Structure of parton quasi-distributions and their moments
Here, 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 \mbox{$$x^{n-2l} k_\perp^{2l}$$-moments} of the transverse momentum distribution (TMD) $${\cal F} (x,k_\perp^2)$$, we establish a connection between the large-$|y|$ behavior of $$Q(y,P_3)$$ and large-$$k_\perp^2$$ behavior of $${\cal F} (x,k_\perp^2)$$. In particular, we show that the $$1/k_\perp^2$$ 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 $$\mathfrak{M} (\nu, z_3^2)$$. Converting the operator product expansion for $$\mathfrak{M} (\nu, z_3^2)$$ into a matching relation between the quasi-PDF $$Q(y,P_3)$$ and the light-cone PDF $$f(x, \mu^2)$$, 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 $$f(x, \mu^2)$$.
- Research Organization:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
- Grant/Contract Number:
- AC05-06OR23177; FG02-97ER41028
- OSTI ID:
- 1489647
- Report Number(s):
- DOE/OR/23177-4499; JLAB-THY-18-2768; arXiv:1807.07509; PII: S0370269318308931
- Journal Information:
- Physics Letters. B, Journal Name: Physics Letters. B Journal Issue: C Vol. 788; ISSN 0370-2693
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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