General Tensor Structure for Inclusive and Semi-inclusive Electron Scattering from Spin-1/2 Targets *

We study inclusive and semi-inclusive polarized electron scattering from polarized spin ½ targets. These reactions are of interest for experiments at fixed target accelerators like CEBAF at Jefferson Lab, and the planned electron-ion collider (EIC). We find that there are four sectors which may be separated by employing beam and target polarizations. When unpolarized electrons are used, only symmetric tensors enter, whereas antisymmetric tensors enter for longitudinally polarized electron beams. In the different sectors, we identify a total of 18 invariant response functions which depend on four Lorentz scalars. We classify these according to their properties under parity and time reversal.

Most theoretical calculations are performed in the target rest frame. It is in general quite difficult to model everything covariantly so that results can be obtained in another frame, e.g. the collider frame. We outline how to find the results in any frame by first calculating the invariant response functions relevant to the reaction under consideration at the correct values for the Lorentz scalars, and then constructing the non-invariant response functions based on the helicity decomposition of the virtual photon in the desired frame.