Quasi-pdfs and pseudo-PDFs

Abstract

We discuss the physical nature of quasi-PDFs, especially the reasons for the strong nonperturbative evolution pattern which they reveal in actual lattice gauge calculations. We argue that quasi-PDFs may be treated as hybrids of PDFs and the rest-frame momentum distributions of partons. The latter is also responsible for the transverse momentum dependence of TMDs. The resulting convolution structure of quasi-PDFs necessitates using large probing momenta p3 & 3 GeV to get reasonably close to the PDF limit. To deconvolute the rest-frame distribution effects, we propose to use a method based directly on the coordinate representation. We treat matrix elements M(z3, p3) as distributions M(,z23) depending on the Ioffe-time = p3z3 and the distance parameter z23. The rest-frame spatial distribution is given by M(0,z23). Using the reduced Ioffe function M(,z23) = M(,z23)/M(0,z23) we divide out the rest frame effects, including the notorious link renormalization factors. The -dependence remains intact and determines the shape of PDFs in the small z3 region. The residual z23 dependence of the M(,z23) is governed by perturbative evolution. The Fourier transform of M(,z23) produces pseudo-PDFs P(x,z23) that generalize the light-front PDFs onto spacelike intervals. On the basis of these findings we propose a new method for extraction of PDFs from lattice calculations.