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Employing the standard hard-scattering approach (HSA) in conjunction with therunning-coupling (RC) method, the latter joined with the infrared-renormaloncalculus, we compute power-suppressed corrections $\sim 1/Q^{2n}, n=1, 2,...$to the massless $\eta^{\prime}$ meson - virtual gluon transition form factor(FF) $Q^2F_{\eta ^{\prime}g^{*}g^{*}}(Q^2,\omega)$. Contributions to the formfactor from the quark and gluon components of the $\eta^{\prime}$ meson aretaken into account. Analytic expressions for the FF's$F_{\eta^{\prime}gg^{*}}(Q^2,\omega=\pm 1)$ and$F_{\eta^{\prime}g^{*}g^{*}}(Q^2,\omega=0)$ are also presented, as well asBorel transforms $B[Q^{2}F_{\eta^{\prime}g^{*}g^{*}}](u)$ and resummedexpressions. It is shown that except for $\omega=\pm 1, 0$, the Borel transformcontains an infinite number of infrared renormalon poles. It is demonstratedthat in the explored range of the total gluon virtuality $1 \rm {GeV}^{2} \leqQ^2 \leq 25 \rm {GeV}^{2}$, power corrections found with the RC methodconsiderably 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.Comment: 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.

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

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