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 $p_3\gtrsim 3$ 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 $\mathcal{M}(\nu ,z_3^2)$ 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 $\mathcal{M}(0,z_3^2)$. Using the reduced Ioffe function $\mathfrak{M}(\nu ,z_3^2)\equiv \mathcal{M}(\nu ,z_3^2)/\mathcal{M}(0,z_3^2)$ 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 $\mathcal{M}(\nu ,z_3^2)$ produces pseudo-PDFs $\mathcal{P}(x,z_3^2)$ 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.

11 pages, Talk at QCD Evolution 2017 Workshop

Cited by in corpus (1)

• Generalized Parton Distributions and Pseudo-Distributions