二体Dirac方程在三对二协变相互作用介子谱、SU（3）混合中的应用及与准势方法的比较
Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach
摘要：
在之前的一篇论文中，Crater和Van Alstine将约束动力学的两体狄拉克方程应用于介子夸克-反夸克束缚态，并使用Adler-Piran势的相对论扩展，并将他们的光谱结果与其他方法的结果进行了比较，这些方法也将介子光谱视为整体而不是部分。在本文中，我们将更详细地探讨这些方法的一个重要子集，准势方法的差异和相似之处。在早期的论文中，夸克-反夸克势的变换性质被限制在标量和类电磁四矢量中，前者占总势的限制方面，后者占短程部分。这项工作的一部分包括开发一种方法，其中静态阿德勒-皮兰潜力之间的分配这两种不同类型的潜力，除了协变。在这里，我们在这个分配的变化，导致在所得的光谱的大幅改善，包括一个类似时间的限制矢量势以上的标量限制和电磁类矢量势。我们的拟合比以前的结果多包括19个介子，并且我们修改了势的标量部分，使得这种形式主义能够解释以前工作中没有包括的等密度介子η和η'。继续与其他方法的介子光谱在前一份文件中所作的比较，我们检查在本文中的准势方法的埃伯特，Faustov和Galkin的比较与我们的形式主义和光谱结果。
英文摘要：
In a previous paper Crater and Van Alstine applied the Two Body Dirac equations of constraint dynamics to the meson quark-antiquark bound states using a relativistic extention of the Adler-Piran potential and compared their spectral results to those from other approaches, ones which also considered meson spectroscopy as a whole and not in parts. In this paper we explore in more detail the differences and similarities in an important subset of those approaches, the quasipotential approach. In the earlier paper, the transformation properties of the quark-antiquark potentials were limited to a scalar and an electromagnetic-like four vector, with the former accounting for the confining aspects of the overall potential, and the latter the short range portion. A part of that work consisted of developing a way in which the static Adler-Piran potential was apportioned between those two different types of potentials in addition to covariantization. Here we make a change in this apportionment that leads to a substantial improvement in the resultant spectroscopy by including a time-like confining vector potential over and above the scalar confining one and the electromagnetic-like vector potential. Our fit includes 19 more mesons than the earlier results and we modify the scalar portion of the potential in such a way that allows this formalism to account for the isoscalar mesons η and η' not included in the previous work. Continuing the comparisons made in the previous paper with other approaches to meson spectroscopy we examine in this paper the quasipotential approach of Ebert, Faustov, and Galkin for a comparison with our formalism and spectral results.
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