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General Helicity Formalism for Polarized Semi-Inclusive Deep Inelastic Scattering

M. Anselmino, M. Boglione, U. D'Alesio, S. Melis, F. Murgia, E. R. Nocera, A. Prokudin

TL;DR

The paper develops a general helicity-based formalism for polarized SIDIS within LO QCD TMD factorization, incorporating full intrinsic transverse momenta of partons and fragmenting hadrons to yield the complete cross section and all spin asymmetries. It derives expressions for the polarized cross section in terms of TMD PDFs and FFs, matching existing formalisms, and presents a Gaussian-parametrization-based phenomenology that yields analytic results and azimuthal moments to isolate Sivers, Boer-Mulders, and Collins effects. The framework clarifies the phase structure arising from non-collinear kinematics and helicity amplitudes, enabling direct interpretation of asymmetries in terms of specific TMDs. The work highlights opportunities to extract 3D nucleon structure information from SIDIS data, notes the potential for extending the approach to Drell–Yan and hadronic processes, and discusses open questions on factorization validity and universality of TMDs.

Abstract

We study polarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes, within the QCD parton model and a factorization scheme, taking into account all transverse motions, of partons inside the initial proton and of hadrons inside the fragmenting partons. We use the helicity formalism. The elementary interactions are computed at LO with non collinear exact kinematics, which introduces phases in the expressions of their helicity amplitudes. Several Transverse Momentum Dependent (TMD) distribution and fragmentation functions appear and contribute to the cross sections and to spin asymmetries. Our results agree with those obtained with different formalisms, showing the consistency of our approach. The full expression for single and double spin asymmetries is derived. Simplified, explicit analytical expressions, convenient for phenomenological studies, are obtained assuming a factorized Gaussian dependence on intrinsic momenta for the TMDs.

General Helicity Formalism for Polarized Semi-Inclusive Deep Inelastic Scattering

TL;DR

The paper develops a general helicity-based formalism for polarized SIDIS within LO QCD TMD factorization, incorporating full intrinsic transverse momenta of partons and fragmenting hadrons to yield the complete cross section and all spin asymmetries. It derives expressions for the polarized cross section in terms of TMD PDFs and FFs, matching existing formalisms, and presents a Gaussian-parametrization-based phenomenology that yields analytic results and azimuthal moments to isolate Sivers, Boer-Mulders, and Collins effects. The framework clarifies the phase structure arising from non-collinear kinematics and helicity amplitudes, enabling direct interpretation of asymmetries in terms of specific TMDs. The work highlights opportunities to extract 3D nucleon structure information from SIDIS data, notes the potential for extending the approach to Drell–Yan and hadronic processes, and discusses open questions on factorization validity and universality of TMDs.

Abstract

We study polarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes, within the QCD parton model and a factorization scheme, taking into account all transverse motions, of partons inside the initial proton and of hadrons inside the fragmenting partons. We use the helicity formalism. The elementary interactions are computed at LO with non collinear exact kinematics, which introduces phases in the expressions of their helicity amplitudes. Several Transverse Momentum Dependent (TMD) distribution and fragmentation functions appear and contribute to the cross sections and to spin asymmetries. Our results agree with those obtained with different formalisms, showing the consistency of our approach. The full expression for single and double spin asymmetries is derived. Simplified, explicit analytical expressions, convenient for phenomenological studies, are obtained assuming a factorized Gaussian dependence on intrinsic momenta for the TMDs.

Paper Structure

This paper contains 21 sections, 117 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Cross sections in polarized SIDIS
  3. TMD partonic distribution functions
  4. TMD fragmentation functions
  5. Elementary interaction
  6. Single and double spin asymmetries in SIDIS
  7. Nucleon transverse single spin asymmetry, $A_{UT}$
  8. Nucleon longitudinal single spin asymmetry, $A_{UL}$
  9. Nucleon longitudinal double spin asymmetry, $A_{LL}$
  10. Lepton longitudinal double spin asymmetry, $\tilde{A}_{LL}$
  11. Nucleon longitudinal-transverse double spin asymmetry, $A_{LT}$
  12. Lepton longitudinal-transverse double spin asymmetry $\tilde{A}_{LT}$
  13. Other asymmetries
  14. Phenomenology of spin asymmetries
  15. Conclusions and further remarks
  16. ...and 6 more sections

Figures (2)

  • Figure 1: Kinematical configuration and conventions for SIDIS processes. The initial and final lepton momenta define the $(X-Z)_{cm}$ plane.
  • Figure 2: Kinematics of the fragmentation process.