Abstract
The total gluon helicity in a polarized proton is shown to be a matrix element of a gauge-invariant but nonlocal, frame-dependent gluon spin operator [Formula: see text] in the large momentum limit. The operator [Formula: see text] is fit for the calculation of the total gluon helicity in lattice QCD. This calculation also implies that parton physics can be studied through the large momentum limit of frame-dependent, equal-time correlation functions of quarks and gluons.
Highlights
Ever since the EMC “spin crisis” [1], the gluon polarization has been one of the most important pursuits of the hadron physics community
We report a breakthrough in understanding the physics of the gluon helicity, and propose a practical way to calculate this quantity in lattice quantum chromodynamics (QCD).10
We have shown that in the infinite momentum frame (IMF) limit the gauge-invariant, frame-dependent operator E × A⊥ has a clear physical meaning and is just the gluon-helicity operator from factorization theorems
Summary
Ever since the EMC “spin crisis” [1], the gluon polarization has been one of the most important pursuits of the hadron physics community. The difficulty of calculating ∆G has raised fundamental questions on the gaugeinvariance of the gluon spin.9 In this talk, we report a breakthrough in understanding the physics of the gluon helicity, and propose a practical way to calculate this quantity in lattice QCD.. We will provide a well-defined procedure for taking the large momentum limit, and give an explicit example on how to obtain ∆G from the IMF limit of a frame-dependent, time-independent matrix element. This example indicates that ∆G can be predicted in lattice QCD by studying the large momentum limit of a frame-dependent matrix element of the Euclidean operator E×A⊥. We will extend this approach to direct calculation of parton physics on a Euclidean lattice, which was considered otherwise infeasible for light-cone correlations
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