PoS - Proceedings of Science
Volume 308 - QCD Evolution 2017 (QCDEV2017) - Tuesday, May 23, 2017- Morning 2
Quasi-PDFs and pseudo-PDFs
A. Radyushkin
Full text: pdf
Published on: March 23, 2018
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 $p_3 \gtrsim 3$ 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 $M(z_3,p_3)$ as distributions ${\cal M} (\nu, z_3^2)$ depending on the Ioffe-time $\nu = p_3 z_3$ and the distance parameter $z_3^2$. The rest-frame spatial distribution is given by ${\cal M} (0, z_3^2)$. Using the reduced Ioffe function ${\mathfrak M} (\nu, z_3^2) \equiv {\cal M} (\nu, z_3^2)/ {\cal M} (0, z_3^2)$ we divide out the rest frame effects, including the notorious link renormalization factors. The $\nu$-dependence remains intact and determines the shape of PDFs in the small $z_3$ region. The residual $z_3^2$ dependence of the ${\mathfrak M} (\nu,z_3^2)$ is governed by perturbative evolution. The Fourier transform of ${\cal M} (\nu, z_3^2)$ produces
pseudo-PDFs ${\cal P}(x, z_3^2)$ 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.
DOI: https://doi.org/10.22323/1.308.0021
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