Improved ${\eta }^{\prime }$-Meson Distribution Amplitudes from Inclusive ${\rm Y}(1S)\to {\eta }^{\prime }X$ Decay

Abstract

We calculate the ${\eta }^{\prime }$-meson energy spectrum in the ${\rm Y}(1S)\to {\eta }^{\prime }ggg\to {\eta }^{\prime }X$ 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 ${\eta }^{\prime }{g}^{\ast }g$ 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 $B_2^{(q)}$ and $B_2^{(g)}$ 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 ${\eta }^{\prime }-\gamma$ transition form factor and the requirement of positivity of the EVF, yielding $B_2^{(q)}({\mu }_0^2)=-0.008\pm 0.054$ and $B_2^{(g)}({\mu }_0^2)=4.6\pm 2.5$ for ${\mu }_0^2=2Ge{V}^2$. This reduces significantly the current uncertainty on these coefficients.

Comments: 4 pages, 4 figures, use svjour.cls and svepj.clo; talk given at the International Europhysics Conference on High-Energy Physics (HEP 2003), 17-23 July 2003, Aachen, Germany. Title changed