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

TL;DR

This paper calculates all transverse momentum dependent parton distribution functions (TMDs) of quarks up to twist-4 within the spectator model, providing analytical results and exploring their potential impact on physical observables like azimuthal asymmetries.

Contribution

It offers the first complete analytical calculation of twist-4 TMDs, including T-even functions, in the spectator model with both scalar and axial-vector spectators.

Findings

Complete analytical expressions for twist-2 to twist-4 TMDs.

First calculation of T-even twist-4 TMDs.

Approximate formula for Sivers asymmetry including twist-4 contributions.

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.