论文标题
三通道矩阵统一的分析图和Mittag-Leffler膨胀
Analytic Map of Three-Channel S Matrix -Generalized Uniformization and Mittag-Leffler Expansion-
论文作者
论文摘要
我们通过概括均匀化并为三通道$ s $矩阵制作单值地图，探索三通道$ s $矩阵的分析结构。首先，通过反向雅各比的椭圆函数，我们构建了从八个质量中心能量平方复合平面的八层床单上的转换，到了三频道$ s $矩阵的圆环。其次，我们表明，三通散射幅度的Mittag-Leffler膨胀（极点膨胀）不仅包括拓扑琐碎，而且还包括非平底贡献，并且由Weierstrass Zeta功能给出。最后，我们在简单的三通道模型的背景下检查获得的公式。在$ s = -2 $，$ i = 0 $，$ j^p = 0^+$，$λλ-λ-nξ-σ观点$耦合 - 通道散射的情况下，采取简单的非相关性有效的现场理论，并进行接触互动，$ s = -2 $，$ i = 0 $，$ j^p = 0^p = 0^p = 0^p = 0 $来自相邻的杆子。
We explore the analytic structure of the three-channel $S$ matrix by generalizing uniformization and making a single-valued map for the three-channel $S$ matrix. First, by means of the inverse Jacobi's elliptic function we construct a transformation from eight Riemann sheets of the center-of-mass energy squared complex plane onto a torus, on which the three-channel $S$ matrix is represented single-valued. Secondly, we show that the Mittag-Leffler expansion, a pole expansion, of the three-channel scattering amplitude includes not only topologically trivial but also nontrivial contributions and is given by the Weierstrass zeta function. Finally, we examine the obtained formula in the context of a simple three-channel model. Taking a simple non-relativistic effective field theory with contact interaction for the $S=-2$, $I=0$, $J^P = 0^+$, $ΛΛ-NΞ-ΣΣ$ coupled-channel scattering, we demonstrate that the scattering amplitude as a function of the uniformization variable is, in fact, given by the Mittag-Leffler expansion with the Weierstrass zeta function and that it is dominated by contributions from neighboring poles.
