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 the two photon virtualities. The series possess the remarkable feature that only the Gegenbauer coefficients of the meson distribution amplitudes of order l≤m contribute to the term ∼ωm. Thus, for ω→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 an 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.
Highlights
The photon-meson transition form factors have always found much attention; there is a rich literature about these simple observables
The purpose of the present paper is to study this property in some detail and to generalize it to next-to-leading order (NLO) of perturbative QCD for the case of the γ∗η and γ∗η′
For comparison we have made an alternative evaluation of the transition form factors for which we have assumed a82 = a12 = 0.25, positive values for these Gegenbauer coefficients are favored by QCD sum rules [15], and, in order to have the γ∗η′
Summary
The photon-meson transition form factors have always found much attention; there is a rich literature about these simple observables. These form factors have been measured in a rather large range of photon virtualities and the data are analyzed within the framework of collinear. This property of the collinear factorization approach has first been pointed out in [3]. The purpose of the present paper is to study this property in some detail and to generalize it to next-to-leading order (NLO) of perturbative QCD for the case of the γ∗η and γ∗η′. A comparison with the BaBar data will be made
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