Title: Different manifestations of S-matrix poles Show Chinese title

Title: S矩阵极点的不同表现形式

Abstract: Making use of the analytical properties of the $S$-matrix and a theorem of Mittag-Leffler, model independent non-relativistic expressions for cross sections in single channel elastic scattering, scattering phase shifts and survival probabilities of resonances are derived. Provided certain conditions are satisfied by the poles, the residues can also be estimated analytically. Considerations of the low energy behaviour of the $S$-matrix and cross sections reveal additional conditions on the residues of the poles appearing in the Mittag-Leffler expansions. The exact expressions for the resonant cross section and phase shift are shown to reduce to the commonly used Breit-Wigner formula plus corrections. The latter is shown to approach the exact result with the example of a meson and a baryon resonance. Finally, a comparison of the exact expressions with some realistic examples is presented. The calculations of survival probabilities in particular reveal the reason behind the non-observability of non-exponential decay. Show Chinese abstract

Abstract: 利用$S$矩阵的解析性质和 Mittag-Leffler 定理，推导出单通道弹性散射的截面、散射相移和共振的存活概率的模型无关的非相对论表达式。 如果极点满足某些条件，也可以解析地估计留数。 对$S$矩阵和截面的低能行为的考虑揭示了在 Mittag-Leffler 展开中出现的极点的留数的附加条件。 显示了共振截面和相移的精确表达式可以简化为常用的 Breit-Wigner 公式加上修正项。 后者通过介子和重子共振的例子被证明趋近于精确结果。 最后，给出了精确表达式与一些实际例子的比较。 特别是存活概率的计算揭示了非指数衰减不可观测的原因。