Proton Spin Sum Rule from Large Momentum Effective Field Theory

Abstract

In high energy scattering experiments, the proton spin is understood as the sum of the spin and orbital angular momentum of the quarks and gluons in Feynman’s parton picture. The Jaffe–Manohar form of the proton spin sum rule is justified as physical, and it is shown that the individual terms can be related to the proton matrix elements of certain quasi-obervables through a large momentum effective field theory. The relation is expressed as a factorization formula where the leading contribution to the quasi-observable is factorized into the parton observables and perturbative matching coefficients, and we present the results for the latter at one-loop order in perturbation theory. This will provide us with the basis to extract the proton spin content from the lattice QCD calculations of the quasi-observables.