Virtuality Distributions and γγ * -> π 0 Transition at Handbag Level
We outline a new approach to transverse momentum dependence in hard processes using as an example the exclusive transition ${\gamma^{*}\gamma \to \pi^{0}}$ at the handbag level. We start with the coordinate representation for a matrix element ${\langle p |{\cal O}(0,z) |0 \rangle}$ of a bilocal operator ${{\cal O} (0,z)}$ describing a hadron with momentum p. Treated as a function of (pz) and z$^{2}$, it is parametrized through virtuality distribution amplitude (VDA) Φ (x, σ), with x being Fourier-conjugate to (pz) and σ Laplace-conjugate to z$^{2}$. For intervals with z$^{+}$ = 0, we introduce the transverse momentum distribution amplitude (TMDA) ${\Ψ (x,k_{\perp})}$ , 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 ${\Ψ (x,k_{\perp})}$ . 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.