Single-spin observables and orbital structures in hadronic distributions

Single-spin observables in scattering processes (either analyzing powers or polarizations) are highly constrained by rotational invariance and finite symmetries. For example, it is possible to demonstrate that all single-spin observables are odd under the finite transformation O=PAτ where P is parity and Aτ is a finite symmetry that can be designated 'artificial time reversal'. The operators P, O and Aτ all have eigenvalues ±1 so that all single-spin observables can be classified into two distinct categories: (1) P-odd and Aτ-even (2) P-even and Aτ-odd. Within the light-quark sector of the standard model, P-odd observables are generated from pointlike electroweak processes while Aτ-odd observables (neglecting quark mass parameters) come from dynamic spin-orbit correlations within hadrons or within larger composite systems, such as nuclei. The effects of Aτ-odd dynamics can be inserted into transverse-momentum dependent constituent distribution functions and, in this paper, we construct the contribution from an orbital quark to the Aτ-odd quark parton distribution ΔNGq/p↑front(x,kTN;μ2). Using this distribution, we examine the crucial role of initial- and final-state interactions in the observation of the scattering asymmetries in different hard-scattering processes. This construction provides a geometrical and dynamical interpretation of the Collins conjugation relation between single-spin asymmetries in semi-inclusive deep inelastic scattering and the asymmetries in Drell-Yan production. Finally, our construction allows us to display a significant difference between the calculation of a spin asymmetry generated by a hard-scattering mechanism involving color-singlet exchange (such as a photon) and a calculation of an asymmetry with a hard-scattering exchange involving gluons. This leads to an appreciation of the process-dependence inherent in measurements of single-spin observables