Il Nuovo Cimento A (1965-1970)

, Volume 108, Issue 7, pp 867–882 | Cite as

Quantum statistics and Altarelli-Parisi evolution equations

  • G. Mangano
  • G. Miele
  • G. Migliore


The phenomenological evidence of quantum statistical effects in parton physics is here briefly summarized, and the recent good results obtained by parameterizing the parton distributions in terms of Fermi-Dirac and Bose-Einstein statistical functions are discussed. In this framework we study the modification of the scaling behaviour of parton distributions due to quantum statistical effects. In particular, by following a well-known formal analogy which holds between the Altarelli-Parisi evolution equations, at leading-log approximation, and a set of Boltzmann equations, we suggest a generalization of evolution equations to take into account Pauli exclusion principle and gluon-induced emission.


13.60 - Photon and charged-lepton interactions with hadrons 


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  1. [1]
    Wolf G., Preprint DESY 94-022 (February 1994).Google Scholar
  2. [2]
    Altarelli G. andParisi G.,Nucl. Phys. B,126 (1977) 298;Gribov V. N. andLipatov L. N.,Sov. J. Nucl. Phys.,15 (1972) 438, 675;Lipatov L. N.,Sov. J. Nucl. Phys.,20 (1975) 94;Dokshitzer Y. L.,Sov. Phys. JETP,46 (1977) 641.CrossRefADSGoogle Scholar
  3. [3]
    Kuraev E. A., Lipatov L. N. andFadin V. S.,Sov. Phys. JETP,45 (1977) 199;Balitskii Ya. Ya. andLipatov L. N.,Sov. J. Nucl. Phys.,28 (1978) 822.MathSciNetADSGoogle Scholar
  4. [4]
    Girbov L. V., Levin E. M. andRyskin M. G.,Phys. Rep.,100 (1983) 1.CrossRefADSGoogle Scholar
  5. [5]
    Bourrely C., Buccella F., Miele G., Migliore G., Soffer J. andTibullo V.,Z. Phys. C,62 (1994) 431.CrossRefADSGoogle Scholar
  6. [6]
    Buccella F. andSoffer J.,Mod. Phys. Lett. A,8 (1993) 225;Europhys. Lett.,24 (1993) 165;Phys. Rev. D,48 (1993) 5416.CrossRefADSGoogle Scholar
  7. [7]
    Gottfried K.,Phys. Rev. Lett.,18 (1967) 1174.CrossRefADSGoogle Scholar
  8. [8]
    New Muon Collaboration (M. Arneodo et al.),Phys. Rev. D,50 (1994) R1.Google Scholar
  9. [9]
    European Muon Collaboration (J. Ashman et al.),Phys. Lett. B,206 (1988) 364;Nucl. Phys. B,328 (1989) 1.CrossRefADSGoogle Scholar
  10. [10]
    E142Muon Collaboration (P. L. Anthony et al.),Phys. Rev. Lett.,71 (1993) 959.CrossRefGoogle Scholar
  11. [11]
    Collins J. C. andJianwei Qiu,Phys. Rev. D,39 (1989) 1398.CrossRefADSGoogle Scholar
  12. [12]
    Mangano G., Miele G. andMigliore G., preprint FERMILAB-Pub-93/380-A (December 1993).Google Scholar
  13. [13]
    Preparata G., Ratcliffe P. andSoffer J.,Phys. Rev. Lett.,66 (1991) 687.CrossRefADSGoogle Scholar
  14. [14]
    Field R. D. andFeynman R. P.,Phys. Rev. D,15 (1977) 259.CrossRefADSGoogle Scholar
  15. [15]
    Bourquin M. et al., Z. Phys. C,21 (1983) 27;Ratcliffe P.,Phys. Lett. B,242 (1990), 271.CrossRefADSGoogle Scholar
  16. [16]
    Ellis J. andJaffe R. L.,Phys. Rev. D,9 (1974) 1444.CrossRefADSGoogle Scholar
  17. [17]
    Foudas C. et al., Phys. Rev. Lett.,64 (1990) 1207;Mishra S. R. et al., Phys. Rev. Lett.,68 (1992) 3499;Rabinowitz S. A. et al., Phys. Rev. Lett.,70 (1993) 134.CrossRefADSGoogle Scholar
  18. [18]
    UA6Collaboration G. Balocchi et al.), preprint CERN-PPE/93-129, to appear inPhys. Lett. B.;Oberson P. et al., talk at theXXVIII Recontres de Moriond, Les Arcs, March 1993;Werlen M. et al., talk at theInternational Europhysics Conference on HEP, Marseille, July 1993.Google Scholar
  19. [19]
    CCFRCollaboration (M. Shaevitz et al.), talk at theRecontres de Physique de la Valle d’Aoste, La Thuile, March 1993, preprint NEVIS R-1491.Google Scholar
  20. [20]
    Mueller A. H.,Phys. Rev. D,18 (1978) 3705;Gupta S. andMueller A. H.,Phys. Rev. D,20 (1979) 118.CrossRefADSGoogle Scholar
  21. [21]
    See, for example:Tolman R. C.,The Principles of Statistical Mechanics (Oxford University Press) 1938.Google Scholar
  22. [22]
    Ynduráin F. J.,The Theory of Quark and Gluon Interactions (Springer-Verlag) 1993.Google Scholar
  23. [23]
    Efremov A. V. andTeryaev O. V., Preprint JINR-EL-88-287;Altarelli G. andRoss G. G.,Phys. Lett. B,212 (1988) 391;Carlitz R., Collins J. C. andMueller A. H.,Phys. Lett.,214 (1988) 229.Google Scholar
  24. [24]
    Ross D. A. andSachrajda C. T.,Nucl. Phys. B,149 (1979) 497.CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1995

Authors and Affiliations

  • G. Mangano
    • 1
    • 2
  • G. Miele
    • 1
    • 2
  • G. Migliore
    • 1
    • 2
  1. 1.Dipartimento di Scienze FisicheUniversità di Napoli «Federico II»Napoli
  2. 2.INFN, sSezione di Napoli — Mostra D’OltremareNapoli

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