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

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.

Figures (2)

• Figure 1: Azimuthal angles and coordinate systems in the collinear frames. The angles $\phi_h$ and $\phi_S$ conform to the Trento convention Bacchetta:2004jz. The $xyz$ coordinate system is aligned with the lepton plane, with the $z$ direction opposite to $\bm{q}$ and the $x$ direction along $\bm{l}_T = \bm{l}_T'$. The $x'y'z$ coordinate system is aligned with the hadron plane, with the $x'$ direction along $\bm{P}_{hT}$.
• Figure 2: Target polarization relative to the lepton beam axis in the target rest frame. Shown are the spatial components of the vector $\bm{N}$ in the target rest frame. For parallel polarization ($\parallel$), $\bm{N}$ points in the direction opposite to the initial lepton momentum. For perpendicular polarization ($\perp$), the angle $\psi_N$ is measured from the plane spanned by the final lepton momentum in the sense as indicated.