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The \(\eta^\prime g^* g^{(*)}\) vertex including the \(\eta^\prime\)-meson mass

  • A. Ali
  • A. Ya Parkhomenko
theoretical physics

Abstract.

The \(\eta^\prime g^* g^{(*)}\) effective vertex function is calculated in the QCD hard-scattering approach, taking into account the \(\eta^\prime\)-meson mass. We work in the approximation in which only one non-leading Gegenbauer moment for both the quark-antiquark and the gluonic light-cone distribution amplitudes for the \(\eta^\prime\)-meson is kept. The vertex function with one off-shell gluon is shown to have the form (valid for \(\vert q_1^2 \vert > m_{\eta^\prime}^2\)) \(F_{\eta^\prime g^* g} (q_1^2, 0, m_{\eta^\prime}^2) = m_{\eta^\prime}^2 H(q_1^2)/(q_1^2 - m_{\eta^\prime}^2)\), where H(q 1 2) is a slowly varying function, derived analytically in this paper. The resulting vertex function is in agreement with the phenomenologically inferred form of this vertex obtained from an analysis of the CLEO data on the \(\eta^\prime\)-meson energy spectrum in the decay \(\Upsilon(1S) \to \eta^\prime X\). We also present an interpolating formula for the vertex function \(F_{\eta^\prime g^* g} (q_1^2, 0, m_{\eta^\prime}^2)\) for the space-like region of the virtuality q 1 2, which satisfies the QCD anomaly normalization for on-shell gluons and the perturbative QCD result for the gluon virtuality \(\vert q_1^2\vert \gtrsim 2\) GeV2.

Keywords

Energy Spectrum Distribution Amplitude Vertex Function Meson Mass Gluon Virtuality 
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References

  1. 1.
    T. Muta, M.Z. Yang, Phys. Rev. D 61, 054007 (2000) [hep-ph/9909484]CrossRefGoogle Scholar
  2. 2.
    A. Ali, A.Y. Parkhomenko, Phys. Rev. D 65, 074020 (2002) [hep-ph/0012212]CrossRefGoogle Scholar
  3. 3.
    P. Kroll, K. Passek-Kumericki, Phys. Rev. D 67, 054017 (2003) [hep-ph/0210045]CrossRefGoogle Scholar
  4. 4.
    S.S. Agaev, N.G. Stefanis, hep-ph/0212318Google Scholar
  5. 5.
    A.L. Kagan, A.A. Petrov, hep-ph/9707354Google Scholar
  6. 6.
    D. Atwood, A. Soni, Phys. Lett. B 405, 150 (1997) [hep-ph/9704357]CrossRefGoogle Scholar
  7. 7.
    A.L. Kagan, AIP Conference Proceedings 618, 310 (2002) [hep-ph/0201313]CrossRefGoogle Scholar
  8. 8.
    M. Artuso [CLEO Collaboration], Phys. Rev. D 67, 052003 (2003) [hep-ex/0211029]Google Scholar
  9. 9.
    A. Ali, A.Y. Parkhomenko, Eur. Phys. J. C (2003) Online First, DOI: 10.1140/epjc/s2003-01260-y [hep-ph/0304278]Google Scholar
  10. 10.
    P. Ball, JHEP 9901, 010 (1999) [hep-ph/9812375]Google Scholar
  11. 11.
    V.M. Braun, I.E. Halperin, Z. Phys. C 44, 157 (1989) [Sov. J. Nucl. Phys. 50, 511 (1989)]Google Scholar
  12. 12.
    V.M. Braun, I.E. Halperin, Z. Phys. C 48, 239 (1990) [Sov. J. Nucl. Phys. 52, 126 (1990)]Google Scholar
  13. 13.
    M.V. Terentev, Sov. J. Nucl. Phys. 33, 911 (1981) [Yad. Fiz. 33, 1692 (1981)]Google Scholar
  14. 14.
    M. Beneke, M. Neubert, Nucl. Phys. B 651, 225 (2003) [hep-ph/0210085]CrossRefGoogle Scholar
  15. 15.
    B. Geyer, M. Lazar, D. Robaschik, Nucl. Phys. B 559, 339 (1999) [hep-th/9901090]CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    B. Geyer, M. Lazar, Nucl. Phys. B 581, 341 (2000) [hep-th/0003080]CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    A.V. Radyushkin, Phys. Lett. B 385, 333 (1996) [hep-ph/9605431]CrossRefGoogle Scholar
  18. 18.
    T. Ohrndorf, Nucl. Phys. B 186, 153 (1981)Google Scholar
  19. 19.
    M.A. Shifman, M.I. Vysotsky, Nucl. Phys. B 186, 475 (1981)Google Scholar
  20. 20.
    V.N. Baier, A.G. Grozin, Nucl. Phys. B 192, 476 (1981)Google Scholar
  21. 21.
    M.V. Terentev, JETP Lett. 33, 67 (1981) [Pisma Zh. Eksp. Teor. Fiz. 33, 71 (1981)]Google Scholar
  22. 22.
    A.V. Belitsky, D. Muller, Nucl. Phys. B 537, 397 (1999) [hep-ph/9804379]CrossRefGoogle Scholar
  23. 23.
    T. Feldmann, Int. J. Mod. Phys. A 15, 159 (2000) [hep-ph/9907491]CrossRefGoogle Scholar
  24. 24.
    K. Hagiwara [Particle Data Group Collaboration], Phys. Rev. D 66, 010001 (2002)CrossRefGoogle Scholar
  25. 25.
    S.J. Brodsky, G.P. Lepage, Phys. Rev. D 24, 1808 (1981)Google Scholar
  26. 26.
    T. Feldmann, P. Kroll, Phys. Rev. D 58, 057501 (1998) [hep-ph/9805294]CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • A. Ali
    • 1
  • A. Ya Parkhomenko
    • 2
  1. 1.Theory DivisionCERNSwitzerland
  2. 2.Institut für Theoretische PhysikUniversität BernBernSwitzerland

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