Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. I. Cross section and spin observables

TL;DR

This paper develops a relativistically covariant theoretical framework for semi-inclusive deep-inelastic scattering on polarized spin-1 targets, providing general expressions for cross sections and polarization observables applicable across all kinematic regions.

Contribution

It introduces a comprehensive formalism for analyzing semi-inclusive scattering on polarized spin-1 targets, including polarization effects and invariant structure functions, validated through symmetry properties.

Findings

Derived general semi-inclusive cross section formulas for spin-1 targets.

Expressed structure functions as photon-target helicity amplitudes.

Validated the formalism's kinematic generality across all deep-inelastic regions.

Abstract

We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (this article) we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. A relativistically covariant formulation in terms of 4-vectors and invariant polarization parameters is employed. The target polarization is described by a spin density matrix with vector and tensor polarization. The spin and azimuthal angle dependence of the semi-inclusive cross section is derived and parametrized in terms of invariant structure functions. To validate the result, the structure functions are expressed as photon-target helicity amplitudes with known symmetry properties. The expressions presented here are kinematic (no assumptions about particle production dynamics) and valid in all regions of the deep-inelastic final state (current and target fragmentation regions). In Part II (following article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. The semi-inclusive structure functions are computed by separating nuclear and hadronic structure, and the polarization observables are explored as functions of the tagged nucleon momentum.