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.
Categories: hep-ph