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. All the structure functions are expressed in terms of iterated generalized parton distributions of n-th order. In addition, we showed that the absorptive part of twist-2 virtual Compton amplitude is determined by the non-forward extensions of g1, W1 and W2 only. PACS: 24.85.+p, 13.88.+e, 11.30.Cp Keywords: Off-cone twist-2 Compton operator, Fourier transform of QCD vector operators, Generalized parton distributions of twist-2, non-forward Wandzura-Wilczek and Callan-Gross relationsleading to the well-known WW-relations and extending the CG-relation. However, that method is tailored to the forward case and cannot be extended to the non-forward one.3 Quite differently, the group theoretical method for the determination of target mass corrections using harmonic scalar operators of definite spin and the corresponding matrix elements in terms of Gegenbauer polynomials has been introduced for the first by Nachtmann [40] and continued by Baluni and Eichten [42]. Remarkably, this method can be generalized for the consideration of target mass resp. power corrections to virtual Compton scattering in non-forward case [30,51]. Thereby, in order to get information about the target mass contributions one is forced to consider the (geometric) twist decomposition off-cone, taking into account all the trace terms leading to power suppressed expressions depending on M 2 /Q 2 .Concerning the twist-2 part Belitsky and Müller [51] were able to completely sum up the mass corrections to a closed form in terms of (di)logarithms depending on unique variable M 2 approaching 4x 2 M 2 /Q 2 in the forward case. On the other hand, in the previous work [30] it has been shown how the well-known twist decomposition of nonlocal scalar off-cone operators according to the method of harmonic extension can be used for the non-local vector and skew-symmetric tensor quark-antiquark operators, leading to power corrections of the related off-forward double distributions as well as the vector meson distribution amplitudes in x−space. But, the application to virtual Compton scattering which requires to carry-out the Fourier transformation of the operator matrix elements times the coefficient functions (in Born approximation), due to its complexity, remained open.In a previous consideration a straightforw...

Using the framework of the nonlocal 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 nonforward scattering for general nucleon spin with an additional scalar meson in the final state. A useful kinematic parametrization 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 noncollinear components. These amplitudes obey Wandzura-Wilczekand 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.

A general procedure is introduced allowing for the infinite decomposition of non-local vector operators off the light cone into operators of definite geometric twist. The method is applied to the operators (x)␥ (Ϫx) and (x) x (Ϫx) as well as to their matrix elements thereby determining all geometrical power ͑target mass͒ corrections being relevant for the related distribution amplitudes.

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