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Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. II. Deuteron and spectator nucleon tagging

W. Cosyn, C. Weiss

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 (previous article) we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. In Part II (this article) we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. Methods of light-front quantization are employed to separate nuclear and hadronic structure in the high-energy process and achieve a composite description. The light-front wave function of the polarized deuteron is obtained from a rotationally covariant 3-dimensional wave function in the center-of-mass frame of the proton-neutron system. The tagged structure functions are computed in the impulse approximation. The momentum and spin distribution of the active nucleon are controlled by the deuteron polarization and the detected spectator momentum ($D/S$ wave ratio). The cross section and spin asymmetries are evaluated for general deuteron polarization (vector and tensor, longitudinal and transverse) as functions of the spectator momentum. Tensor-polarized spin asymmetries of order unity are achieved for spectator momenta $\sim$ 300 MeV, which select configurations with large $D$-wave. Sum rules for the tagged spin structure functions are derived. The results can be used for simulations of spectator tagging in future polarized fixed-target experiments (Jefferson Lab) or at the Electron-Ion Collider.

Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. II. Deuteron and spectator nucleon tagging

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 (previous article) we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. In Part II (this article) we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. Methods of light-front quantization are employed to separate nuclear and hadronic structure in the high-energy process and achieve a composite description. The light-front wave function of the polarized deuteron is obtained from a rotationally covariant 3-dimensional wave function in the center-of-mass frame of the proton-neutron system. The tagged structure functions are computed in the impulse approximation. The momentum and spin distribution of the active nucleon are controlled by the deuteron polarization and the detected spectator momentum ( wave ratio). The cross section and spin asymmetries are evaluated for general deuteron polarization (vector and tensor, longitudinal and transverse) as functions of the spectator momentum. Tensor-polarized spin asymmetries of order unity are achieved for spectator momenta 300 MeV, which select configurations with large -wave. Sum rules for the tagged spin structure functions are derived. The results can be used for simulations of spectator tagging in future polarized fixed-target experiments (Jefferson Lab) or at the Electron-Ion Collider.
Paper Structure (32 sections, 232 equations, 17 figures, 3 tables)

This paper contains 32 sections, 232 equations, 17 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Tagged DIS on polarized deuteron
  3. Kinematic variables
  4. Collinear frames
  5. Cross section
  6. Deuteron polarization
  7. Nuclear structure and DIS process
  8. Light-front quantization
  9. Quantum-mechanical formulation
  10. Spin structure
  11. Impulse approximation
  12. Virtual nucleon formulation
  13. Neutron distribution in deuteron
  14. Neutron spin density matrix
  15. Neutron momentum distributions
  16. ...and 17 more sections

Figures (17)

  • Figure 1: DIS of polarized electrons on the polarized deuteron with detection of a proton (or neutron) in the nuclear fragmentation region ("tagged DIS"), Eq. (\ref{['spin1_deuteron:eq:tagged_reaction']}).
  • Figure 2: Composite description of tagged DIS process in LF quantization. (a) IA in quantum-mechanical formulation (LFQM). (b) IA in virtual nucleon formulation (VNA). (c) FSI.
  • Figure 3: The distribution of unpolarized neutrons in the unpolarized deuteron, $P_{[U,U]}$, Eq. (\ref{['spin1_deuteron:spectral_U_U']}), as a function of the tagged proton transverse momentum $p_{pT}$, for several values of the longitudinal momentum fraction $\alpha_p$.
  • Figure 4: Same as Fig. \ref{['spin1_deuteron:fig:PUU_log']}, but showing the distributions multiplied by the phase space factor $2\pi p_{pT}$, and divided by the integral over $p_{pT}$ (normalized radial distributions in $p_{pT}$).
  • Figure 5: The distribution of unpolarized neutrons in the unpolarized and tensor-polarized deuteron, Eqs. (\ref{['spin1_deuteron:spectral_U_U']}) and (\ref{['spin1_deuteron:distribution_tensor']}), as functions of $\alpha_p$ and $p_{pT}$. Upper left panel: Distribution in unpolarized deuteron, $P_{[U,U]}$, Upper right panel: $T_{LL}$ tensor-polarized deuteron, $P_{[T_{LL},U]}$. Lower left panel: $T_{LT}$ tensor-polarized deuteron, $P_{[T_{LT},U]}$. Lower right panel: $T_{TT}$ tensor-polarized deuteron, $P_{[T_{TT},U]}$.
  • ...and 12 more figures