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Analytical results for the classical and quantum Tsallis hadron transverse momentum spectra: the zeroth order approximation and beyond

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Abstract

We derive analytical expressions for the first and second order terms in the hadronic transverse momentum spectra obtained from the Tsallis normalized (Tsallis-1) statistics. We revisit the zeroth order quantum Tsallis distributions in this formulation and obtain the corresponding analytical closed form expressions. It is observed that unlike the classical case, the phenomenological distributions used in the literature do not resemble the analytical closed forms of the zeroth order quantum spectra after the \(q\rightarrow q^{-1}\) substitution, where q is the Tsallis entropic parameter. Though the factorization approximation increases the extent of similarity, it does not make them exactly the same. Since our results are based on the basic formulations of the statistical mechanics, the zeroth order Tsallis quantum distributions derived in this paper will be a better choice than their phenomenological counterparts.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment:Experimental data analyzed in Fig. 3 are available in the references cited.]

References

  1. C. Tsallis, J. Stat. Phys. 52, 479 (1988)

    Article  ADS  Google Scholar 

  2. J. Cleymans, D. Worku, Eur. Phys. J. A 48, 160 (2012)

    Article  ADS  Google Scholar 

  3. I. Bediaga, E.M.F. Curado, J.M. de Miranda, Physica A 286, 156 (2000)

    Article  ADS  Google Scholar 

  4. C. Beck, Physica A 286, 164 (2000)

    Article  ADS  Google Scholar 

  5. A.S. Parvan, Eur. Phys. J. A 52, 355 (2016)

    Article  ADS  Google Scholar 

  6. A.S. Parvan, Eur. Phys. J. A 53, 53 (2017)

    Article  ADS  Google Scholar 

  7. A.S. Parvan, T. Bhattacharyya, Eur. Phys. J. A 56, 72 (2020)

    Article  ADS  Google Scholar 

  8. A.S. Parvan, Eur. Phys. J. A 56, 106 (2020)

    Article  ADS  Google Scholar 

  9. M. Rahaman, T. Bhattacharyya, J.E. Alam, eprint. arXiv:1906.02893 [hep-ph]

  10. T. Bhattacharyya et al., Eur. Phys. J. A 52, 30 (2016)

    Article  ADS  Google Scholar 

  11. C. Tsallis, R.S. Mendes, A.R. Plastino, Physica A 261, 534 (1998)

    Article  ADS  Google Scholar 

  12. J.M. Conroy, H.G. Miller, A.R. Plastino, Phys. Lett. A 374, 4581 (2010)

    Article  ADS  Google Scholar 

  13. F. Büyükkiliç, D. Demirhan, Phys. Lett. A 181, 24 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  14. A.S. Parvan, Eur. Phys. J. A 51, 108 (2015)

    Article  ADS  Google Scholar 

  15. D. Prato, Phys. Lett. A 203, 165 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  16. K. Huang, Introduction to Statistical Physics (Taylor and Francis, London, 2001), p. 179

    Book  Google Scholar 

  17. R.B. Paris, D. Kaminski, Asymptotics and Mellin–Barnes Integrals (Cambridge University Press, New York, 2001), pp. 114–116

    Book  Google Scholar 

  18. A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, vol. 1 (Krieger, New York, 1981). See §1.10 for the Hurwitz-zeta function and §1.16 for the poly-gamma function

  19. H. Hasegawa, Phys. Rev. E 80, 011126 (2009)

    Article  ADS  Google Scholar 

  20. N. Abgrall et al. (NA61/SHINE), Eur. Phys. J. C 74(3), 2794 (2014)

  21. J. Adams et al. (PHENIX), Phys. Lett. B. 616, 8 (2005)

  22. M. Amaku, F.A.B. Coutinho, O.J.P. Eboli, W.F. Wreszinski, arXiv:2101.03930 [math-ph]

  23. T. Tao, The Euler–Maclaurin formula, Bernoulli numbers, the zeta function and real variable analytic continuation. https://terrytao.wordpress.com/2010/04/10/

  24. F. Büyükkiliç, D. Demirhan, A. Güleç, Phys. Lett. A 197, 209 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  25. A.S. Parvan, T. Bhattacharyya, arXiv:1904.02947 [cond-mat.stat-mech]

  26. T. Bhattacharyya, J. Cleymans, S. Mogliacci, Phys. Rev. D 94, 094026 (2016)

    Article  ADS  Google Scholar 

  27. A. Lavagno, D. Pigato, P. Quarati, J. Phys. G Nucl. Part. Phys. 37, 11 (2010)

    Article  Google Scholar 

  28. P.H.G. Cardoso, T.N. da Silva, A. Deppman, D.P. Menezes, Eur. Phys. J. A 53, 191 (2017)

    Article  ADS  Google Scholar 

  29. K. Javidan, M. Yazdanpanah, H. Nematollahi, Eur. Phys. J. A 57, 78 (2021)

    Article  ADS  Google Scholar 

  30. S. Mitra, Eur. Phys. J. C 78(1), 66 (2018)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Authors acknowledge the support from the joint project between the JINR and IFIN-HH. They thank the anonymous reviewers whose comments and questions helped improve the understanding and the quality of the manuscript.

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Moscow Region, Russian Federation

    Trambak Bhattacharyya & Alexandru S. Parvan

  2. Department of Theoretical Physics, Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania

    Alexandru S. Parvan

Authors
  1. Trambak Bhattacharyya
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  2. Alexandru S. Parvan
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Correspondence to Trambak Bhattacharyya.

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Communicated by Tamas Biro.

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Bhattacharyya, T., Parvan, A.S. Analytical results for the classical and quantum Tsallis hadron transverse momentum spectra: the zeroth order approximation and beyond. Eur. Phys. J. A 57, 206 (2021). https://doi.org/10.1140/epja/s10050-021-00527-3

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