Partonic quasi-distributions of the proton and pion from transverse-momentum distributions.
The parton quasi-distribution functions (QDFs) of Ji have been found by Radyushkin to be directly related to the transverse momentum distributions (TMDs) 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 Kwiecinski 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 ITD and moments of the parton distribution functions (PDFs), which i.a. allow for consistency checks of the lattice calculations, are also presented.
Publisher URL: http://arxiv.org/abs/1711.03377
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