Singularities in twist-3 quark distributions

We find in one-loop calculations and spectator models that twist-3 generalized parton distributions exhibit discontinuities. In the forward limit, these discontinuities grow into Dirac delta functions which are essential to satisfy the sum rules involving twist-3 parton distribution functions (PDFs). We calculate twist3 quasi-PDFs as a function of longitudinal momentum and identify the Dirac delta function terms with momentum components in the nucleon state that do not scale as the nucleon is boosted to the infinite momentum frame.