Gauge invariance of the deeply virtual Compton scattering amplitude

We analyze in detail the problem of gauge invariance of the deeply virtual Compton scattering (DVCS) amplitude. Using twist-3 one-gluon exchange diagram contributions and the QCD equations of motion, we derive the general gauge invariant expression of the DVCS amplitude on a (pseudo)scalar particle (pion, ${\mathrm{He}}^{4}).$ Similarly to the case of deep inelastic scattering, the amplitude does not depend on the twist-3 quark-gluon correlations at the Born level. The contribution of the derived amplitude to the single-spin asymmetry with longitudinally polarized lepton is calculated.