Target mass corrections for virtual Compton scattering at twist-2 and generalized, non-forward Wandzura-Wilczek and Callan-Gross relations

Abstract

The off-cone Compton operator of twist-2 is Fourier transformed using a general procedure which is applicable, in principle, to any QCD tensor operator of definite (geometric) twist. That method allows, after taking the non-forward matrix elements, to separate quite effectively their imaginary part and to reveal some hidden structure in terms of appropriately defined variables, including generalized Nachtmann variables. In this way, without using the equations of motion, generalizations of the Wandzura-Wilzcek relation and of the mass-corrected Callan-Gross relation to the non-forward scattering, having the same shape as in the forward case, are obtained. In addition, new relations for those structure functions which vanish in the forward case are derived. These structure functions are written in terms of iterated generalized parton distributions of $n$-th order.