On the structure of the virtual Compton amplitude with additional final-state meson in the extended Bjorken region

Using the framework of the non-local light-cone expansion a systematic study is performed for the structure of the twist-2 contributions to the virtual Compton amplitude in polarized deep-inelastic non-forward scattering for general nucleon spin with an additional scalar meson in the final state. A useful kinematic parameterization allowing for appropriate triple-valued off-forward parton distribution amplitudes is given. One-variable amplitudes being adapted to the fixed parameters of the extended Bjorken region are introduced by decomposing the Compton amplitude into collinear and non-collinear components. These amplitudes obey Wandzura-Wilczek and Callan-Gross like relations. The evolution equations for all the distribution amplitudes are determined showing that the additional meson momentum does not appear in the evolution kernels. The generalization to $n$ outgoing mesons is given.