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

The ${\eta }^{\mathrm{\prime }}{g}^{\ast }{g}^{(\ast )}$ effective vertex function (EVF) is calculated in the QCD hard-scattering approach, taking into account the ${\eta }^{\mathrm{\prime }}$-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 ${\eta }^{\mathrm{\prime }}$-meson is kept. The EVF with one off-shell gluon is shown to have the form $F_{\eta^\prime g^* g} (q_1^2, 0, m_{\eta^\prime}^2) = m_{\eta^\prime}^2 H(q_1^2)/(q_1^2 - m_{\eta^\prime}^2)$,validfor$|q_1^2| > m_{\eta^\prime}^2$. 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 $\mathrm{\mid }{q}_1^2\mathrm{\mid }\gtrsim 2Ge{V}^2$, is also presented.