| Summary: | We perform a one-loop study of the small-z32 behavior of the Ioffe-time distribution (ITD) M(ν,z32), the basic function that may be converted into parton pseudo- and quasi-distributions. We calculate the corrections on the operator level, so that our results may be also used for pseudo-distribution amplitudes and generalized parton pseudodistributions. We separate two sources of the z32-dependence at small z32. One is related to the ultraviolet (UV) singularities generated by the gauge link. Our calculation shows that, for a finite UV cut-off, the UV-singular terms vanish when z32=0. The UV divergences are absent in the reduced ITD given by the ratio M(ν,z32)/M(0,z32). Still, it has a non-trivial short-distance behavior due to lnz32Λ2 terms generating perturbative evolution of parton densities. We give an explicit expression, up to constant terms, for the reduced ITD at one loop. It may be used in extraction of PDFs from lattice QCD simulations. We also use our results to get new insights concerning the structure of parton quasi-distributions at one-loop level.
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