The $η^\prime g^* g^{(*)}$ Vertex Function in Perturbative QCD and $η^\prime$-Meson Mass Effects

Abstract

The $η^\prime g^* g^{(*)}$ effective vertex function (EVF) is calculated in the QCD hard-scattering approach, taking into account the $η^\prime$-meson mass. We work in the approximation in which only one non-leading Gegenbauer moment in both the quark-antiquark and gluonic light-cone distribution amplitude for the $η^\prime$-meson is kept. The EVF with one off-shell gluon is shown to have the form $F_{η^\prime g^* g} (q_1^2, 0, m_{η^\prime}^2) = m_{η^\prime}^2 H(q_1^2)/(q_1^2 - m_{η^\prime}^2)$, valid for $|q_1^2| > m_{η^\prime}^2$. An interpolating formulae for the EVF in the space-like region of the virtuality $q_1^2$, which satisfies the QCD-anomaly normalization for on-shell gluons and the perturbative-QCD result for the gluon virtuality $|q_1^2| \gtrsim 2 GeV^2$, is also presented.