Accessing the quark orbital angular momentum with Wigner distributions

TL;DR

This paper explores how Wigner distributions in quantum field theory can be used to access and quantify the quark orbital angular momentum within the proton, offering a potentially more natural approach than traditional methods.

Contribution

It demonstrates the relationship between Wigner distributions, GPDs, and TMDs, and discusses how quark OAM can be extracted from phase-space distributions.

Findings

Wigner distributions relate to GPDs and TMDs.

Different definitions of quark OAM are summarized.

Extraction methods from Wigner distributions are discussed.

Abstract

The quark orbital angular momentum (OAM) has been recognized as an important piece of the proton spin puzzle. A lot of effort has been invested in trying to extract it quantitatively from the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs), which are accessed in high-energy processes and provide three-dimensional pictures of the nucleon. Recently, we have shown that it is more natural to access the quark OAM from the phase-space or Wigner distributions. We discuss the concept of Wigner distributions in the context of quantum field theory and show how they are related to the GPDs and the TMDs. We summarize the different definitions discussed in the literature for the quark OAM and show how they can in principle be extracted from the Wigner distributions.