We investigate the skewness dependent quark Wigner distributions of the pion to reveal the multidimensional picture of pion. We have used the spin improved wave functions of pion deduced from the light-front holographic model of mesons. By using the Fock-state overlap representation, the skewness dependent Wigner distributions of an unpolarized, longitudinally polarized and transversely polarized quark inside the pion are calculated. We have compared the skewness dependent Wigner distributions of pion with Wigner distributions of pion with zero skewness in the impact-parameter space. For more detailed picture, we have presented the results of transverse Wigner distributions in impact-parameter space as well as in momentum space with zero skewness. We also study the six-dimensional phase-space distribution: the generalized transverse momentum dependent parton distributions of pion for the case of zero skewness as well as for nonzero value of skewness. To compare with the future experimental data, we also perform the evoluted generalized transverse momentum dependent parton distribution.

中文翻译：

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光前全息模型中Pion的Quark Wigner分布和GTMD

我们研究了介子的偏度夸克维格纳分布，以揭示介子的多维图片。我们使用了介子的光前全息模型推论得出的自旋改进的介子的波函数。通过使用Fock状态重叠表示，可以计算介子内非极化，纵向极化和横向极化的夸克的偏度相关Wigner分布。我们在冲击参数空间中比较了偏态依赖的介子的Wigner分布与零偏态的介子的Wigner分布。对于更详细的图片，我们介绍了冲击参数空间以及零偏角动量空间中横向Wigner分布的结果。我们还研究了六维相空间分布：在零偏度以及非零偏度值的情况下，pion的依赖于横向动量的parton分布的广义分布。为了与将来的实验数据进行比较，我们还执行了演化的广义横向动量依赖的parton分布。