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

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 $\sim 1/Q^{2n},n=1,2,...$ to the massless ${\eta }^{\prime }$ meson - virtual gluon transition form factor (FF) $Q^2{F}_{{\eta }^{\prime }{g}^{\ast }{g}^{\ast }}(Q^2,\omega )$. Contributions to the form factor from the quark and gluon components of the ${\eta }^{\prime }$ meson are taken into account. Analytic expressions for the FF's $F_{{\eta }^{\prime }g{g}^{\ast }}(Q^2,\omega =\pm 1)$ and $F_{{\eta }^{\prime }{g}^{\ast }{g}^{\ast }}(Q^2,\omega =0)$ are also presented, as well as Borel transforms $B[Q^2{F}_{{\eta }^{\prime }{g}^{\ast }{g}^{\ast }}](u)$ 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 $1{\mathrm{GeV}}^2\le {\mathrm{Q}}^2\le 25{\mathrm{GeV}}^2$, power corrections found with the RC method considerably enhance the FF $F_{{\eta }^{\prime }{g}^{\ast }{g}^{\ast }}(Q^2,\omega )$ relative to results obtained only in the context of the standard HSA with a ``frozen'' coupling.

Comments: 38 pages, RevTeX4 used. 18 figures as PS/EPS files. Discussion extended; some typos corrected; change of renormalization scale to 1 GeV. Main results unchanged. Matches version to be published in Eur. Phys. J. C