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We calculate the $\eta^\prime$-meson energy spectrum in the decay $\Upsilon(1S) \to \eta^\prime g g g \to \eta^\prime X$ in the leading-order perturbativeQCD in the static quark limit for the Orthoquarkonium. Our principal result isthe extraction of parameters of the $\eta^\prime g^* g$ effective vertexfunction (EVF) involving a virtual and a real gluon from the available data onthe hard part of the $\eta^\prime$-meson energy spectrum. The perturbative QCDbased framework provides a good description of the available CLEO data,allowing to constrain the lowest Gegenbauer coefficients $B^{(q)}_2$ and$B^{(g)}_2$ of the quark-antiquark and gluonic distribution amplitudes of the$\eta^\prime$-meson. The resulting constraints are combined with the existingones on these coefficients from an analysis of the $\eta-\gamma$ and$\eta^\prime-\gamma$ transition form factors and the requirement of positivityof the EVF, yielding $B^{(q)}_2(\mu_0^2) = -0.008 \pm 0.054$ and$B^{(g)}_2(\mu_0^2) = 4.6 \pm 2.5$ for $\mu_0^2 = 2$ GeV$^2$. This reducessignificantly the current uncertainty on these coefficients. The resulting EFV$F_{\eta^\prime g^* g} (p^2, 0, m_{\eta^\prime}^2)$, including the$\eta^\prime$-meson mass effects, is presented.Comment: 23 pages, 8 figures; use epsfig.sty; Typos corrected, numerical  analysis further refined; added an equation; to appear in the European  Physical Journal

An analysis of the inclusive decay $\Upsilon (1S) \to \eta^\prime X$ and constraints on the $\eta^\prime$ -meson distribution amplitudes