On some implications of the BaBar data on the ${\gamma }^{\ast }{\eta }^{\prime }$ transition form factor

Abstract

At leading-twist accuracy the form factors for the transitions from a virtual photon to the $\eta$ or ${\eta }^{\prime }$ can be expanded into a power series of the variable $\omega$, being related to the difference of two photon virtualities. The series possess the remarkable feature that only the Gegenbauer coefficients of the meson distribution amplitudes of order $l\le m$ contribute to the term $\sim {\omega }^m$. Thus, for $\omega \to 0$ only the asymptotic meson distribution amplitude contributes, allowing for a test of the mixing of the $\eta$ and ${\eta }^{\prime }$ decay constants. Employing the Gegenbauer coefficients determined in analysis of the form factors in the real photon limit, we present predictions for the ${\gamma }^{\ast }\eta$ and ${\gamma }^{\ast }{\eta }^{\prime }$ form factors and compare them to the BaBar data.

arXiv comment14 pages, 2 figures

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Cited by in corpus (2)

• The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c(1S,2S)$ transition form factors for spacelike photons
• Two-gluon production of $\varphi$ and ${\eta }^{\prime }$ mesons in proton-proton collisions at high energies