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Deep inelastic leptoproduction of spin-one hadrons

A. Bacchetta, P. J. Mulders

TL;DR

This work extends the leading-twist description of deep inelastic scattering to spin-1 hadrons, introducing a comprehensive framework of spin-1 distribution and fragmentation functions with transverse momentum dependence and time-reversal odd contributions. It formalizes the spin-1 density matrix and correlation functions, derives the hadronic tensor, and provides a complete set of cross sections for one-particle inclusive leptoproduction under all beam/target polarization configurations, including tensor polarization in the final state. A key result is that LT configurations can access the chiral-odd transversity distribution $h_1(x)$ via a T-odd fragmentation function $H_{1LT}(z)$ without requiring explicit transverse momentum measurements. The paper thus establishes a rigorous theoretical base for extracting and constraining the new spin-1 functions in vector-meson leptoproduction, with rho decays providing a practical polarization observable.

Abstract

In this paper we analyze deep inelastic one-particle inclusive processes for the case of spin-one targets or for the case of spin-one produced hadrons, such as rho mesons. This allows the measurement of new distribution and fragmentation functions not available in the spin-half case, and provides new ways to probe functions otherwise difficult to measure. We will analyze only contributions leading order in 1/Q, but we will include effects of the transverse momentum of partons. We also include time-reversal odd functions.

Deep inelastic leptoproduction of spin-one hadrons

TL;DR

This work extends the leading-twist description of deep inelastic scattering to spin-1 hadrons, introducing a comprehensive framework of spin-1 distribution and fragmentation functions with transverse momentum dependence and time-reversal odd contributions. It formalizes the spin-1 density matrix and correlation functions, derives the hadronic tensor, and provides a complete set of cross sections for one-particle inclusive leptoproduction under all beam/target polarization configurations, including tensor polarization in the final state. A key result is that LT configurations can access the chiral-odd transversity distribution via a T-odd fragmentation function without requiring explicit transverse momentum measurements. The paper thus establishes a rigorous theoretical base for extracting and constraining the new spin-1 functions in vector-meson leptoproduction, with rho decays providing a practical polarization observable.

Abstract

In this paper we analyze deep inelastic one-particle inclusive processes for the case of spin-one targets or for the case of spin-one produced hadrons, such as rho mesons. This allows the measurement of new distribution and fragmentation functions not available in the spin-half case, and provides new ways to probe functions otherwise difficult to measure. We will analyze only contributions leading order in 1/Q, but we will include effects of the transverse momentum of partons. We also include time-reversal odd functions.

Paper Structure

This paper contains 18 sections, 67 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. The description of spin-one particles
  3. Correlation functions
  4. Semi-inclusive cross sections with tensor polarization in the final state
  5. Unpolarized lepton beam and unpolarized target ($UU$)
  6. Polarized lepton beam and unpolarized target ($LU$)
  7. Unpolarized lepton beam and longitudinally polarized target ($UL$)
  8. Polarized lepton beam and longitudinally polarized target ($LL$)
  9. Unpolarized lepton beam and transversely polarized target ($UT$)
  10. Polarized lepton beam and transversely polarized target ($LT$)
  11. Conclusions
  12. Interpretation of the components of the spin tensor
  13. Measurement of spin tensor via decay analysis
  14. Distribution functions
  15. Hadronic tensor with a tensor polarized outgoing fragment
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Diagrammatic representation of semi-inclusive DIS