On the singular behavior of the chirality-odd twist-3 parton distribution e(x)

Abstract The first moment of the chirality-odd twist-3 parton distribution e ( x ) is related to the pion-nucleon σ-term, which is important for phenomenology. However, the possible existence of a singular contribution proportional to δ ( x ) in the distribution prevents the determination of the σ-term with e ( x ) extracted from experimental data. There are two approaches to show the existence: the first one is based on an operator identity; the second one is based on a perturbative calculation of a single quark state with finite quark mass. We show that all contributions proportional to δ ( x ) in the first approach are canceled. For the second approach we find that e ( x ) of a multiparton state with a massless quark has no contribution with δ ( x ) . Considering that a proton is essentially a multiparton state, the effect of the contribution with δ ( x ) is expected to be suppressed by light quark masses with arguments from perturbation theory. A detailed discussion of the difference between cut diagrams and uncut diagrams of e ( x ) is provided.