Perturbative renormalization of quasi-parton distribution functions

Abstract

In this paper we present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one-loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions.The extended nature of such 'long-link' operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors.On the lattice there is also mixing among certain subsets of these nonlocal operators; we calculate the corresponding finite mixing coefficients, which are necessary in order to disentangle individual matrix elements for each operator from lattice simulation data. Finally, extending our perturbative setup, we present non-perturbative prescriptions to extract the linearly divergent contributions.

Recent progress in hadron structure from Lattice QCD

“…Two to five HYP smearing steps are applied to the gauge links of the operator, which as mentioned above, it is expected to bring the renormalization function closer to unity. Since the renormalization function for this quantity is not yet available (a perturbative calculation is in progress [51]), a comparison between the unsmeared results with the data from various HYP smearing steps, reveals the influence of the renormalization; it appears that the smearing affect is stronger in the imaginary part. However, the authors of Ref.…”

Perturbative Renormalization of Wilson line operators

“…Finally, we point out some open questions for future investigations. A long write-up of our work, together with an extended list of references, can be found in [1] (see also the companion paper [2]). …”

Progress in computing parton distribution functions from the quasi-PDF approach

“…We use the oneloop conversion factor from Ref. [32]. The evolution to the MS renormalization scaleμ=2 GeV is performed using the intermediate Renormalization Group Invariant scheme (RGI), see Refs.…”

“…[33], where it is made finite by using the gradient flow. An additional aspect in qPDFs renormalization is also that qPDFs operators exhibit mixing for certain Dirac structures [32]. The aim of our present work is to perform the renormalization procedure in a fully non-perturbative manner.…”

“…At one-loop in perturbation theory, the divergence appears as a linear divergence, and was calculated in Ref. [32] for different fermionic and gluonic actions. A way to eliminate the linear divergence was also developed in Ref.…”