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

Abstract

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

Comments: 4 pages, 2 figures, use svjour.cls and svepj.clo; talk given at the International Europhysics Conference on High-Energy Physics (HEP 2003), 17-23 July 2003, Aachen, Germany. Title changed