A contact interaction is used to calculate an array of pion twist-two, -three and -four generalised transverse light-front momentum dependent parton distribution functions (GTMDs). Despite the interaction’s simplicity, many of the results are physically relevant, amongst them a statement that GTMD size and shape are largely prescribed by the scale of emergent hadronic mass. Moreover, proceeding from GTMDs to generalised parton distributions, it is found that the pion’s mass distribution form factor is harder than its electromagnetic form factor, which is harder than the gravitational pressure distribution form factor; the pressure in the neighbourhood of the pion’s core is commensurate with that at the centre of a neutron star; the shear pressure is maximal when confinement forces become dominant within the pion; and the spatial distribution of transversely polarised quarks within the pion is asymmetric. Regarding transverse momentum dependent distribution functions, their magnitude and domain of material support decrease with increasing twist. The simplest Wigner distribution associated with the pion’s twist-two dressed-quark GTMD is sharply peaked on the kinematic domain associated with valence-quark dominance; has a domain of negative support; and broadens as the transverse position variable increases in magnitude.

接触相互作用用于计算由π介子扭曲的二，三和四广义广义光前动量相关的帕顿分布函数（GTMD）组成的数组。尽管交互作用很简单，但是许多结果在物理上都是相关的，其中有一个说法是GTMD的大小和形状在很大程度上取决于出现的强子质量。此外，从GTMDs到广义parton分布，发现介子的质量分布形状系数比其电磁形状系数要硬，电磁系数也比重力分布系数要大。介子核心附近的压力与中子星中心的压力相当。当约束力在小子内占主导时，剪切压力最大。介子内横向极化夸克的空间分布是不对称的。关于横向动量相关的分布函数，它们的大小和材料支撑范围会随着扭曲的增加而减小。介子的加捻二夸克夸脱GTMD相关的最简单Wigner分布在与价夸克占优势相关的运动学领域急剧上升。有负面支持的领域；并且随着横向位置变量幅度的增加而变宽。介子的加捻二夸克夸脱GTMD相关的最简单Wigner分布在与价夸克占优势相关的运动学领域急剧上升。有负面支持的领域；并且随着横向位置变量幅度的增加而变宽。介子的加捻二夸克夸脱GTMD相关的最简单Wigner分布在与价夸克占优势相关的运动学领域急剧上升。有负面支持的领域；并且随着横向位置变量幅度的增加而变宽。