干扰共振组合多解性的一般数学分析
General mathematical analysis on multiple solutions of interfering resonances combinations
摘要：
当拟合具有多个共振或干扰背景和共振的截面时，通常获得具有相同拟合质量的多个参数解。在目前的工作中，我们找到了多个共振或干扰的背景和共振的组合的多个解决方案的来源，通过分析的Breit-Wigner函数的数学结构。我们发现，对于$n+1$共振，存在等质量的$2^n$拟合解，并且干扰背景和共振的多重性依赖于复平面中振幅的零点.我们提供了一个简单的，一般的方法来推断所有其他解决方案具有相同的拟合质量从一个已知的解决方案。
英文摘要：
When fitting cross sections with several resonances or interfering background and resonances, one usually obtains multiple solutions of parameters with equal fitting quality. In the present work, we find the source of multiple solutions for a combination of several resonances or interfering background and resonances by analyzing the mathematical structure of the Breit-Wigner function. We find that there are $2^n$ fitting solutions with equal quality for $n+1$ resonances, and the multiplicity of the interfering background and resonances depends on zeros of the amplitudes in the complex plane. We provide a simple, general method to infer all other solutions with equal fitting quality from a known solution.
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