On some implications of the BaBar data on the $γ^*η'$ transition form factor

Abstract

At leading-twist accuracy the form factors for the transitions from a virtual photon to the $η$ or $η'$ can be expanded into a power series of the variable $ω$, 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 $l\leq m$ contribute to the term $\sim ω^m$. Thus, for $ω\to 0$ only the asymptotic meson distribution amplitude contributes, allowing for a test of the mixing of the $η$ and $η'$ decay constants. Employing the Gegenbauer coefficients determined in analysis of the form factors in the real photon limit, we present predictions for the $γ^*η$ and $γ^*η'$ form factors and compare them to the BaBar data.

14 pages, 2 figures