Double Distributions, Wide-Angle Compton Scattering, and $\gamma \gamma \to \pi\pi$

Double Distributions (DD) are the basis of a novel approach to describe hadronic structure. They represent a form of Generalized Parton Distributions, which attracted recently a considerable attention both from theoretical and experimental side. We develop a DD-based approach to wide-angle Compton scattering and annihilation processes like $\gamma \gamma \to \pi^+ \pi^-$ in kinematics when all Mandelstam variables $s,t,u$ are large. We take into account both twist-2 and twist-3 effects, and also show that $t$-dependence of the short-distance propagator can be treated as a generalized target mass correction, in a treatment analogous to that developed by Nachtmann and Georgi and Politzer for deep inelastic scattering. We study the dependence of the amplitude on polarization of participating photons and give estimates for cross sections. To this end we propose models for double distributions in spacelike and timelike regions.