An Analysis of the Inclusive Decay $Υ(1S) \to η^\prime X$ and Constraints on the $η^\prime$-Meson Distribution Amplitudes

Details An Analysis of the Inclusive Decay $Υ(1S) \to η^\prime X$ and Constraints on the $η^\prime$-Meson Distribution Amplitudes An Analysis of the Inclusive Decay $Υ(1S) \to η^\prime X$ and Constraints on the $η^\prime$-Meson Distribution Amplitudes

2003-04-29

arxiv.org/abs/hep-ph/0304278v2

Eur.Phys.J.C30:183-195,2003

Physics

High Energy Physics

High Energy Physics - Phenomenology

23 pages, 8 figures; use epsfig.sty; Typos corrected, numerical analysis further refined; added an equation; to appear in the

Scientific paper

10.1140/epjc/s2003-01260-y

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 perturbative QCD in the static quark limit for the Orthoquarkonium. Our principal result is the extraction of parameters of the $\eta^\prime g^* g$ effective vertex function (EVF) involving a virtual and a real gluon from the available data on the hard part of the $\eta^\prime$-meson energy spectrum. The perturbative QCD based 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 existing ones on these coefficients from an analysis of the $\eta-\gamma$ and $\eta^\prime-\gamma$ transition form factors and the requirement of positivity of 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 reduces significantly 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.

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