AI 中文总结
该研究通过弹性幺正性推导连接反应阈值、S矩阵极点与Breit-Wigner峰的几何规则，验证其在宽能区的适用性，预测多种粒子的留数相位，并反演得到Υ(4S)的极点参数。
AI 中文摘要
对共振振幅施加弹性幺正性可得到连接反应阈值、S矩阵极点与Breit-Wigner峰的几何规则。该规则在从⁵He到希格斯玻色子的6个数量级能量范围内得到验证，可预测未知留数相位：⁵He为-44(12)°、Σ(1385)⁺为-24(7)°、Ξ(1530)⁰为-7(13)°；通过该形式化方法的逆运算，从Υ(4S)的经验峰确定其极点为10575(1)-i8.3(13) MeV，相位为-52(6)°。
英文摘要
Imposing elastic unitarity on resonant amplitudes yields a geometric rule connecting the reaction threshold, S-matrix pole, and Breit-Wigner peak. Validated across six orders of magnitude in energy, from $^5\text{He}$ to the Higgs boson, this rule predicts currently unknown residue phases: $-44(12)^\circ$ for $^5\mathrm{He}$, $-24(7)^\circ$ for $Σ(1385)^+$, and $-7(13)^\circ$ for $Ξ(1530)^0$. By inverting this formalism, we determine the $Υ(4S)$ pole from its empirical peak to be $10575(1)-i\,8.3(13)$ MeV, with a $-52(6)^\circ$ phase.
Comments5 pages, 2 figures, and 1 table
