Relations between generalized and transverse momentum dependent parton distributions

TL;DR

The paper investigates whether intrinsic connections exist between generalized parton distributions (GPDs) and transverse momentum dependent distributions (TMDs), focusing on naive-T-odd TMDs and their role in single-spin asymmetries. It surveys model-independent considerations, introduces a detailed impact-parameter and momentum-space framework, and extends spectator-model calculations (including gluons) to test proposed relations. The authors find that, while several intriguing analogies arise in simple models, there are no nontrivial model-independent GPD–TMD relations; higher-order effects in spectator models can break proposed links, underscoring the need for additional theory and data. The work advances the understanding of how GPDs and TMDs might be connected, clarifies the limitations of such relations, and highlights directions for future research on gluon distributions and spin-orbit correlations.

Abstract

Recent work suggests non-trivial relations between generalized parton distributions on the one hand and (naive time-reversal odd) transverse momentum dependent distributions on the other. Here we review the present knowledge on such type of relations. Moreover, as far as spectator model calculations are concerned, the existing results are considerably extended. While various relations between the two types of parton distributions can be found in the framework of spectator models, so far no non-trivial model-independent relations have been established.

Figures (9)

• Figure 1: Kinematics for GPDs.
• Figure 2: Kinematics for TMDs.
• Figure 3: Path of Wilson line for TMDs in SIDIS.
• Figure 4: (a) Lowest order diagram for T-odd TMDs in spectator model calculations containing the interaction of the active quark with the target remnant. The eikonal propagator arising from the Wilson line in the operator definition of TMDs is indicated by a double line. Note that only the imaginary part of the box diagram on the left-hand side (LHS) of the cut is relevant for the calculation of T-odd functions. The Hermitian conjugate diagram (h.c.) is not shown. (b) Lowest order diagram for GPDs in spectator model calculations. The topology of diagram (a) matches with the one of diagram (b) if the quark-spectator interaction, described by the lensing function $\mathcal{I}^{q,i}$, is factored out.
• Figure 5: (a) Particular higher order diagram for T-odd TMDs in spectator model calculations containing the interaction of the quark with the target remnants. (b) Topology of diagram (a) if the quark-spectator interaction is factored out. Diagram (b) cannot represent a Feynman graph for a GPD because there is a mismatch between the number of particles on the LHS and the RHS of the cut.