Relation between transverse momentum dependent distribution functions and parton distribution functions in the covariant parton model approach

Abstract

We derive relations between transverse momentum dependent distribution functions and the usual parton distribution functions in the 3D covariant parton model, which follow from Lorentz invariance and the assumption of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known parton distribution functions ${f}_{1}^{a}(x)$ and ${g}_{1}^{a}(x)$ as input we predict the $x$- and ${\mathbf{p}}_{T}$-dependence of all twist-2 T-even transverse momentum dependent distribution functions.