Generalized Cahn effect and parton 3D motion in a covariant approach

The Cahn effect and the unintegrated unpolarized parton distribution function ${f}_{1}^{q}(x,{\mathbf{p}}_{T})$ are studied in a covariant approach. The Cahn effect is compared with some other effects due to the parton intrinsic motion. The comparison suggests that the present understanding of parton transverse momenta and intrinsic motion in general is still rather incomplete. The new relation for ${f}_{1}^{q}(x,{\mathbf{p}}_{T})$ is obtained in the framework of the covariant parton model from which a prediction for this distribution function follows.