Virtuality Distributions in Application to $\gamma \gamma^* \to \pi^0$ Transition Form Factor at Handbag Level

Understand

We outline basics of a new approach to transverse momentum dependence in hard processes.

• As an illustration, we consider hard exclusive transition process $\gamma^* \gamma \to \pi^0$ at the handbag level.
• Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal ${\cal O}(0,z)$) describing a hadron with momentum $p$.
• Treated as functions of $(pz)$ and $z^2$, they are parametrized through virtuality distribution amplitudes (VDA) $\Phi (x, \sigma)$, with $x$ being Fourier-conjugate to $(pz)$ and $\sigma$ Laplace-conjugate to $z^2$.