On the renormalization of quasi parton distribution

TL;DR

This work tackles the renormalization of quasi parton distributions, nonlocal spacelike bilinears whose UV structure complicates lattice access to PDFs. By working in the axial gauge $A^z=0$ and using dimensional regularization, the authors show that the renormalization of the unpolarized non-singlet quasi quark distribution is governed by quark-wave-function renormalization, with a one-loop equivalence to the heavy-light quark current in HQET. They demonstrate at two loops that vertex subdivergences do not affect the overall UV renormalization, and derive a two-loop renormalization factor $Z^{(2)}(\eta)$ whose coefficients are fixed by HQET results and color factors, reinforcing multiplicative renormalizability in this gauge. The findings provide a concrete framework for lattice renormalization of quasi distributions and clarify their connection to light-cone PDFs through matching, while leaving open the prospect of higher-loop confirmations.

Abstract

Recent developments showed that light-cone parton distributions can be studied by investigating the large momentum limit of the hadronic matrix elements of spacelike correlators, which are known as quasi parton distributions. Like a light-cone parton distribution, a quasi parton distribution also contains ultraviolet divergences and therefore needs renormalization. The renormalization of non-local operators in general is not well understood. However, in the case of quasi quark distribution, the bilinear quark operator with a straight-line gauge link appears to be multiplicatively renormalizable by the quark wave function renormalization in the axial gauge. We first show that the renormalization of the self energy correction to the quasi quark distribution is equivalent to that of the heavy-light quark vector current in heavy quark effective theory at one-loop order. Assuming this equivalence at two-loop order, we then show that the multiplicative renormalizability of the quasi quark distribution is true at two-loop order.

Figures (4)

• Figure 1: One-loop diagrams for quasi quark distribution in Feynman gauge, the conjugate diagrams are not shown.
• Figure 2: Two-loop self energy diagrams for quasi quark distribution in Feynman gauge. The disjoint and conjugate diagrams are not shown. The two-loop Wilson line self energy diagrams are the same as the first four diagrams for quark self energy, but with gluons attached to the Wilson line.
• Figure 3: Feynman gauge two-loop vertex diagrams that contain subdivergences, the conjugate diagrams are not shown (to be continued).
• Figure 4: Feynman gauge two-loop vertex diagrams that contain subdivergences (continued).