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