Toward the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics

We present the first exploratory lattice quantum chromodynamics (QCD) calculation of the polarized gluon Ioffe-time pseudodistribution in the nucleon. The Ioffe-time pseudodistribution provides a frame-independent and gauge-invariant framework to determine the gluon helicity in the nucleon from first principles. We employ a high-statistics computation using a ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice ensemble characterized by a 358 MeV pion mass and a 0.094 fm lattice spacing. We establish the pseudodistribution approach as a feasible method to address the proton spin puzzle with successive improvements in statistical and systematic uncertainties anticipated in the future. Within the statistical precision of our data, we find a good comparison between the lattice determined polarized gluon Ioffe-time distribution and the corresponding expectations from the state-of-the-art global analyses. We find a hint for a nonzero gluon spin contribution to the proton spin from the model-independent extraction of the gluon helicity pseudodistribution over a range of Ioffe-time, $\ensuremath{\nu}\ensuremath{\lesssim}9$.