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arXiv 2301.11599hep-ph
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具有Minkowski动力学的π介子中夸克的非极化横动量分布函数

Unpolarized transverse-momentum dependent distribution functions of a quark in a pion with Minkowskian dynamics

E. Ydrefors, W. de Paula, T. Frederico, G. Salmè

摘要:

利用Minkowski空间动力学方程的实际解,首次计算了π介子中非极化的twist-2(主导)和twist-3(次主导)、T偶、横动量相关的夸克分布.所采用的理论框架是基于齐次Bethe-Salpeter积分方程的相互作用内核给出了一个胶子交换,具有扩展的夸克胶子顶点。夸克和胶子的质量以及相互作用的顶点标度都是在格点QCD计算建议的范围内选择的,并被校准以再现π介子的质量和衰变常数。的总和规则要履行的横向动量相关的分布进行了仔细研究,特别是领先的扭曲之一,必须匹配的共线部分子分布函数,因此可以仔细检查现有的数据以及理论预测。值得注意的是,联合使用的Fock展开的π介子状态有利于更深入的分析的内容的π介子Bethe-Salpeter振幅,允许第一次确定胶子的贡献夸克平均纵向分数,其结果是$\sim 6\%$。目前的分析突出了胶子交换的作用,通过共线和横向动量分布的定量分析,显示,例如,无论是领导和subleading扭转,早期偏离广泛采用的指数下降,为$|k_\perp|^2 > m^2$,夸克质量$\sim Λ_{QCD}$。

英文摘要:

The unpolarized twist-2 (leading) and twist-3 (subleading), T-even, transverse-momentum dependent quark distributions in the pion are evaluated for the first time by using the actual solution of a dynamical equation in Minkowski space. The adopted theoretical framework is based on the homogeneous Bethe-Salpeter integral equation with an interaction kernel given by a one-gluon exchange, featuring an extended quark-gluon vertex. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice-QCD calculations, and calibrated to reproduce both pion mass and decay constant. The sum rules to be fulfilled by the transverse-momentum dependent distributions are carefully investigated, particularly the leading-twist one, that has to match the collinear parton distribution function, and hence can be scrutinized in terms of existing data as well as theoretical predictions. Noteworthy, the joint use of the Fock expansion of the pion state facilitates a more in-depth analysis of the content of the pion Bethe-Salpeter amplitude, allowing for the first time to determine the gluon contribution to the quark average longitudinal fraction, that results to be $\sim 6\%$. The current analysis highlights the role of the gluon exchanges through quantitative analysis of collinear and transverse-momentum distributions, showing, e.g. for both leading and subleading-twists, an early departure from the widely adopted exponential fall-off, for $|k_\perp|^2 > m^2$, with the quark mass $\sim Λ_{QCD}$.

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