Understanding the proton spin from lattice QCD

The aim is to understand the spin structure of the proton using lattice field theory techniques as well as large-momentum effective theory (LaMET). Only about 30% of the proton’s total spin comes from its valence-quarks. We wish to measure the spin-content of the sea-quarks and gluons (known collectively as partons) using the methods of lattice quantum chromodynamics (QCD).

The proton structure is best studied in the infinite momentum limit in which the partons are free particles. However, on a Euclidean lattice, we cannot study physics on the light cone or in the light-cone gauge. In addition, the operator for gluon spin is not a gauge invariant quantity and, thus, we must fix the gauge. After the extraction of the observable quantities, we must apply the process of renormalization.

In order to renormalize the spin operator, we must determine with which operators it mixes. This process can be carried out with a perturbative calculation as well as determining the most general tensors with which the spin-operator can mix given the set of constraints.

Our approach to measuring the spin content is to use the Coulomb gauge which, when boosted to infinite momentum, becomes the light-cone gauge. We compute the ratio of three-point- and two-point-correlation functions of proton states with definite momentum. This combined function encodes the gluon spin matrix-element which can be extracted with curve-fitting techniques. The process of renormalization is then applied to these bare quantities.