Virtuality Distributions and γγ^∗→π⁰ Transition Form Factor at Handbag Level

We outline a new approach to transverse momentum dependence in hard processes using as an example the exclusive transition γ^∗γ→π⁰ at the handbag level. We start with the coordinate representation for a matrix element of a bilocal operator O(0,z) describing a hadron with momentum p. Treated as a function of (pz) and z², it is parametrized through virtuality distribution amplitude (VDA) Φ (x, σ), with x being Fourier-conjugate to (pz) and σ Laplace-conjugate to z². For intervals with z⁺ = 0, we introduce the transverse momentum distribution amplitude (TMDA) Ψ(x,k_⊥) , and write it in terms of VDA Φ (x, σ). The results of covariant calculations, written in terms of Φ (x, σ) are converted into expressions involving Ψ(x,k_⊥). We propose simple models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data on the pion transition form factor. (author)