Power correctionsto 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) $Q^2F_{\eta ^{\prime}g^{*}g^{*}}(Q^2,\omega)$. Contributions to the form factor from the quark and gluon components of the $\eta^{\prime}$ meson are taken into account. Analytic expressions for the 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 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 $1 \rm {GeV}^{2} \leq Q^2 \leq 25 \rm {GeV}^{2}$, 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.