Gluon momentum fraction of the nucleon from lattice QCD

TL;DR

This paper calculates the gluon momentum fraction in the nucleon using lattice QCD with different pion masses, employing stout smearing and perturbative renormalization, providing results consistent across ensembles.

Contribution

It presents a direct lattice QCD calculation of the gluon momentum fraction with improved operator definitions and renormalization techniques at physical and unphysical pion masses.

Findings

Gluon momentum fraction at 370 MeV pion mass: 0.284(23)(23)

Gluon momentum fraction at physical pion mass: 0.283(23)(15)

Consistent results across different lattice ensembles

Abstract

We perform a direct calculation of the gluon momentum fraction of the nucleon using maximally twisted mass fermion ensembles with $N_f=2+1+1$ flavors at a pion mass of about $370\,\mathrm{MeV}$ and a lattice spacing of $a\approx 0.082\,\mathrm{fm}$ and with $N_f=2$ flavors at the physical pion mass and a lattice spacing of $a\approx 0.093\,\mathrm{fm}$. In the definition of the gluon operator we employ stout smearing to obtain a statistically significant result for the bare matrix elements. In addition, we perform a lattice perturbative calculation including 2 levels of stout smearing to carry out the mixing and the renormalization of the quark and gluon operators. We find, after conversion to the $\overline{\mathrm{MS}}$ scheme at a scale of $2\,\mathrm{GeV}$: $\langle x\rangle^R_g {=} 0.284(23)(23)$ for pion mass of about $370\,\mathrm{MeV}$ and $\langle x\rangle^R_g {=} 0.283(23)(15)$ for the physical pion mass.