Power corrections to the $π^0γ$ 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 $π^0γ$ transition form factor (FF) $Q^2F_{πγ}(Q^2)$ arising from the end-point $x \to 0,1$ integration regions. In the investigations we use a hard-scattering amplitude of the subprocess $γ+γ^{*} \to q +\bar{q}$, symmetrized under exchange $μ_R^2 \leftrightarrow \barμ_R^2$ 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 $b_2(μ_0^2)$ and $b_4(μ_0^2)$ at the normalization point $μ_0^2=1 GeV^2$ are extracted. Further restrictions on the pion DA's are deduced from the experimental data on the electromagnetic FF $F_π(Q^2)$.