Power corrections to the ${\pi }^0\gamma$ transition form factor and pion distribution amplitudes

Abstract

Employing the standard hard-scattering approach and the running coupling method we calculate a class of power-suppressed corrections $\sim 1/Q^{2n},n=1,2,3,...$ to the electromagnetic ${\pi }^0\gamma$ transition form factor (FF) $Q^2{F}_{\pi \gamma }(Q^2)$ arising from the end-point $x\to 0,1$ integration regions. In the investigations we use a hard-scattering amplitude of the subprocess $\gamma +{\gamma }^{\ast }\to q+\bar{q}$, symmetrized under exchange ${\mu }_R^2\leftrightarrow {\bar{\mu }}_R^2$ important for exclusive processes containing two external photons. In the computations the pion model distribution amplitudes (DA's) with one and two non-asymptotic terms are employed. The obtained predictions are compared with the CLEO data and constraints on the DA parameters $b_2({\mu }_0^2)$ and $b_4({\mu }_0^2)$ at the normalization point ${\mu }_0^2=1Ge{V}^2$ are extracted. Further restrictions on the pion DA's are deduced from the experimental data on the electromagnetic FF $F_{\pi }(Q^2)$.

Comments: 23 pages, 6 figures; the version published in Phys. Rev. D69, 094010 (2004)