Matthias Burkardt

What is orbital angular momentum?

While the total angular momentum of an isolated system is uniquely defined, ambiguities arise when decomposing the total angular momentum of an interacting multi-constituent system into contributions from various constituents.
Moreover,in a gauge theory, switching the gauge may result in shuffling angular momentum between matter and gauge degrees of freedom. I will discuss some of the resulting subtleties in defining these quantities and implications on the nucleon's spin budget(s).

Elliot Leader

A transverse-spin sum rule

We argue that the claim that it is not possible to have an angular momentum sum rule, relating the spin of the nucleon to the angular momentum of its constituents, for a transversely polarized nucleon, is based on an incorrect expression in the literature for the matrix elements of the angular momentum operator. The error arises because of the peculiar singular nature of the operators. When this is corrected we find a very intuitive form for such a sum rule. Moreover we have found an alternative approach, which completely avoids the singular operators, and leads us to the same result.We also discuss the properties of the separate quark and gluon orbital angular momentum in the transversely polarized nucleon.

Leslie C. Bland

Experimental Overview of TMDs:  hadronic probes

Analyzing power is the dependence of inclusive particle production on the polarization of colliding protons.  It is one example of transverse single spin asymmetries (SSA).  Traditionally, experiments were done with either polarized beams incident on polarized or unpolarized targets.  The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory has now extended spin physics to a collider.  RHIC has collided polarized proton beams at center-of-mass energies, $\sqrt{s}=62, 200 and 500 GeV.  SSA are observed for particles produced with large Feynman-x and with transverse momenta associated with hard scattering.  Present understanding is that SSA are produced through spin- and transverse-momentum dependence in distribution and fragmentation functions.  This talk will review SSA from polarized proton collisions, emphasizing recent work at RHIC, and present an outlook towards future prospects.

Philipp Hägler

Lattice QCD studies of quark orbital angular momentum

In this talk, I will concentrate on recent lattice QCD results from the LHP Collaboration on moments of GPDs and the resulting quark spin and OAM contributions to the nucleon spin.
On the basis of a significantly improved statistics, we confirm the earlier observations that the angular momentum of the down quarks in the proton is negligible, and that the total orbital angular momentum carried by the light quarks is very small.
These findings will be compared to general expectations from quark model calculations and studies employing light-cone wave function representations.I will also discuss sources of systematic uncertainties, and possible future improvements of the lattice calculations.