Abstract
We revisit the connection between generalized parton distributions in impact parameter space and T-odd effects in single spin asymmetries of the semi-inclusive deep inelastic process. We show that nontrivial relations can be established only under very specific conditions, typically realized only in models that describe hadrons as two-body bound systems and involving a helicity-conserving coupling between the gauge boson and the spectator system. Examples of these models are the the scalar-diquark spectator model or the quark-target model for the nucleon, and relativistic models for the pion at the lowest order in the Fock-space expansion.
Highlights
Generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are fundamental nonperturbative objects that help unraveling the quark-gluon dynamics inside hadrons
There are eight independent GPDs and eight independent TMDs, in a one to one correspondence depending on the active parton and target polarizations
This correspondence arises from the projection of the fully unintegrated and off diagonal correlator, defining the generalized transverse momentum dependent parton distributions, into two independent subspaces of the whole space spanned by the parton and target momentum [1,2,3,4,5]
Summary
Generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are fundamental nonperturbative objects that help unraveling the quark-gluon dynamics inside hadrons. Factorization of the effects of final state interactions (FSIs), incorporated in a so-called “chromodynamics lensing function,” and a spatial distortion of GPDs in impact parameter space [9,10] These relations have been established for the Sivers effect and the IPD for unpolarized partons in a transversely polarized nucleon target, using spectator models [11,12] and a quark target model [7], and used in a phenomenological extraction of the Sivers function [13]. We demonstrate that very specific conditions have to be imposed on the FSIs in order to express T-odd TMDs in terms of an impact-parameter distortion and a lensing function These conditions are typically fulfilled only in models where the target is described as a two-body bound system and the FSIs do not change any of the spectator’s quantum numbers and modifies only its transverse momentum. In the Appendix we show the derivation of the conditions that should be satisfied for the lensing relation
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