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Description
Quasi-parton distribution functions (qPDFs) are defined through QCD fields at spacelike separations evaluated in matrix elements of hadrons moving with finite velocity $v$. In the limit $v \to 1$, qPDFs converge to standard parton distribution functions (PDFs). It is therefore instructive to study their properties and convergence in effective models. We present a general analysis of unpolarized quark and antiquark qPDFs in general quark models. For this class of models, we provide general proofs of the convergence of qPDFs to PDFs and of the corresponding sum rules, for both Dirac structures $\gamma^0$ and $\gamma^3$. We then use the Covariant Parton Model as an explicit example to illustrate these general results and to derive analytic expressions for the small-$x$ behavior of qPDFs and for the quark energy-momentum tensor form factor $\bar c^{\,q}(t)$ at zero momentum transfer. These results correspond to a Wandzura-Wilczek-type approximation.