EMPIRICAL EQUATION USING GMDH METHODOLOGY FOR THE CHARGED PARTICLES MULTIPLICITY DISTRIBUTION IN HADRONIC POSITRON-ELECTRON ANNIHILATION
Keywords:
hadronic positron-electron annihilation, charged-particles multiplicity distribution, empirical modeling, neural networks, group method of data handling (GMDH)
Abstract
Multiplicity distributions are the most general characteristics of hadronic multiparticle production processes. The multiplicity distribution of hadronic positron-electron annihilation is investigated using group method data handling (GMDH) technique up to the highest available center of mass energy (√s) (from 14 GeV to 206 GeV). We have obtained an empirical physical equation for the multiplicity distribution as a function of √s and the charged multiplicity (nch) i. e.P(nch,√s) . Based on the obtained equation, we have also calculated the energy dependence of average multiplicity (n) i.e.n̄=n̄(√s). Our results are compared with the available experimental and theoretical values.Downloads
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References
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2. Ghaffary T. Charged Particles Multiplicity and Scaling Violation of Fragmentation Functions in Electron-Positron Annihilation // Advances in High Energy Physics. – 2016. – Vol. 2016. – Article ID 4506809. – P.8; doi:10.1155/2016/4506809.
3. Bzdak A. Universality of multiplicity distribution in proton-proton and electron-positron collisions. – 2015 // e-Print: arXiv:1507.01608 [hep-ph].
4. Biebel O. Experimental tests of the strong interaction and
its energy dependence in electron–positron annihilation // Phys. Rev. – 2001. – Vol. 340. – P.165-289.
5. Derrick M., Gan K.K., Kooijman P., Loos J.S., Musgrave B., Price L.E., Wood D.E. Study of quark fragmentation in e+e− annihilation at =29 GeV: Charged-particle multiplicity and single-particle rapidity distributions // Phys. Rev. D. – 1986. – Vol. 34. – P.3304-3320.
6. Wyatt T. High-energy colliders and the rise of the standard model // Nature. – 2007. – Vol.448. – P. 274-280.
7. Ackerstaff K., Alexander G., Allison J., Altekamp N., Ametewee K., Anderson K.J., Azuelos G. QCD studies with e+ e-annihilation data at =161 GeV // Z. Phys. C Part. Fields. – 1997. – Vol. 75. – P.193-207.
8. Beggio P.C., Luna E.G.S. Cross sections, multiplicity and moment distributions at the LHC // Nucl. Phys. A,. – 2014. – Vol. 929. – P. 230-245.
9. Acton P.D., Alexander G., Allison J., Allport P.P., Anderson K.J., Arcelli S., Bahan G.A. A study of charged particle multiplicities in hadronic decays of the Z0 // Z. Phys. C Part. Fields. – 1992. – Vol. 53. – P. 539-554.
10. Abreu P., Adam W., Adami F., Adye T., Alexeev G.D., Allen P., Anassontzis E. Charged particle multiplicity distributions in Z0 hadronic decays // Z. Phys. C Part. Fields. – 1991. – Vol. 50. – P.185-194.
11. Dremin I.M. QCD and models on multiplicities in e+e− and interactions // Phys Atom Nucl+. – 2005. – Vol. 68. – P. 758-770.
12. ALEPH Collaboration, DELPHI collaboration, L3 Collaboration, OPAL Collaboration, & LEP Electroweak Working Group. Electroweak measurements in electron–positron collisions at W-boson-pair energies at LEP // Phys. Rept. – 2013. – Vol. 532. –P. 119-244.
13. Braunschweig W., Gerhards R., Kirschfink F.J., Martyn H.U., Fischer H.M., Hartmann H., Foster B. Charged multiplicity distributions and correlations in e+e− annihilation at PETRA energies // Z. Phys. C Part. Fields. C45. – 1989. – Vol. 45. - P. 193-208.
14. Achard P., Adriani O., Aguilar-Benitez M., Alcaraz J., Alemanni G., Allaby J., Anselmo F. Studies of hadronic event structure in e+e- annihilation from 30 to 209GeV with the L3 detector // Phys. Rept. – 2004. – Vol. 399. – P. 71-174.
15. Alexander G., Allison J., Altekamp N., Ametewee K., Anderson K.J., Anderson S., Ball A.H. QCD studies with e+e− annihilation data at 130 and 136 GeV // Z. Phys. C Part. Fields. – 1996. – Vol. 72. – P. 191-206.
16. Radchenko N.V. About agreement of PYTHIA and the experimental results in e+e- annihilation to hadrons. – 2007. e-print: arXiv:0706.3453 [hep-ph].
17. Abbiendi G. QCD studies with annihilation data at = 172-189 GeV // The Eur. Phys. J. C. – 2000. – Vol. 16. – P. 185 210.
18. Abreu P., Adam W., Adye T., Agasi E., Ajinenko I., Aleksan R., Amaldi U. Charged particle multiplicity in e+e− interactions at = 130 GeV // Phys. Lett. B. – 1996. – Vol. 372. – P.172-180.
19. Heisenberg W. Production of meson showers // Nature. – 1949. – Vol. 164. - No. 4158. – P. 65-65.
20. Fermi E. High energy nuclear events // Prog. Theor. Phys. – 1950. – Vol. 5. – P. 570-583.
21. Dewanto A., Chan A.H., Oh C.H., Chen R., Sitaram K. Lee-Yang circle analysis of e+e− and generalized multiplicity distribution // Eur. Phys. J. C. – 2008. – Vol. 57. – P. 515-523.
22. Chew C.K., Kiang D., Zhou H. A generalized non-scaling multiplicity distribution // Phys Lett. B. – 1987. – Vol. 186. – P. 411-415.
23. Chan A.H., Chew C.K. e+e− multiplicity distribution from branching process // Z. Phys. C Part. Fields. – 1992. – Vol. 55. – P. 503-508.
24. Zborovský I. Multiplicity distributions in proton-(anti) proton and electron-positron collisions with parton recombination. – 2011. e-print arXiv:1106.4697 [hep-ph].
25. Link J.M., Yager P.M., Anjos J.C., Bediaga I., Castromonte C., Göbel C., Pepe I.M. Application of genetic programming to high energy physics event selection // Nucl. Instr. Meth. Phys. Res. A. – 2005. – Vol. 55. – P. 504-527.
26. Schmidt M., Lipson H. Distilling free-form natural laws from experimental data // Science. – 2009. – Vol. 324. – P. 81-85.
27. Akkoyun S., Bayram T. Estimations of fission barrier heights for Ra, Ac, Rf and Db nuclei by neural networks // Int. J. Mod. Phys. E. – 2014. – Vol. 23. – P. 1450064.
28. Akkoyun S., Bayram T., Turker T. Estimations of beta-decay energies through the nuclidic chart by using neural network // Radiat. Phys. Chem. – 2014. – Vol. 96. – P. 186-189.
29. Bhat P., Lonnblad L., Meier K., Sugano K. Using neural networks to identify jets in hadron-hadron collisions. / Research directions for the decade: Proceedings of the 1990 summer study on high energy physics. – 1992.
30. Baldi Pierre, Cranmer K., Faucett T., Sadowski P., Whiteson D. Parameterized neural networks for high-energy physics // Eur. Phys. J. C. – 2016. – Vol. 76:235.
31. Alves A. Stacking machine learning classifiers to identify Higgs bosons at the LHC. (2016). e-print arXiv:1612.07725 [hep-ph].
32. Haykin S.S. Neural networks and learning machines (Vol. 3). – 2009. Uppr Saddle River, NJ, USA. Pearson.
33. Ivakhnenko A.G. Polynomial theory of complex systems // IEEE Trans. on Systems, Man and Cybernetics SMC. – 1971. – Vol. 1. – P. 364-378.
34. Madala H.R., Ivakhnenko A.G. Inductive learning algorithms for complex systems modeling // Boca Raton. – 1994. – 368p. – CrC Press.
35. Mueller J.A., Ivachnenko A.G., Lemke F. GMDH algorithms for complex systems modeling // Math. Comput. Model. Dyn. Syst. – 1998. – Vol. 4. – P. 275-316.
36. Farlow S.J. Self-organizing methods in modeling: GMDH type algorithms. – 1984. – Vol. 54. – CrC Press.
37. Bezdek J.C. On the relationship between neural networks, pattern recognition and intelligence // Int J Approx Reason. – 1992. – Vol. 6. – P. 85-107.
38. Sherrod P.H. DTREG Predictive Modeling Software. – 2008. – Manual for software available online: www.dtreg.com.
Published
2017-10-20
Cited
How to Cite
El-Dahshan, E. A., & El-Bakry, S. Y. (2017). EMPIRICAL EQUATION USING GMDH METHODOLOGY FOR THE CHARGED PARTICLES MULTIPLICITY DISTRIBUTION IN HADRONIC POSITRON-ELECTRON ANNIHILATION. East European Journal of Physics, 4(3), 18-25. https://doi.org/10.26565/2312-4334-2017-3-02
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