Revisiting model relations between T -odd transverse-momentum-dependent parton distributions and generalized parton distributions

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.

Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons

“…The predicted relationship is consistent with experiment [40]. A quantitative estimate of orbital angular momentum based on the Sivers function was attempted [46], but it was based on restrictive assumptions [47].…”

Potential linear and angular momentum in the scalar diquark model

“…Sivers effect) as originating from an asymmetry of the parton distribution in the impact-parameter space (due to the orbital motion of partons) convoluted with a lensing function that accounts for the effects of attractive initial/final-state interactions (ISI/FSI). Even if the notion of a lensing function is intuitive and is supported by some model calculations [17][18][19][20], its factorization depends on strong assumptions that cannot be strictly satisfied in QCD [21]. Nevertheless, a non-zero Sivers function necessarily requires a non-vanishing orbital motion of the partons.…”

Relations between generalized parton distributions and transverse momentum dependent parton distributions

“…The above relation ( 63) is applicable in models where the nucleon state is approximated as an effective two-particle bound state like a diquark model and at the level of one gluon exchange [37]; however it is found to be not valid when vector and axial vector diquarks are included [10]. Here I q,i contains the effect of the one gluon exchange in the final state interaction between the active quark and the spectator system.…”

“…In [9] a systematic study of all possible non-trivial model-dependent relations between TMDs and GPDs was performed and such relations were arranged in four categories depending on the number of derivatives in impact parameter space. In [10] it was shown that the relation connecting a T-odd TMD to a distortion in impact parameter space through a lensing function holds only in models where the nucleon is described as a two-particle bound state, like a quark and a diquark. Further, such relations are not satisfied if axial vector diquarks are included in the model.…”