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SpinQuest can testing the interplay between time-reversal symmetry and gauge symmetry: This can be understood by applying time-reversal to the quark fields in the operator definitions of the parton densities and how the gauge link provide the phase for the interference. The Sivers asymmetry is manifest like other naive T-odd observables because one is not integrating in such a measurement over transverse momentum.
The transverse SSA are odd under naive time reversal (time reversal of three momenta and angular momenta) requiring interference of amplitudes with different helicities and phases.
The Sivers function and other TMDs are recognized as a tool to study spin-orbit correlations, providing experimental observables for studying orbital angular momentum.
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