零平面上π介子的闵可夫斯基动力学观测
Observing the Minkowskian dynamics of the pion on the null-plane
摘要：
利用动力学模型研究了π价光阵面的波函数，该波函数是由Bethe-Salpeter方程在Minkowski空间的实际解，借助于Nakanishi积分表示得到的。核被简化为包含组分夸克、有效质量胶子交换和扩展夸克-胶子相互作用顶点尺度的梯形近似。这三个输入参数携带红外尺度ΛQCD，并在晶格计算建议的范围内进行微调以再现π介子弱衰变常数。除了fπ之外，我们还提出并讨论了零平面上的其他有趣的量，例如：（i）价几率，（ii）依赖于光阵面（LF）动量的纵向或横向分量的动力学函数，由LF动量分布和分布振幅表示，和（iii）由协变Ioffe-时间和横坐标的笛卡尔乘积给出的LF-动量空间和3D空间中的概率密度，以便以互补的方式执行动态特征的分析。所提出的分析π介子内部的闵可夫斯基动力学，虽然在初始阶段进行，资格Nakanishi积分表示作为一个有吸引力的有效工具，仍然未开发的潜力，以解决动力学和可观察的属性之间的相关性被利用。
英文摘要：
A dynamical model is applied to the study of the pion valence light-front wave function, obtained from the actual solution of the Bethe-Salpeter equation in Minkowski space, resorting to the Nakanishi integral representation. The kernel is simplified to a ladder approximation containing constituent quarks, an effective massive gluon exchange, and the scale of the extended quark-gluon interaction vertex. These three input parameters carry the infrared scale ΛQCD and are fine-tuned to reproduce the pion weak decay constant, within a range suggested by lattice calculations. Besides fπ, we present and discuss other interesting quantities on the null-plane, like: (i) the valence probability, (ii) the dynamical functions depending upon the longitudinal or the transverse components of the light-front (LF) momentum, represented by LF-momentum distributions and distribution amplitudes, and (iii) the probability densities both in the LF-momentum space and the 3D space given by the Cartesian product of the covariant Ioffe-time and transverse coordinates, in order to perform an analysis of the dynamical features in a complementary way. The proposed analysis of the Minkowskian dynamics inside the pion, though carried out at the initial stage, qualifies the Nakanishi integral representation as an appealing effective tool, with still unexplored potentialities to be exploited for addressing correlations between dynamics and observable properties.
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