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

TL;DR

This paper develops a comprehensive, frame-independent tensor formalism for semi-inclusive polarized electron scattering from polarized spin-1/2 targets applicable across all energy scales, unifying nuclear and particle physics approaches.

Contribution

It introduces a general covariant tensor framework with 18 invariant response functions for semi-inclusive polarized electron scattering, connecting traditional helicity response descriptions.

Findings

Constructed leptonic and hadronic tensors in a covariant form.

Identified 18 invariant response functions depending on four Lorentz scalars.

Demonstrated how semi-inclusive cross sections relate through integrations and sums.

Abstract

The general structure of semi-inclusive polarized electron scattering from polarized spin-1/2 targets is developed for use at all energy scales, from modest-energy nuclear physics applications to use in very high energy particle physics. The leptonic and hadronic tensors that enter in the formalism are constructed in a general covariant way in terms of kinematic factors that are frame dependent but model independent and invariant response functions which contain all of the model-dependent dynamics. In the process of developing the general problem the relationships to the conventional responses expressed in terms of the helicity components of the exchanged virtual photon are presented. For semi-inclusive electron scattering with polarized electrons and polarized spin-1/2 targets one finds that 18 invariant response functions are required, each depending on four Lorentz scalar invariants. Additionally it is shown how the semi-inclusive cross sections are related via integrations over the momentum of the selected coincidence particle and sums over open channels.