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

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 $η^{\prime}$ meson - virtual gluon transition form factor (FF) $Q^2F_{η^{\prime}g^{*}g^{*}}(Q^2,ω)$. Contributions to the form factor from the quark and gluon components of the $η^{\prime}$ meson are taken into account. Analytic expressions for the FF's $F_{η^{\prime}gg^{*}}(Q^2,ω=\pm 1)$ and $F_{η^{\prime}g^{*}g^{*}}(Q^2,ω=0)$ are also presented, as well as Borel transforms $B[Q^{2}F_{η^{\prime}g^{*}g^{*}}](u)$ and resummed expressions. It is shown that except for $ω=\pm 1, 0$, 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 $F_{η^{\prime}g^{*}g^{*}}(Q^{2}, ω)$ relative to results obtained only in the context of the standard HSA with a ``frozen'' coupling.