Abstract
We discuss in detail the spatial distribution of angular momentum inside the nucleon. We show that the discrepancies between different definitions originate from terms that integrate to zero. Even though these terms can safely be dropped at the integrated level, they have to be taken into account when discussing distributions. Using the scalar diquark model, we illustrate our results and, for the first time, check explicitly that the equivalence between kinetic and canonical orbital angular momentum persists at the level of distributions, as expected in a system without gauge degrees of freedom.
Highlights
Understanding how the spin of the nucleon originates from the spin and orbital motion of its constituent is one of the current key questions in hadronic physics
Ji has shown that the total angular momentum of quarks and gluons can be expressed in terms of generalized parton distributions (GPDs) [4]
Where T μν(x) is the Energy-Momentum Tensor (EMT) density associated with the system, which accounts for the fact that the fields are affected by Lorentz transformations owing to their dependence on space-time points
Summary
Understanding how the spin of the nucleon originates from the spin and orbital motion of its constituent is one of the current key questions in hadronic physics. One of the main conceptual issues is that the decomposition of the nucleon spin is not unique [1,2,3] This intrinsic ambiguity is sometimes considered as a sign indicating that the question is not physical. Ji has shown that the (kinetic) total angular momentum of quarks and gluons can be expressed in terms of generalized parton distributions (GPDs) [4]. As shown by Burkardt [8, 9], GPDs contain information about the spatial distribution of quarks and gluons inside the nucleon. Adhikari and Burkardt compared different definitions of the angular momentum density and reached the conclusion that none of the definitions agree at the density level They attributed some of the discrepancies to missing total divergence terms, as it had been pointed out earlier in Refs.
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