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Mathematical modelling for pseudorapidity distribution of hadron-hadron collisions

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Abstract.

The modelling of proton-proton collisions at high energies using both group method data handling (GMDH) and gene expression programming (GEP) approaches is investigated over a wide range of center-of-mass energy (from \( \sqrt{s} = 23.6\) GeV to 7 TeV). We have used GMDH and GEP models to obtain two different mathematical formulae expressing the complex relation of the charged-particle pseudorapidity distribution \((\frac{d N_{ch}}{d \eta})\) of proton-proton interactions as a function of the center-of-mass energy \((\sqrt{s})\) in a simple explicit form. We have used the obtained formulae to simulate and predict \( \frac{d N_{ch}}{d \eta}\). Predictions are made at \( \sqrt{s}= 10\) TeV and 14 TeV. Compared to the available experimental data and to some widely used Monte Carlo generators (PYTHIA, PHOJET, and QGSM models), it is found that our models can accurately simulate and predict the charged-particle pseudorapidity distribution of proton-proton collisions.

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References

  1. I.M. Dremin, J.W. Gary, Phys. Rep. 349, 301 (2001)

    Article  ADS  MATH  Google Scholar 

  2. ALICE Collaboration (B. Alessandro et al.), J. Phys. G: Nucl. Part. Phys. 32, 1295 (2006)

    Article  ADS  Google Scholar 

  3. ALICE Collaboration (F. Carminati et al.), J. Phys. G: Nucl. Part. Phys. 30, 1517 (2004)

    Article  ADS  Google Scholar 

  4. CMS Collaboration (D.G. d’Enterria et al.), J. Phys. G: Nucl. Part. Phys. 34, 2737 (2007)

    Article  Google Scholar 

  5. CMS Collaboration (G.L. Bayatian et al.), J. Phys. G: Nucl. Part. Phys. 34, 995 (2007)

    Article  ADS  Google Scholar 

  6. ATLAS Collaboration (G. Aad), arXiv:0901.0512 [hep-ex]

  7. J.X. Sun, F.H. Liu, E.Q. Wang, Y. Sun, Z. Sun, Phys. Rev. C 83, 014001 (2011)

    Article  ADS  Google Scholar 

  8. F.H. Liu, J.S. Li, Phys. Rev. C 78, 044602 (2008)

    Article  ADS  Google Scholar 

  9. H.M. Wang, F.H. Liu, Z.Y. Hou, X.J. Sun, arXiv:1305.5106v1 [nucl-th]

  10. TOTEM Collaboration (G. Antchev et al.), EPL 98, 31002 (2012)

    Article  ADS  Google Scholar 

  11. Yu.L. Dokshitzer, V.A. Khoze, A.H. Mueller, S.I. Troyan, Basics Perturbative QCD (Editions Frontieres, Gif-sur-Yvette, France, 1991)

  12. M. Sumbera, High energy nuclear physics and multi-particledynamics, Thesis presented for the degree of Doctor of Sciences (Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Prague, Czech Republic, 2009)

  13. STAR Collaboration (J. Adams et al.), Nucl. Phys. A 757, 102 (2005)

    Article  ADS  Google Scholar 

  14. D. Kharzeev, E. Levin, Phys. Lett. B 523, 79 (2001)

    Article  ADS  Google Scholar 

  15. D.E. Kahana, S.H. Kahana, arXiv:nucl-th/0208063v1

  16. T. Hirano, Phys. Rev. C 65, 011901 (2002)

    Article  ADS  Google Scholar 

  17. M. Biyajima et al., Prog. Theor. Phys. 108, 559 (2002)

    Article  ADS  MATH  Google Scholar 

  18. V.N. Vapnik, Statistical Learning Theory (Wiley, New York, 1998)

  19. J. Zimmermann, Christian M. Kiesling, Nucl. Instrum. Methods A 534, 204 (2004)

    Article  ADS  Google Scholar 

  20. M. Schmidt, H. Lipson, Science 324, 81 (2009)

    Article  ADS  Google Scholar 

  21. J.M. Link, Nucl. Instrum. Methods Phys. Res. A 551, 504 (2005)

    Article  ADS  Google Scholar 

  22. L. Teodorescu, D. Sherwood, Comput. Phys. Commun. 178, 409 (2008)

    Article  ADS  Google Scholar 

  23. E. El-dahshan, A. Radi, M.Y. El-Bakry, Int. J. Mod. Phys. C 20, 1817 (2009)

    Article  ADS  MATH  Google Scholar 

  24. E. El-dahshan, A. Radi, M.Y. El-Bakry, Int. J. Mod. Phys. C 19, 1787 (2008)

    Article  ADS  MATH  Google Scholar 

  25. E.A. El-Dahshan, Cent. Eur. J. Phys. 9, 874 (2011)

    Article  Google Scholar 

  26. G. Bohm, G. Zech, Introduction to Statistics and Measurement Analysis for Physicists (DESY, Hamburg, Germany, 2010)

  27. S. Haykin, Neural Networks and Learning Machines, 3rd edition (Prentice Hall, 2008)

  28. J.H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975)

  29. A.G. Ivakhnenko, IEEE Trans. Syst., Man and Cybern. SMC-1, 364 (1971)

    Article  MathSciNet  Google Scholar 

  30. H.R. Madala, A.G. Ivakhnenko, Inductive Learning Algorithms for Complex Systems Modelling (CRC Press, Boca Raton, 1994)

  31. J.A. Müller, F. Lemke, A.G. Ivakhnenko, Math. Comput. Model. Dyn. Syst. 4, 275 (1998)

    Article  MATH  Google Scholar 

  32. S.J. Farlow, Self-Organizing Methods in Modelling: GMDH Type Algorithms (Marcel Decker Inc., New York, Bazel, 1984)

  33. C. Ferreira, Complex Syst. 13, 87 (2001)

    MATH  Google Scholar 

  34. J.R. Koza, M.A. Keane, M.J. Streeter, W. Mydlowec, J. Yu, G. Lanza, Genetic Programming IV: Routine Human-Competitive Machine Intelligence (Kluwer Academic Publishers, 2003)

  35. W. Thome et al., Nucl. Phys. B 129, 365 (1977)

    Article  ADS  Google Scholar 

  36. UA5 Collaboration (G.J. Alner et al.), Phys. Rep. 154, 247 (1987)

    Article  ADS  Google Scholar 

  37. CDF Collaboration (F. Abe et al.), Phys. Rev. D 41, 2330 (1990)

    Article  Google Scholar 

  38. CMS Collaboration (V. Khachatryan et al.), Phys. Rev. Lett. 105, 022002 (2010)

    Article  ADS  Google Scholar 

  39. ALICE Collaboration (K. Aamodt et al.), Eur. Phys. J. C 65, 111 (2010)

    Article  ADS  Google Scholar 

  40. Jian-Xin Sun, Fu-Hu Liu, Er-Qin Wang, Yan Sun, Zhu Sun, Phys. Rev. C 83, 014001 (2011)

    Article  ADS  Google Scholar 

  41. CMS Collaboration (V. Khachatryan et al.), JHEP 01, 41 (2010)

    Google Scholar 

  42. T. Sjostrand et al., Comput. Phys. Commun. 135, 238 (2001)

    Article  ADS  Google Scholar 

  43. R. Engel, J. Ranft, S. Roesler, Phys. Rev. D 52, 1459 (1995)

    Article  ADS  Google Scholar 

  44. A.B. Kaidalov, Phys. Lett. B 116, 459 (1982)

    Article  ADS  Google Scholar 

  45. P. Sherrod, DTREG Predictive Modelling Software (2008) Manual for software available online: www.dtreg.com

  46. Wei-Chiang Hong, Appl. Math. Comput. 200, 41 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  47. G. Wolschin, EPL 95, 61001 (2011)

    Article  ADS  Google Scholar 

  48. G. Wolschin, arXiv:1301.1868v2 [hep-ph]

  49. A.K. Dash, B. Mohanty, J. Phys. G: Nucl. Part. Phys. 37, 025102 (2010)

    Article  ADS  Google Scholar 

  50. A.B. Kaidalov, M.G. Poghosyan, Eur. Phys. J. 67, 397 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Education, Ain Shams University, Cairo, Egypt

    Mahmoudi Y. El-Bakry

  2. Department of physics, Faculty of Science, University of Tabuk, Tabuk, K.S.A.

    Mahmoudi Y. El-Bakry

  3. Egyptian E-Learning University (EELU), 33 Elmeshah Street, Eldoki, Postal Code: l1261, El-Geiza, Egypt

    El-Sayed A. El-Dahshan

  4. Department of Physics, Faculty of Sciences, Ain Shams University, Abbassia, Postal Code: 11566, Cairo, Egypt

    El-Sayed A. El-Dahshan & Salah Y. El-Bakry

Authors
  1. Mahmoudi Y. El-Bakry
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  2. El-Sayed A. El-Dahshan
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  3. Salah Y. El-Bakry
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Correspondence to Mahmoudi Y. El-Bakry.

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El-Bakry, M., El-Dahshan, ES. & El-Bakry, S. Mathematical modelling for pseudorapidity distribution of hadron-hadron collisions. Eur. Phys. J. Plus 130, 17 (2015). https://doi.org/10.1140/epjp/i2015-15017-5

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  • DOI: https://doi.org/10.1140/epjp/i2015-15017-5

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