On the Renormalizability of Quasi Parton Distribution Functions

TL;DR

This paper proves that quasi-parton distribution functions, despite their ultraviolet divergences, can be multiplicatively renormalized to all orders in QCD, facilitating their use in lattice QCD and perturbative analyses.

Contribution

It identifies all sources of ultraviolet divergences in quasi-parton distribution functions and demonstrates their multiplicative renormalizability to all orders in QCD perturbation theory.

Findings

Power divergences can be renormalized multiplicatively.

Logarithmic divergences are also multiplicatively renormalizable.

Renormalization applies to all orders in perturbation theory.

Abstract

Quasi-parton distribution functions have received a lot of attentions in both perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton distribution functions, but also could be evaluated by lattice QCD simulations. However, unlike the parton distribution functions, the quasi-parton distribution functions have perturbative ultraviolet power divergences because they are not defined by twist-2 operators. In this paper, we identify all sources of ultraviolet divergences for the quasi-parton distribution functions in coordinate-space, and demonstrate that power divergences, as well as all logarithmic divergences can be renormalized multiplicatively to all orders in QCD perturbation theory.