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Cut moments and a generalization of DGLAP equations

  • D. Kotlorz
  • S.V. Mikhailov
Open Access
Article

Abstract

We elaborate a cut (truncated) Mellin moments (CMM) approach that is constructed to study deep inelastic scattering in lepton-hadron collisions at the natural kinematic constraints. We show that generalized CMM obtained by multiple integrations of the original parton distribution f (x, μ 2) as well as ones obtained by multiple differentiations of this f (x, μ 2) also satisfy the DGLAP equations with the correspondingly transformed evolution kernel P (z). Appropriate classes of CMM for the available experimental kinematic range are suggested and analyzed. Similar relations can be obtained for the structure functions F (x), being the Mellin convolution F = C * f , where C is the coefficient function of the process.

Keywords

Deep Inelastic Scattering Renormalization Group QCD 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    V.N. Gribov and L.N. Lipatov, Deep inelastic ep scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].Google Scholar
  2. [2]
    V.N. Gribov and L.N. Lipatov, e + e pair annihilation and deep inelastic ep scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 675 [INSPIRE].Google Scholar
  3. [3]
    Y.L. Dokshitzer, Calculation of the structure functions for deep inelastic scattering and e + e annihilation by perturbation theory in quantum chromodynamics, Sov. Phys. JETP 46 (1977) 641 [INSPIRE].ADSGoogle Scholar
  4. [4]
    G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    A. Deur et al., Experimental study of isovector spin sum rules, Phys. Rev. D 78 (2008) 032001 [arXiv:0802.3198] [INSPIRE].ADSGoogle Scholar
  6. [6]
    S. Forte and L. Magnea, Truncated moments of parton distributions, Phys. Lett. B 448 (1999) 295 [hep-ph/9812479] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    S. Forte, L. Magnea, A. Piccione and G. Ridolfi, Evolution of truncated moments of singlet parton distributions, Nucl. Phys. B 594 (2001) 46 [hep-ph/0006273] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Piccione, Solving the Altarelli-Parisi equations with truncated moments, Phys. Lett. B 518 (2001) 207 [hep-ph/0107108] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    S. Forte, J.I. Latorre, L. Magnea and A. Piccione, Determination of α s from scaling violations of truncated moments of structure functions, Nucl. Phys. B 643 (2002) 477 [hep-ph/0205286] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    D. Kotlorz and A. Kotlorz, Evolution equations for truncated moments of the parton distributions, Phys. Lett. B 644 (2007) 284 [hep-ph/0610282] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    D. Kotlorz and A. Kotlorz, Evolution equations of the truncated moments of the parton densities. A possible application, Acta Phys. Polon. B 40 (2009) 1661 [arXiv:0906.0879] [INSPIRE].ADSGoogle Scholar
  12. [12]
    D. Kotlorz and A. Kotlorz, Truncated Mellin moments: useful relations and implications for the spin structure function g 2, Acta Phys. Polon. B 42 (2011) 1231 [arXiv:1106.3753] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    D. Kotlorz and A. Kotlorz, Evolution of the truncated Mellin moments of the parton distributions in QCD analysis, Phys. Part. Nucl. 45 (2014) 357 [arXiv:1405.5315] [INSPIRE].Google Scholar
  14. [14]
    A. Psaker, W. Melnitchouk, M.E. Christy and C. Keppel, Quark-hadron duality and truncated moments of nucleon structure functions, Phys. Rev. C 78 (2008) 025206 [arXiv:0803.2055] [INSPIRE].ADSGoogle Scholar
  15. [15]
    E.G. Floratos, R. Lacaze and C. Kounnas, Space and timelike cut vertices in QCD beyond the leading order. 1. The singlet sector, Phys. Lett. B 98 (1981) 285 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    O. Teryaev, QCD evolution and density matrix positivity, in the proceedings of the XXX PNPI International Winter School, February 26-March 5, Repino, Russia (2005).Google Scholar
  17. [17]
    X. Artru, M. Elchikh, J.-M. Richard, J. Soffer and O.V. Teryaev, Spin observables and spin structure functions: inequalities and dynamics, Phys. Rept. 470 (2009) 1 [arXiv:0802.0164] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Opole University of Technology, Division of PhysicsOpolePoland
  2. 2.Bogoliubov Laboratory of Theoretical Physics, JINRDubnaRussia

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