The ηgg Vertex with Arbitrary Gluon Virtualities in the Perturbative QCD Hard Scattering Approach

We study the η ′ g * g * vertex for arbitrary gluon virtualities in the time-like and space-like regions, using the perturbative QCD hard scattering approach and an input wave-function of the η ′-meson consistent with the measured η ′ γ * γ transition form factor. The contribution of the gluonic content of the η ′-meson is taken into account, enhancing the form factor over the entire virtuality considered. However, data on the electromagnetic form factor of the η ′-meson is not sufficient to quantify the gluonic enhancement. We also study the effect of the transverse momenta of the partons in the η ′-meson on the η ′ g * g * vertex, using the modified hard scattering approach based on Sudakov formalism, and contrast the results with the ones in the standard hard scattering approach in which such effects are neglected. Analytic expressions for the η ′ g * g * vertex are presented in limiting kinematic regions and parametrizations are given satisfying the QCD anomaly, for real gluons, and perturbative QCD behavior for large gluon virtualities, in both the time-like and space-like regions. Our results have implications for the inclusive decay B → η ′ X and exclusive decays, such as B → η ′ (K, K *), and in hadronic production processes N + N(¯ N) → η ′ X.