The $η^\prime g^* g^{(*)}$ Vertex Including the $η^\prime$-Meson Mass

Details The $η^\prime g^* g^{(*)}$ Vertex Including the $η^\prime$-Meson Mass The $η^\prime g^* g^{(*)}$ Vertex Including the $η^\prime$-Meson Mass

2003-07-07

arxiv.org/abs/hep-ph/0307092v1

Eur.Phys.J.C30:367-380,2003

Physics

High Energy Physics

High Energy Physics - Phenomenology

26 pages, 6 figures; use epsfig.sty; submitted to the European Physical Journal C

Scientific paper

10.1140/epjc/s2003-01302-6

The $\eta^\prime g^* g^{(*)}$ effective vertex function 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 for both the quark-antiquark and the gluonic light-cone distribution amplitudes for the $\eta^\prime$-meson is kept. The vertex function with one off-shell gluon is shown to have the form (valid for $| q_1^2 | > m_{\eta^\prime}^2$) $F_{\eta^\prime g^* g} (q_1^2, 0, m_{\eta^\prime}^2) = m_{\eta^\prime}^2 H(q_1^2)/(q_1^2 - m_{\eta^\prime}^2)$, where $H(q_1^2)$ is a slowly varying function, derived analytically in this paper. The resulting vertex function is in agreement with the phenomenologically inferred form of this vertex obtained from an analysis of the CLEO data on the $\eta^\prime$-meson energy spectrum in the decay $\Upsilon(1S) \to \eta^\prime X$. We also present an interpolating formula for the vertex function $F_{\eta^\prime g^* g} (q_1^2, 0, m_{\eta^\prime}^2)$ for 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$^2$.

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