On the renormalization of quasi parton distribution

TL;DR

This paper investigates the renormalization properties of quasi parton distributions, demonstrating their multiplicative renormalizability at two-loop order and establishing an equivalence with heavy-light quark vector current renormalization.

Contribution

It shows that the renormalization of quasi quark distributions can be understood through an equivalence with heavy quark effective theory, extending to two-loop order.

Findings

Quasi quark distributions are multiplicatively renormalizable at two-loop order.

Renormalization of the self energy correction is equivalent to heavy-light quark vector current renormalization.

The study advances understanding of non-local operator renormalization in QCD.

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.