标题： 解决$Δ(1232)$部分宽度异常：复极点残差不是基本共振性质 显示英文标题

标题： Resolving the $Δ(1232)$ partial width anomaly: Complex pole residue is not a fundamental resonance property

摘要： 共振激发强子的性质通常通过散射振幅的复极点位置和留数来识别。质量及其总衰变宽度由位置给出，而部分宽度由留数的大小给出。如果这种识别是正确的，著名$\Delta(1232)$的部分宽度将大于其总宽度。通过使用一个简单的模型，该模型预测了显著的重子$N^*$、$\Delta$、$\Lambda$、$\Sigma$和低质量介子的留数相位，我们解决了这一异常现象，并表明留数不能作为基本共振属性。 显示英文摘要

摘要： The resonant properties of excited hadrons are commonly identified with the complex pole positions and residues of the scattering amplitude. The mass and total decay width are given by position, whereas the partial width is given by the magnitude of the residue. If this identification was correct, the partial width of famous $\Delta(1232)$ would be larger than its total width. By using a simple model that predicts residue phases of prominent baryons $N^*$, $\Delta$, $\Lambda$, $\Sigma$, and low mass mesons, we resolve this anomaly and show that the residue cannot be a fundamental resonant property.