AI 中文总结
本研究利用πN向前色散关系和修正总截面数据，计算了πN散射的稳定极点，提取了Δ(1232)、罗珀共振等的参数，还建立了共振留数的求和规则。
AI 中文摘要
我们利用一套修正后的3 GeV以内的π⁺p和π⁻p总截面数据，以及该能量以上的雷吉渐近行为，对πN向前色散关系及其向复平面的解析延拓进行了与模型无关的计算。在该能量范围内，我们发现每种同位旋组合都存在四个稳定极点。I=3/2道中最轻的极点对应Δ(1232)共振，I=1/2道中最轻的极点对应罗珀共振，尽管后者在数据中几乎不可察觉。我们不依赖分波分析，提取了这些极点的参数以及Δ⁰和Δ⁺⁺之间的参数差。其余极点无法单独对应某一个共振，它们并非人为结果，而是仅靠总截面数据无法分辨的多个共振的综合效应。最后，我们写出了将这些组成共振的留数与从色散表示中提取的极点留数关联起来的求和规则。
英文摘要
We present a model-independent calculation of $πN$ forward dispersion relations and their analytic continuation to the complex plane, using a revised set of $π^\pm p$ total cross-section data up to 3 GeV, and Regge asymptotics above. Up to that energy, we find four stable poles for each isospin combination. The lightest pole in the $I=3/2$ channel corresponds to the $Δ(1232)$ resonance, while the lightest in the $I=1/2$ channel corresponds to the Roper resonance, even though the latter is imperceptible in the data. We extract their pole parameters and the parameter difference between the $Δ^0$ and $Δ^{++}$, without relying on a partial-wave analysis. The remaining poles cannot be identified with a single resonance each. They are not artifacts but the combined effect of multiple resonances unresolved by total cross-section data alone. Finally, we write sum rules relating the residues of these constituent resonances to the residues of the poles extracted from the dispersive representation.
Comments17 pages, 8 figures
