https://doi.org/10.1140/epjc/s2003-01260-y
theoretical physics
An analysis of the inclusive decay $\Upsilon (1S) \to \eta^\prime X$ and constraints on the $\eta^\prime$-meson distribution amplitudes
1
Theory Division, CERN, 1211, Geneva 23, Switzerland
2
Institut für Theoretische Physik, Universität Bern, 3012, Bern, Switzerland
We calculate the $\eta^\prime$-meson energy spectrum in the decay $\Upsilon (1S) \to \eta^\prime g g g \to \eta^\prime X$ in leading-order perturbative QCD in the static quark limit for 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 one 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 $\mu_0^2 = 2$ GeV2. This significantly reduces 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.
© Springer-Verlag, 2003
