Partonic quasi-distributions of the proton and pion from transverse-momentum distributions

Abstract: The parton quasi-distribution functions (QDFs) of Ji have been found by Radyushkin to be directly related to the transverse momentum distributions (TMDs), to the pseudo-distributions, and to the Ioffe-time distributions (ITDs). This makes the QDF results at finite longitudinal momentum of the hadron interesting in their own right. Moreover, the QDF-TMD relation provides a gateway to the pertinent QCD evolution, with respect to the resolution scale Q, for the QDFs. Using the Kwieci\'nski evolution equations and well established parameterizations at a low initial scale, we analyze the QCD evolution of quark and gluon QDF components of the proton and the pion. We discuss the resulting breaking of the longitudinal-transverse factorization and show that it has little impact on QDFs at the relatively low scales presently accessible on the lattice, but the effect is visible in reduced ITDs at sufficiently large values of the Ioffe time. Sum rules involving derivatives of ITDs and moments of the parton distribution functions (PDFs) are applied to the ETMC lattice data. This allows us for a lattice determination of the transverse-momentum width of the TMDs from QDF studies.