An Analysis of the Inclusive Decay ${\rm Y}(1S)\to {\eta }^{\prime }X$ and Constraints on the ${\eta }^{\prime }$-Meson Distribution Amplitudes

Abstract

We calculate the ${\eta }^{\prime }$-meson energy spectrum in the decay ${\rm Y}(1S)\to {\eta }^{\prime }ggg\to {\eta }^{\prime }X$ in the leading-order perturbative QCD in the static quark limit for the Orthoquarkonium. Our principal result is the extraction of parameters of the ${\eta }^{\prime }{g}^{\ast }g$ 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 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 $\eta -\gamma$ and ${\eta }^{\prime }-\gamma$ transition form factors 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 ${\mu }_0^2=2$ GeV${}^2$. This reduces significantly the current uncertainty on these coefficients. The resulting EFV $F_{{\eta }^{\prime }{g}^{\ast }g}(p^2,0,m_{{\eta }^{\prime }}^2)$, including the ${\eta }^{\prime }$-meson mass effects, is presented.

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

References in corpus (5)

• Flavor-Singlet B-Decay Amplitudes in QCD Factorization
• The two-gluon components of the eta and eta' mesons to leading-twist accuracy
• The ${\eta }^{\prime }{g}^{\ast }{g}^{(\ast )}$ Vertex Including the ${\eta }^{\prime }$-Meson Mass
• Inclusive eta' Production from the Upsilon(1S)
• Improved ${\eta }^{\prime }$-Meson Distribution Amplitudes from Inclusive ${\rm Y}(1S)\to {\eta }^{\prime }X$ Decay

Cited by in corpus (15)

• B->eta(') Form Factors in QCD
• Gluonic contribution to $B\to {\eta }^{(\prime )}$ form factors
• The eta (eta') gamma transition form factor and the gluon-gluon distribution amplitude
• Semileptonic decays $B/B_s \to (η,\etar, G)(l^+l^-,l\barν,ν\barν)$ in the perturbative QCD approach beyond the leading order
• Rare $B_s$ decays to $\eta$ and ${\eta }^{\prime }$ final states
• The ${\eta }^{\prime }{g}^{\ast }{g}^{(\ast )}$ Vertex Including the ${\eta }^{\prime }$-Meson Mass
• Revisiting the OZI-forbidden Radiative Decays of Orthoquarkonia
• $B^0\to \omega {\eta }^{(\prime )}$ and $\varphi {\eta }^{(\prime )}$ decays in the perturbative QCD approach
• The gluon content of the $\eta$ and ${\eta }^{\prime }$ mesons and the $\eta \gamma$, ${\eta }^{\prime }\gamma$ electromagnetic transition form factors
• Exclusive processes $e^{+}{e}^{-}\to VP$ in $k_T$ factorization
• Okubo-Zweig-Iizuka-rule violation and B\to η^{(\prime)}K branching ratios
• Comprehensive Calculations on the OZI-forbidden Nonleptonic Decays of Orthoquarkonia $J/\psi ({\rm Y})\to \pi \pi ,\rho \pi$
• The annihilation decays $B_c^{-}\to {\eta }^{{}^{\prime }}(\eta ,{\pi }^0)l^{-}\bar{\nu }$
• Improved Measurement of the Branching Fraction and Energy Spectrum of eta' from Upsilon(1S) Decays
• Soft end-point and mass corrections to the eta' g*g* vertex function