugal, by the project UID/04564/2020. The work of O.I.I. was supported by the project CENTRO-01-0145-FEDER-000014 via the CENTRO 2020 program, and POCI-01-0145-FEDER-029912 with financial support from POCI, in its FEDER component and by the FCT/ MCTES budget via national funds (OE). The work of L.V.B. and E.E.Z. was supported by the Norwegian Research Council (NFR) under grant No. 255253/ F53 CERN Heavy Ion Theory, and by the Russian Foundation for Basic Research (RFBR) grants 18-02-40085 and 18-02-40084. K.A.B., O.V.V., N.S. Ya. and L.V.B. thank the Norwegian Agency for International Cooperation and Quality Enhancement in Higher Education for the financial support under grants CPEA-LT-2016/10094 and UTF-2016-long-term/10076. A.V.T acknowledges partial support from RFBR under grant No.18-02-40086 and from the Ministry of Science and Higher Education of the Russian Federation, Project “Fundamental properties of elementary particles and cosmology” No. 0723-2020-0041. D.B.B. received funding from the RFBR under grant No. 18-02-40137. D.B.B. and A.V.T. acknowledge partial support from the National Research Nuclear University “MEPhI” in the framework of the Russian Academic Excellence Project (contract no. 02.a03.21.0005, 27. 08.2013). The authors are grateful to the COST Action CA15213 “THOR” for supporting their networking.

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Authors and Affiliations

  1. Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14B, Kyiv, 03680, Ukraine

    K. A. Bugaev, B. E. Grinyuk, V. V. Sagun, O. I. Ivanytskyi & G. M. Zinovjev

  2. Department of Physics, Taras Shevchenko National University of Kyiv, Kyiv, 03022, Ukraine

    K. A. Bugaev, O. V. Vitiuk & N. S. Yakovenko

  3. University of Oslo, POB 1048 Blindern, 0316, Oslo, Norway

    O. V. Vitiuk, L. V. Bravina & E. E. Zabrodin

  4. Department of Physics, CFisUC, University of Coimbra, 3004-516, Coimbra, Portugal

    V. V. Sagun & O. I. Ivanytskyi

  5. Institute of Theoretical Physics, University of Wroclaw, Max Born Pl. 9, 50-204, Wroclaw, Poland

    D. B. Blaschke

  6. Bogoliubov Laboratory of Theoretical Physics, JINR Dubna, Joliot-Curie Str. 6, 141980, Dubna, Russia

    D. B. Blaschke

  7. National Research Nuclear University (MEPhI), Kashirskoe Shosse 31, 115409, Moscow, Russia

    D. B. Blaschke, E. S. Zherebtsova & A. V. Taranenko

  8. Laboratory for Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Russia

    E. G. Nikonov

  9. Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia

    E. E. Zabrodin

  10. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    S. Kabana

  11. Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago, Chile

    S. V. Kuleshov

  12. Department of Physics, New York University, New York, NY, 10003, USA

    G. R. Farrar

  13. Institute for Nuclear Research, Russian Academy of Science, 108840, Moscow, Russia

    E. S. Zherebtsova

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  1. K. A. Bugaev
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  2. O. V. Vitiuk
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  3. B. E. Grinyuk
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  8. D. B. Blaschke
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Contributions

KAB developed the idea behind this work and together with DBB took the lead in writing the manuscript. OVV, BEG, VVS and ESZ performed fit of the experimental data on the light (anti)nuclei and hadrons. OII, NSY and EGN verified the analytical methods. Both NSY and SVK, helped in calculating the CFO volume of hadrons and designed the figures. GMZ, LVB, EEZ, SK, GRF and AVT contributed to the interpretation of the results and provided a critical feedback. All authors discussed the results and contributed to the final manuscript.

Corresponding author

Correspondence to K. A. Bugaev.

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Communicated by Laura Tolos.

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Bugaev, K.A., Vitiuk, O.V., Grinyuk, B.E. et al. Second virial coefficients of light nuclear clusters and their chemical freeze-out in nuclear collisions. Eur. Phys. J. A 56, 293 (2020). https://doi.org/10.1140/epja/s10050-020-00296-5

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