A Comprehensive Analysis on the Pion-Photon Transition Form Factor Beyond the Leading Fock State

Abstract

We perform a comprehensive analysis of the pion-photon transition form factor $F_{\pi \gamma }(Q^2)$ involving the transverse momentum corrections with the present CLEO experimental data, in which the contributions beyond the leading Fock state have been taken into consideration. As is well-known, the leading Fock-state contribution dominates of $F_{\pi \gamma }(Q^2)$ at large momentum transfer ($Q^2$) region. One should include the contributions beyond the leading Fock state in small $Q^2$ region. In this paper, we construct a phenomenological expression to estimate the contributions beyond the leading Fock state based on its asymptotic behavior at $Q^2\to 0$. Our present theoretical results agree well with the experimental data in the whole $Q^2$ region. Then, we extract some useful information of the pionic leading twist-2 distribution amplitude (DA) by comparing our results of $F_{\pi \gamma }(Q^2)$ with the CLEO data. By taking best fit, we have the DA moments, $a_2({\mu }_0^2)=0.002_{-0.054}^{+0.063}$, $a_4({\mu }_0^2)=-0.022_{-0.012}^{+0.026}$ and all of higher moments, which are closed to the asymptotic-like behavior of the pion wavefunction.

25 pages, 7 figures. Typo error corrected

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