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Particles and Fields
Eur. Phys. J. C 32, 507-528 (2004)
DOI: 10.1140/epjc/s2003-01463-2

Power corrections to the space-like transition form factor ${{F_{\eta^{\prime}g^{*}g^{*}}(Q^2,\omega )}}$

S.S. Agaev1 and N.G. Stefanis2

1  The Abdus Salam International Centre for Theoretical Physics, 34014 Trieste, Italy
2  Institut für Theoretische Physik II, Ruhr-Universität Bochum, 44780 Bochum, Germany

agaev_shahin@yahoo.com
stefanis@tp2.ruhr-uni-bochum.de

(Received: 19 May 2003 / Revised version: 24 October 2003 / / Published online: 8 December 2003)

Abstract
Employing the standard hard-scattering approach (HSA) in conjunction with the running coupling (RC) method, the latter joined with the infrared renormalon calculus, we compute power-suppressed corrections $\sim
1/Q^{2n},~n=1,2,\ldots $ to the massless $\eta^{\prime}$-meson-virtual-gluon transition form factor (FF) $Q^2F_{\eta ^{\prime }g^{*}g^{*}}(Q^2,\omega)$. Contributions to the form factor from the quark and gluon components of the $\eta^{\prime}$ meson are taken into account. Analytic expressions for the FFs $F_{\eta^{\prime}gg^{*}}(Q^2,\omega=\pm 1)$ and $F_{\eta^{\prime}g^{*}g^{*}}(Q^2,\omega=0)$ are also presented, as well as Borel transforms $B[Q^{2}F_{\eta^{\prime}g^{*}g^{*}}](u)$ and resummed expressions. It is shown that except for $\omega=\pm 1,\: 0$, the Borel transform contains an infinite number of infrared renormalon poles. It is demonstrated that in the explored range of the total gluon virtuality $1 \, {\mathrm {GeV}}^{2} \leq Q^2
\leq 25 \,{\mathrm {GeV}}^{2}$ , power corrections found with the RC method considerably enhance the FF ${{F_{\eta^{\prime}g^{*}g^{*}}(Q^2,\omega )}}$ relative to results obtained only in the context of the standard HSA with a "frozen" coupling.



© Società Italiana di Fisica, Springer-Verlag 2004