Leading and higher twist transverse momentum dependent parton distribution functions in the spectator model

Transverse momentum dependent parton distribution functions, also abbreviated as TMDs, offer a three-dimensional picture of hadrons by taking the intrinsic transverse momentum of the parton into consideration. Hence, they are very important for us to understand the structure of hadrons. In this article, we calculate and summarize all TMDs of quark through the spectator model, from twist-2 to twist-4. Especially, we give complete results of TMDs at twist-4. We adopt a general analytical framework to calculate TMDs, with both scalar and axial-vector spectators being considered. All TMDs are calculated analytically in the light-cone coordinate, and single gluon rescattering is considered to generate T-odd TMDs. T-even TMDs are also calculated to this level, maybe for the first time. Different from the traditional point of view, the twist-4 TMDs can contribute to some physical observables like azimuthal asymmetries. An approximate formula of the Sivers asymmetry, including twist-4 TMDs, is given.

Figure 1

Tree level cut diagram for ${\overline{\mathcal{M}}}^{(0)}{\mathcal{M}}^{(0)}$. The dashed line denotes the diquark.

Figure 2

One-loop level cut diagram for ${\overline{\mathcal{M}}}^{(0)}{\mathcal{M}}^{(1)}$. The Hermitian conjugate diagram is not shown.

Figure 3

Schematic view of the azimuthal angles in the SIDIS process.