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.
Highlights
A longstanding problem raised by deep-inelastic scattering and Drell-Yan experiments on the nucleon is that the gluons contribute almost as large a fraction of the nucleon momentum as the quarks [1,2], contradicting the naive quark model
Nonperturbative renormalization (NPR) of hxig is essential to check whether different lattice definitions of the gauge energy-momentum tensor (EMT) and smearing can provide a consistent prediction of hxig
We present the first NPR of the gauge EMT using the cluster-decomposition error reduction (CDER)
Summary
A longstanding problem raised by deep-inelastic scattering and Drell-Yan experiments on the nucleon is that the gluons contribute almost as large a fraction of the nucleon momentum as the quarks [1,2], contradicting the naive quark model. Besides the importance in understanding the nucleon momentum, the value of hxig is an important input to obtain the glue contributions to the nucleon mass and spin [3,4], so calculating it from a first-principle lattice-QCD simulation is of fundamental interest, in addition to providing an independent input and check of the experimental PDF determinations. Nonperturbative renormalization (NPR) of hxig is essential to check whether different lattice definitions of the gauge EMT and smearing can provide a consistent prediction of hxig. III, this strategy is tested in several cases including the quenched, 2-flavor, and 2 þ 1-flavor ones Based on those tests, a prediction of the renormalized hxig is provided in Sec. IV, with controllable systematic uncertainties from NPR. V, and the additional discussion on the cases with more than one step of HYP smearing is presented in the Appendix
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