三干涉共振参数的数学求解
A mathematical solve on the three-interfering-resonances' parameters
摘要：
从数学的角度考虑了由实验测得的分布拟合确定三干涉共振参数的多解问题。在本文中，它表明，有四个数值解与三个相干Breit-Wigner函数的配合。虽然在这种情况下不能得到显式的解析公式，但我们提供了四个解之间的约束方程。对于振幅函数的非相对论和相对论Breit-Wigner形式，给出了从已得到的解导出其它解的数值方法.在实际的实验测量中，具有类似于Breit-Wigner函数的更复杂的振幅形式，可以推导并执行相同的方法来获得数值解。该数学方法的求解结果与拟合结果吻合良好，直接验证了所提供的约束方程和数学方法的正确性。
英文摘要：
The multiple-solution problem in determining the three-interfering-resonances' parameters from a fit to an experimentally measured distribution is considered in a mathematical viewpoint. In this paper it is shown that there are four numerical solutions for the fit with three coherent Breit-Wigner functions. Although the explicit analytical formulae can not be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, numerical method is provided to derive the other solutions from the already obtained one based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The well agreement between the solved solutions using this mathematical method and those from the fit directly verifies the correctness of the supplied constraint equations and mathematical methodology.
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