Structure of parton quasi-distributions and their moments

Anatoly Radyushkin

doi:10.1016/j.physletb.2018.11.047

paper

Structure of parton quasi-distributions and their moments

arXiv:1807.07509 · doi:10.1016/j.physletb.2018.11.047

Abstract

We discuss the structure of the parton quasi-distributions (quasi-PDFs) $Q (y, P_{3})$ outside the "canonical" $- 1 \leq y \leq 1$ support region of the usual parton distribution functions (PDFs). Writing the $y^{n}$ moments of $Q (y, P_{3})$ in terms of the combined $x^{n - 2 l} k_{⊥}^{2 l}$ -moments of the transverse momentum distribution (TMD) $F (x, k_{⊥}^{2})$ , we establish a connection between the large- $∣ y ∣$ behavior of $Q (y, P_{3})$ and large- $k_{⊥}^{2}$ behavior of $F (x, k_{⊥}^{2})$ . In particular, we show that the $1/ k_{⊥}^{2}$ hard tail of TMDs in QCD results in a slowly decreasing $\sim 1/∣ y ∣$ behavior of quasi-PDFs for large $∣ y ∣$ that produces infinite $y^{n}$ moments of $Q (y, P_{3})$ . We also relate the $\sim 1/∣ y ∣$ terms with the $ln z_{3}^{2}$ -singulariies of the Ioffe-time pseudo-distributions $M (ν, z_{3}^{2})$ . Converting the operator product expansion for $M (ν, z_{3}^{2})$ into a matching relation between the quasi-PDF $Q (y, P_{3})$ and the light-cone PDF $f (x, μ^{2})$ , we demonstrate that there is no contradiction between the infinite values of the $y^{n}$ moments of $Q (y, P_{3})$ and finite values of the $x^{n}$ moments of $f (x, μ^{2})$ .

9 pages, version to appear in Physics Letters B

Structure of parton quasi-distributions and their moments

Abstract

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