Nonperturbatively-renormalized glue momentum fraction at physical pion mass from Lattice QCD

Abstract

We present the first nonperturbatively-renormalized determination of the glue momentum fraction $⟨x{⟩}_g$ in the nucleon, based on lattice-QCD simulations at physical pion mass using the cluster-decomposition error reduction (CDER) technique. We provide the first practical strategy to renormalize the glue energy-momentum tensor (EMT) nonperturbatively in the RI/MOM scheme, and convert the results to the $\overline{\text{MS}}$ scheme with 1-loop matching. The simulation results show that the CDER technique can reduce the statistical uncertainty of its renormalization constant by a factor of $\mathcal{O}$(300) in calculations using typical state-of-the-art lattice volume, and the nonperturbatively-renormalized $⟨x{⟩}_g$ is shown to be independent of the lattice definitions of the glue EMT up to discretization errors. We determine the renormalized $⟨x{⟩}_g^{\overline{\text{MS}}}(2\text{ GeV})$ to be 0.47(4)(11) at physical pion mass, which is consistent with the experimentally-determined value.

Comments: 9 pages, 11 figures, the version accepted by PRD