Transverse Spin / Transverse Momentum Analogy and Gauge Invariance of Deeply Virtual Compton Scattering

Using the similarity between twist 3 contributions to transverse spin for usual parton distributions and transverse momentum for non-diagonal parton distributions, we determine for the simple case of a scalar (pion, $He^4$) target the linear in transverse momentum twist-3 contribution to Deeply Virtual Compton amplitude. This allows to write a gauge invariant amplitude for this non-forward process.