An analysis of the inclusive Υ (1S) → η^′ X decay and constraints on the η^′-meson distribution amplitudes

Abstract

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.