An analysis of the inclusive Υ (1S) → η′ X decay and constraints on the η′-meson distribution amplitudes
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We calculate the η′-meson energy spectrum in the Υ (1S) → η′ g g g → η′ X decay in the leading-order perturbative QCD in the static-quark limit for the orthoquarkonium. Our principal result is the extraction of parameters of the η′ g* g effective vertex function (EVF) involving a virtual and a real gluon from the available data on the hard part of the η′-meson energy spectrum. The perturbative-QCD based framework provides a good description of the available CLEO data, allowing one to constrain the lowest Gegenbauer coefficients B(q)2 and B(g)2 of the quark-antiquark and gluonic distribution amplitudes of the η′-meson. The resulting constraints are combined with the existing ones on these coefficients from an analysis of the η′ – γ transition form factor and the requirement of positivity of the EVF, yielding B(q)2 (μ02) = –0.008 ± 0.054 and B(g)2 (μ02) = 4.6 ± 2.5 for μ02 = 2 GeV2. This reduces significantly the current uncertainty on these coefficients.