Quark and gluon orbital angular momentum: Where are we?
C\'edric Lorc\'e (Ecole polytechnique, CPHT), K.F. Liu (U., Kentucky, Lexington)

TL;DR
This paper reviews the current understanding of quark and gluon orbital angular momentum, its definitions, relation to parton distributions, and discusses ongoing theoretical challenges and future prospects.
Contribution
It provides a comprehensive summary of the different definitions of parton orbital angular momentum and explores their theoretical connections and unresolved issues.
Findings
Summarizes various definitions of parton orbital angular momentum.
Highlights theoretical puzzles in understanding orbital angular momentum.
Discusses future directions and experimental prospects.
Abstract
The orbital angular momentum of quarks and gluons contributes significantly to the proton spin budget and attracted a lot of attention in the recent years, both theoretically and experimentally. We summarize the various definitions of parton orbital angular momentum together with their relations with parton distributions functions. In particular, we highlight current theoretical puzzles and give some prospects.
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