Gluon momentum fraction of the nucleon from lattice QCD

Abstract

We perform a direct calculation of the gluon momentum fraction of the nucleon, taking into account the mixing with the corresponding quark contribution. We use maximally twisted mass fermion ensembles with N f ¼ 2 þ 1 þ 1 flavors at a pion mass of about 370 MeV and a lattice spacing of a ≈ 0.082 fm and with N f ¼ 2 flavors at the physical pion mass and a lattice spacing of a ≈ 0.093 fm. We employ stout smearing to obtain a statistically significant result for the bare matrix elements. In addition, we perform a lattice perturbative calculation including two levels of stout smearing to carry out the mixing and the renormalization of the quark and gluon operators. We find, after conversion to the MS scheme at a scale of 2 GeV, hxi R g ¼ 0.284ð27Þð17Þð24Þ for pion mass of about 370 MeV and hxi R g ¼ 0.267ð22Þð19Þð24Þ for the physical pion mass. In the reported numbers, the first parenthesis indicates statistical uncertainties. The numbers in the second and third parentheses correspond to systematic uncertainties due to excited states contamination and renormalization, respectively.

Perturbative renormalization of quasi-parton distribution functions

“…The setup of this process is extensively described in Refs. [34,35] and is briefly outlined below. As is common practice, we will consider mass-independent renormalization schemes, so that fermion renormalized masses will be vanishing; for the one-loop lattice calculations this implies that the Lagrangian masses must be set to zero.…”

Off-forward gluonic structure of vector mesons

“…While the spin-independent gluon GFFs are clearly quantitatively different from the gluon transversity GFF, this difference is as yet hard to interpret meaningfully, given the limited subset of GFFs which are determined. Within the uncertainties of this calculation, the effects of renormalization, which have been neglected, are not significant [14].…”

“…[14] it is shown numerically that this mixing, i.e., the magnitude of Z qg l;m , is at the few-percent level for a similar action to the one used here, and that the renormalization Z gg l;m is approximately unity, with several levels of stout smearing used on the operator. These small mixing effects are neglected in the present calculation.…”

“…In this work the renormalization factors are not computed, but it is expected based on studies of similar gluonic operators [14] that they are Oð1Þ.…”

Round table: Nucleon tomography. What can we do better today than Rutherford 100 years ago?

“…in the MS at 2 GeV, where the mixing of x u+d+s with the gluon operator is perturbatively computed using one-loop lattice perturbation theory [87]. The systematic error results from the difference between using one-and two-levels of stout smearing.…”