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

Abstract

The ${\eta }^{\prime }{g}^{\ast }{g}^{(\ast )}$ 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 $|q_1^2|>m_{{\eta }^{\prime }}^2$) $F_{{\eta }^{\prime }{g}^{\ast }g}(q_1^2,0,m_{{\eta }^{\prime }}^2)=m_{{\eta }^{\prime }}^{2}H(q_1^2)/(q_1^2-m_{{\eta }^{\prime }}^2)$, 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 ${\rm Y}(1S)\to {\eta }^{\prime }X$. We also present an interpolating formula for the vertex function $F_{{\eta }^{\prime }{g}^{\ast }g}(q_1^2,0,m_{{\eta }^{\prime }}^2)$ 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${}^2$.

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

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• Semileptonic decays $B/B_s \to (η,\etar, G)(l^+l^-,l\barν,ν\barν)$ in the perturbative QCD approach beyond the leading order
• ${\eta }_c$ mixing effects on charmonium and $B$ meson decays
• An Analysis of the Inclusive Decay ${\rm Y}(1S)\to {\eta }^{\prime }X$ and Constraints on the ${\eta }^{\prime }$-Meson Distribution Amplitudes
• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
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• QCD analysis of electromagnetic Dalitz decays $J/\psi \to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$
• Gravitational form factors in the perturbative limit
• Quark distributions and gluon contents of eta and etaprime
• Sub-leading power corrections to transition form factors of $\eta$ and ${\eta }^{\prime }$ mesons from twist-six contributions
• Soft end-point and mass corrections to the eta' g*g* vertex function