Twist-2 generalized transverse-momentum dependent parton distributions and the spin/orbital structure of the nucleon

Generalized transverse-momentum dependent parton distributions (GTMDs) encode the most general parton structure of hadrons. Here we focus on two twist-2 GTMDs which are denoted by $F_{1,4}$ and $G_{1,1}$ in parts of the literature. As already shown previously, both GTMDs have a close relation to orbital angular momentum of partons inside a hadron. However, recently even the mere existence of $F_{1,4}$ and $G_{1,1}$ has been doubted. We explain why this claim does not hold. We support our model-independent considerations by calculating the two GTMDs in the scalar diquark model and in the quark-target model, where we also explicitly check the relation to orbital angular momentum. In addition, we compute $F_{1,4}$ and $G_{1,1}$ at large transverse momentum in perturbative quantum chromodynamics and show that they are nonzero.

Figure 1

(a) Representation of a GTMD in the region $\xi <x<1$. (b) Quark-proton scattering amplitude.

Figure 2

Two-body elastic scattering picture in the center-of-mass frame. In general, the vector ${\overrightarrow{n}}_{-}$ does not belong to the scattering plane.

Figure 3

Leading-order diagrams in the scalar diquark model for the matrix element in Eq. (22) (left panel) and in Eq. (23) (right panel).

Figure 4

Leading-order diagrams in the quark-target model (in light-front gauge) for the matrix element in Eq. (33) (upper row) and in Eq. (35) (lower row). Note that for the amplitude in (35) we only consider diagrams which eventually could contribute to gluon GTMDs for $x\in [0,1]$.

Figure 5

Diagrams determining the leading order of quark GTMDs at large transverse momenta.

Figure 6

Diagrams determining the leading order of gluon GTMDs at large transverse momenta.