Glue Spin and Helicity in the Proton from Lattice QCD.

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor domain-wall fermion gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin S_{G} in the Coulomb gauge in the modified minimal subtraction (MS[over ¯]) scheme is obtained with one-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of S_{G} in the range 0≤|p[over →]|<1.5  GeV is very mild, and we determine it in the large-momentum limit to be S_{G}=0.251(47)(16) at the physical pion mass in the MS[over ¯] scheme at μ^{2}=10  GeV^{2}. If the matching procedure in large-momentum effective theory is neglected, S_{G} is equal to the glue helicity measured in high-energy scattering experiments.