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.

32 pages, Latex 2e, adding two relations (VI.39/40), removing some misprints and changing few notations, adjusting trace terms

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• Operator product expansion in QCD in off-forward kinematics: Separation of kinematic and dynamical contributions
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• Deeply Virtual Compton Scattering to the twist-four accuracy: Impact of finite-$t$ and target mass corrections
• The Complete $O({\alpha }_s^2)$ Non-Singlet Heavy Flavor Corrections to the Structure Functions $g_{1,2}^{ep}(x,Q^2)$, $F_{1,2,L}^{ep}(x,Q^2)$, $F_{1,2,3}^{\nu (\bar{\nu })}(x,Q^2)$ and the Associated Sum Rules
• Finite-t and target mass corrections to deeply virtual Compton scattering
• Finite-t and target mass corrections to DVCS on a scalar target
• Kinematic power corrections in off-forward hard reactions
• Twist-3 GPDs in Deeply-Virtual Compton Scattering
• B-Meson Distribution Amplitudes of Geometric Twist vs. Dynamical Twist
• Target mass and finite $t$ corrections to diffractive deeply inelastic scattering
• Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scatterin
• Elementary Theorems Regarding Blue Isocurvature Perturbations
• Fermionic Isocurvature Perturbations
• Target mass effects in deep-inelastic scattering on the deuteron
• Quadratic Isocurvature Cross-Correlation, Ward Identity, and Dark Matter
• Higher twist nucleon distribution amplitudes in Wandzura-Wilczek approximation
• The twist-2 Compton operator and its hidden Wandzura-Wilczek and Callan-Gross relations
• Implementation of target mass corrections and higher-twist effects in the xFitter framework
• Baryon octet distribution amplitudes in Wandzura-Wilczek approximation
• Generalized Parton Distributions -- theoretical review --
• Finite-t and target mass corrections in off-forward hard reactions