Abstract
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.
Highlights
Different from the traditional point of view, the twist-4 transverse momentum dependent parton distribution functions (TMDs) can contribute to some physical observables like azimuthal asymmetries
It is well known that the parton distribution function (PDF) in high energy particle physics is an important and useful tool to study the properties of hadrons
If we take the transverse motion of partons into consideration, we can get transverse momentum dependent parton distribution functions (TMDs)
Summary
It is well known that the parton distribution function (PDF) in high energy particle physics is an important and useful tool to study the properties of hadrons. A particular realization of the diquark model picture in high energy physics is the light-cone quark-spectatordiquark model [13,14], in which the relativistic effect of quark transverse motions is taken into account [15,16] This model plays an important role in investigating hadron structures by calculating relevant physical quantities, such as helicity distribution functions [13,17,18], transversity distribution functions [14], form factors [19,20,21,22], TMDs [23,24,25,26,27], Wigner functions [27], and so on.
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